My Airframe Finite Element Analysis Capability Studies..pdf
GeoffreyWardleMScMSc
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Jun 24, 2024
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About This Presentation
This is an overview presentation of my current Finite Element Analysis engineering capabilities research. Based on my career and two MSc degrees: - MSc in Advanced Manufacturing Technology University of Portsmouth graduating 1st May 1998, and MSc in Aircraft Engineering Cranfield University 8th June...
Slide Content
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
MY AIRFRAME FINITE ELEMENT ANALYSIS CAPABILITY STUDIES.
By Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS. Current Capabilities.
MY AIRFRAME FINITE ELEMENT ANALYSIS CAPABILITY STUDIES.
By Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS. Current Capabilities.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
2
OBJECTIVES OF THIS PRIVATE STUDY IN SUPPORT OF FDSA & ADTA.
The objective of this study is to support the ATDA airframe design research project with structural
design analysis and will cover the analysis of both metallic and composite components as well as
whole airframe analysis.
To this end the presentation gives examples of the GSA of ATDA metallic airframe design work I
have undertaken, as part of my current AIAA design study. The descriptive background work
contained herein is based Cranfield University MSc and University of Portsmouth MSc academic
studies Cranfield Aerospace design standards, my ATDA airframe technology research project,
INCAT training, EASA CS 25-571 and referenced texts.
This presentation gives examples of the GSA of composite airframe design work I have undertaken
in support of my current ATDA airframe technology research project design study.
The reason behind this work is to preserve my capabilities within the Catia V5.R20 and NASTRAN/
PATRAN toolsets against future employment and to support of the Future Advanced Technology
Aircraft private academic research project.
This study will grow over time as more detail structural work is undertaken on the ATDA project and
will include PATRAN / NASTRAN FEA modeling of ATDA structural components as they are
evolved to the preliminary design stage. On a month by month basis this will reflect development
progress and is to be taken as an indicator of capabilities and a knowledge base which is applicable
to a range of aerospace industry challenges. The (In Work) designations are sections currently
being completed.
2
OBJECTIVES OF THIS PRIVATE STUDY IN SUPPORT OF FDSA & ADTA.
The objective of this study is to support the ATDA airframe design research project with structural
design analysis and will cover the analysis of both metallic and composite components as well as
whole airframe analysis.
To this end the presentation gives examples of the GSA of ATDA metallic airframe design work I
have undertaken, as part of my current AIAA design study. The descriptive background work
contained herein is based Cranfield University MSc and University of Portsmouth MSc academic
studies Cranfield Aerospace design standards, my ATDA airframe technology research project,
INCAT training, EASA CS 25-571 and referenced texts.
This presentation gives examples of the GSA of composite airframe design work I have undertaken
in support of my current ATDA airframe technology research project design study.
The reason behind this work is to preserve my capabilities within the Catia V5.R20 and NASTRAN/
PATRAN toolsets against future employment and to support of the Future Advanced Technology
Aircraft private academic research project.
This study will grow over time as more detail structural work is undertaken on the ATDA project and
will include PATRAN / NASTRAN FEA modeling of ATDA structural components as they are
evolved to the preliminary design stage. On a month by month basis this will reflect development
progress and is to be taken as an indicator of capabilities and a knowledge base which is applicable
to a range of aerospace industry challenges. The (In Work) designations are sections currently
being completed.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
3
Figure 1:- The application of Catia Finite Element Analysis to airframe design.
3
Figure 1:- The application of Catia Finite Element Analysis to airframe design.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Section 1:- Catia V5.R20 GSA evaluation of the toolset and its limitations:
Section 2:- FEA application of the SAFESA procedure to ATDA project work :
Section 3:- Structural design philosophy of airframe structural components:
Section 4:- Structural analysis processes for metallic and composite airframe structures:
Section 5- My CATIA V5.R20 GSA capability metallic analysis examples:
Section 6:- PATRAN / NASTRAN methodology and capability examples (In Work):
Section 7:- ATDA component parts: (1) Wing Spar: (2) Wing Skins: (3) Wing Rib: (4) Frame / Stringer
Fuselage panel (In Work):
Section 8:- Catia V5.R20 GSA analysis of metallic component structures (In Work):
Section 9:- NASTRAN analysis of Composite component structures (In Work):
Section 10:- Comparative hand calculation analysis (In Work):
Section 11:- FEA structural analysis of the as designed structural assemblies (In Work).
4
Contents of this presentation in support of my ATDA airframe design study.
Section 1:- Catia V5.R20 GSA evaluation of the toolset and its limitations:
Section 2:- FEA application of the SAFESA procedure to ATDA project work :
Section 3:- Structural design philosophy of airframe structural components:
Section 4:- Structural analysis processes for metallic and composite airframe structures:
Section 5- My CATIA V5.R20 GSA capability metallic analysis examples:
Section 6:- PATRAN / NASTRAN methodology and capability examples (In Work):
Section 7:- ATDA component parts: (1) Wing Spar: (2) Wing Skins: (3) Wing Rib: (4) Frame / Stringer
Fuselage panel (In Work):
Section 8:- Catia V5.R20 GSA analysis of metallic component structures (In Work):
Section 9:- NASTRAN analysis of Composite component structures (In Work):
Section 10:- Comparative hand calculation analysis (In Work):
Section 11:- FEA structural analysis of the as designed structural assemblies (In Work).
4
Contents of this presentation in support of my ATDA airframe design study.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The objective of this section is to evaluate the Catia V5.R20 GSA toolset, below are the limitations
of the Catia V5 R20 FEA toolset which need to be considered when applying this toolset:-
a)Material Linearity:- In Catia, it is assumed that the stress and strain are linearly related through
Hook‟s law, therefore metals should not be loaded into the plastic deformation region, and rubber
type materials cannot be analyzed by this toolset.
b)Small Strains:- The strains used in Catia are the infinitesimal engineering strains which are
consistent with the limitations above in (a). As an example, problems such as crushing of tubes
cannot be handled by this software.
c)Limited Contact Capabilities:- Although Catia is capable of solving certain contact problems,
they must be within the limitations noted above in (a) and (b). Furthermore, no friction effects can
be modeled by the software.
d)Limited Dynamics:- The transient response in Catia V5 is based on model superposition.
Therefore a sufficient number of modes have to be extracted in order to get good results. The direct
integration of the equations of motion are not available in this version.
e)Beam and Shell Formation:- In these elements shear effects are neglected. Therefore, the
results of thick beams and shells may not be very accurate although not an aerospace issue.
Although these issues seem severe limitations most basic mechanical design problems can be
analyzed using this tool set as such problems are governed by linear elastic analysis.
5
Section 1:- Catia V5.R20 GSA evaluation of the toolsets and its limitations.
The objective of this section is to evaluate the Catia V5.R20 GSA toolset, below are the limitations
of the Catia V5 R20 FEA toolset which need to be considered when applying this toolset:-
a)Material Linearity:- In Catia, it is assumed that the stress and strain are linearly related through
Hook‟s law, therefore metals should not be loaded into the plastic deformation region, and rubber
type materials cannot be analyzed by this toolset.
b)Small Strains:- The strains used in Catia are the infinitesimal engineering strains which are
consistent with the limitations above in (a). As an example, problems such as crushing of tubes
cannot be handled by this software.
c)Limited Contact Capabilities:- Although Catia is capable of solving certain contact problems,
they must be within the limitations noted above in (a) and (b). Furthermore, no friction effects can
be modeled by the software.
d)Limited Dynamics:- The transient response in Catia V5 is based on model superposition.
Therefore a sufficient number of modes have to be extracted in order to get good results. The direct
integration of the equations of motion are not available in this version.
e)Beam and Shell Formation:- In these elements shear effects are neglected. Therefore, the
results of thick beams and shells may not be very accurate although not an aerospace issue.
Although these issues seem severe limitations most basic mechanical design problems can be
analyzed using this tool set as such problems are governed by linear elastic analysis.
5
Section 1:- Catia V5.R20 GSA evaluation of the toolsets and its limitations.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The stresses evaluated in Catia V5.20 GSA are von Mises stresses (after Richard von Mises (1883-
1913) in accordance with Maximum Distortion Energy Theory which states the only that portion of
the normal stress which causes shear distortion acts to promote yielding. These are called the
stress deviations or deviatoric stresses:- σ‟x : σ‟y : σ‟z and are defined such that:-
σx = σ‟x + ρ : σy = σ‟y + ρ : σz = σ‟z + ρ (eq 1.)
Substituting these expressions for the normal stresses in the strain energy density formula yields:-
uo = uv + ud
where:-
Uv = (1/2K) ρ² ud = (1/2E) (σ‟x² + σ‟y² + σ‟z² ) – v /E (σ‟x σ‟y + σ‟x σ‟z + σ‟y σ‟z ) + 1/2G (τ²xy + τ²yz + τ²zx )
Here, uv is the portion of the strain energy density due to volume change, and ud is the distortion
strain energy density. From Equation 1 and the definition of hydrostatic stress, ρ = ⅓ (σx + σy + σz ),
the deviatoric stresses can be written :-
σ‟x = ⅔ σx - ⅓(σy + σz): σ‟y = ⅔ σy - ⅓(σx + σz): σ‟z = ⅔ σz - ⅓(σx + σy)
These together with equation for the shear modulus in isotropic material:- G = E / 2(1+v) gives the
following expression for the distortion strain energy density:-
ud = 1+v / 3E {1/2 [(σx – σy)² + (σx – σz)² + (σy – σz)²] + 3(τ²xy + τ²xz + τ²yz) } (eq 2.)
For example in a uniaxial tension test, the only non zero stress is σx hence the distortion strain
energy density when yield occurs (σx = σyρ) is:-
ud = (1+v / 3E ) σ²yρ
6
Catia V5.R20, FEA Skills toolset enhancement evaluating system limitations.
The stresses evaluated in Catia V5.20 GSA are von Mises stresses (after Richard von Mises (1883-
1913) in accordance with Maximum Distortion Energy Theory which states the only that portion of
the normal stress which causes shear distortion acts to promote yielding. These are called the
stress deviations or deviatoric stresses:- σ‟x : σ‟y : σ‟z and are defined such that:-
σx = σ‟x + ρ : σy = σ‟y + ρ : σz = σ‟z + ρ (eq 1.)
Substituting these expressions for the normal stresses in the strain energy density formula yields:-
uo = uv + ud
where:-
Uv = (1/2K) ρ² ud = (1/2E) (σ‟x² + σ‟y² + σ‟z² ) – v /E (σ‟x σ‟y + σ‟x σ‟z + σ‟y σ‟z ) + 1/2G (τ²xy + τ²yz + τ²zx )
Here, uv is the portion of the strain energy density due to volume change, and ud is the distortion
strain energy density. From Equation 1 and the definition of hydrostatic stress, ρ = ⅓ (σx + σy + σz ),
the deviatoric stresses can be written :-
σ‟x = ⅔ σx - ⅓(σy + σz): σ‟y = ⅔ σy - ⅓(σx + σz): σ‟z = ⅔ σz - ⅓(σx + σy)
These together with equation for the shear modulus in isotropic material:- G = E / 2(1+v) gives the
following expression for the distortion strain energy density:-
ud = 1+v / 3E {1/2 [(σx – σy)² + (σx – σz)² + (σy – σz)²] + 3(τ²xy + τ²xz + τ²yz) } (eq 2.)
For example in a uniaxial tension test, the only non zero stress is σx hence the distortion strain
energy density when yield occurs (σx = σyρ) is:-
ud = (1+v / 3E ) σ²yρ
6
Catia V5.R20, FEA Skills toolset enhancement evaluating system limitations.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
According to the maximum distortion energy theory of failure, yield occurs when the distortion strain
energy density equals the distortion strain energy density at the yield point of a tensile test
specimen therefore:-
1+v / 3E {1/2 [(σx – σy)² + (σx – σz)² + (σy – σz)²] + 3(τ²xy + τ²xz + τ²yz) } = (1+v / 3E) σ²yρ
The von Mises stress, σvm , a point is defined as:-
σvm √1/2 [(σx – σy)² + (σx – σz)² + (σy – σz)²] + 3(τ²xy + τ²xz + τ²yz) (eq 3.)
Therefore according to the maximum distortion energy theory, the failure criterion is:-
σvm = σyρ (eq 4.)
Here σvm is an invariant, having the same value regardless of the coordinate system used, so that in
terms of the maximum, minimum and intermediate values of principle stresses:-
σvm √1/2 [(σmax – σmin)² + (σmax – σint)² + (σint – σmin)²] (eq 5.)
or
σvm 1/√2 (σmax – σmin) √1+ (σmax – σint / σmax – σmin)² + (σint – σmin / σmax – σmin)²
From this one can deduce that:-
0.866 (σmax – σmin) < σvm < (σmax – σmin) (eq 6.)
Therefore von Mises stresses are less than the maximum principle stresses, which means that the
maximum shear stress failure criterion is slightly more conservative than the distortion energy
criterion. In plane stress:-
σvm = √(σ²x + σ²y - σx σy) + 3 τ²xy (eq 7.)
7
Catia V5.R20, FEA Skills toolset enhancement evaluating system limitations.
According to the maximum distortion energy theory of failure, yield occurs when the distortion strain
energy density equals the distortion strain energy density at the yield point of a tensile test
specimen therefore:-
1+v / 3E {1/2 [(σx – σy)² + (σx – σz)² + (σy – σz)²] + 3(τ²xy + τ²xz + τ²yz) } = (1+v / 3E) σ²yρ
The von Mises stress, σvm , a point is defined as:-
σvm √1/2 [(σx – σy)² + (σx – σz)² + (σy – σz)²] + 3(τ²xy + τ²xz + τ²yz) (eq 3.)
Therefore according to the maximum distortion energy theory, the failure criterion is:-
σvm = σyρ (eq 4.)
Here σvm is an invariant, having the same value regardless of the coordinate system used, so that in
terms of the maximum, minimum and intermediate values of principle stresses:-
σvm √1/2 [(σmax – σmin)² + (σmax – σint)² + (σint – σmin)²] (eq 5.)
or
σvm 1/√2 (σmax – σmin) √1+ (σmax – σint / σmax – σmin)² + (σint – σmin / σmax – σmin)²
From this one can deduce that:-
0.866 (σmax – σmin) < σvm < (σmax – σmin) (eq 6.)
Therefore von Mises stresses are less than the maximum principle stresses, which means that the
maximum shear stress failure criterion is slightly more conservative than the distortion energy
criterion. In plane stress:-
σvm = √(σ²x + σ²y - σx σy) + 3 τ²xy (eq 7.)
7
Catia V5.R20, FEA Skills toolset enhancement evaluating system limitations.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
There are two types of solid element available in Catia V5.R20 Generative Structural Analysis
which are Linear and Parabolic. Both are referred to as tetrahedron elements shown below.
Limited Hex elements are also available. As are Linear and Parabolic shell elements as well are
limited QUAD elements.
8
Solid Tetrahedron Elements.
Linear. Parabolic.
The Linear tetrahedron elements are faster computationally but less accurate. On the other hand,
the Parabolic elements require more computational power but lead to more accurate results.
Parabolic elements have the very important feature that they can fit curved surfaces better than
Linear elements. In Catia V5 solid machined parts are generally analyzed using solid elements,
where as thin walled and sheet structures are analyzed using shell elements. Linear triangular
shell elements have three nodes each having six degrees of freedom, i.e. three translations and
three rotations, the thickness of the shell has to be provided as a Catia input. As is the case with
the solid tetrahedron elements the Parabolic elements are more accurate.
Linear
18 DoF.
Parabolic
36 DoF.
Sheet Triangular Shell Elements.
Catia V5.R20, FEA Skills toolset enhancement evaluating system components .
There are two types of solid element available in Catia V5.R20 Generative Structural Analysis
which are Linear and Parabolic. Both are referred to as tetrahedron elements shown below.
Limited Hex elements are also available. As are Linear and Parabolic shell elements as well are
limited QUAD elements.
8
Solid Tetrahedron Elements.
Linear. Parabolic.
The Linear tetrahedron elements are faster computationally but less accurate. On the other hand,
the Parabolic elements require more computational power but lead to more accurate results.
Parabolic elements have the very important feature that they can fit curved surfaces better than
Linear elements. In Catia V5 solid machined parts are generally analyzed using solid elements,
where as thin walled and sheet structures are analyzed using shell elements. Linear triangular
shell elements have three nodes each having six degrees of freedom, i.e. three translations and
three rotations, the thickness of the shell has to be provided as a Catia input. As is the case with
the solid tetrahedron elements the Parabolic elements are more accurate.
Linear
18 DoF.
Parabolic
36 DoF.
Sheet Triangular Shell Elements.
Catia V5.R20, FEA Skills toolset enhancement evaluating system components .
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The element “size” and “sag” icons appear on each part on entering the Analysis & Simulation >
Generative Structural Analysis toolset. The concept of element size is self explanatory, i.e. the
smaller the element size the more accurate the results at the expense of longer computation time
and processor power. The “sag” is a unique Catia term, in FEA the geometry of a part is
approximated with elements, and the surface of the part and FEA approximation of a part do
exactly coincide. The “sag” parameter controls the deviation between the two, therefore the smaller
the “sag” value generally the better the results.
Catia V5‟s Finite Element Analysis module is geometrically based, therefore the boundary
conditions cannot be applied to nodes and elements. The boundary conditions can only be applied
at the part level. On entering the Generative Structural Analysis workbench, the parts are
automatically hidden. Therefore, before boundary conditions can be applied, the part must be
brought back into the visual working space, and this was carried out by pointing the cursor to the
top of the tree, the Links Manager.1 branch, right-clicking, selecting Show. At this point both the
part is visible and the mesh is superimposed on it, the latter was hidden by pointing the cursor at
Nodes and Elements and right-clicking Hide. This has been the methodology for each worked
example in this presentation, figures 43,45,47,48,50,51,53 show the parts, with constraints and
loading, where figures 44,46,49,52,54 show the total displacement magnitude analysis and Von
Mises stress analysis with maximum and minimum values in each case. The three analysis
examples in this presentation form a small part of my Workbook two which is leading into complex
studies of airframe structures.
9
Catia V5.R20, FEA Skills toolset enhancement evaluating system methods.
The element “size” and “sag” icons appear on each part on entering the Analysis & Simulation >
Generative Structural Analysis toolset. The concept of element size is self explanatory, i.e. the
smaller the element size the more accurate the results at the expense of longer computation time
and processor power. The “sag” is a unique Catia term, in FEA the geometry of a part is
approximated with elements, and the surface of the part and FEA approximation of a part do
exactly coincide. The “sag” parameter controls the deviation between the two, therefore the smaller
the “sag” value generally the better the results.
Catia V5‟s Finite Element Analysis module is geometrically based, therefore the boundary
conditions cannot be applied to nodes and elements. The boundary conditions can only be applied
at the part level. On entering the Generative Structural Analysis workbench, the parts are
automatically hidden. Therefore, before boundary conditions can be applied, the part must be
brought back into the visual working space, and this was carried out by pointing the cursor to the
top of the tree, the Links Manager.1 branch, right-clicking, selecting Show. At this point both the
part is visible and the mesh is superimposed on it, the latter was hidden by pointing the cursor at
Nodes and Elements and right-clicking Hide. This has been the methodology for each worked
example in this presentation, figures 43,45,47,48,50,51,53 show the parts, with constraints and
loading, where figures 44,46,49,52,54 show the total displacement magnitude analysis and Von
Mises stress analysis with maximum and minimum values in each case. The three analysis
examples in this presentation form a small part of my Workbook two which is leading into complex
studies of airframe structures.
9
Catia V5.R20, FEA Skills toolset enhancement evaluating system methods.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
To perform an accurate finite element analysis of a structure a number of stages have to be passed
through during the construction of a suitable simulation model. In passing through these stages
several representations of the structural problem have to be crated and subsequently assessed
from an error viewpoint, these correspond to the various levels of abstraction which the stress
engineer has to consider in creating a finite element model.
The most important is the Idealised World which takes the real world model and turns it into a form
which can be analysed by the Finite Element Method. This is a very profound level of abstraction
which converts the structural model with its welds, rivets, bonded joints etc. into a smoothed model
in which each component, together with its boundary condition, loading situation etc. can be
mathematically defined. Thus, the decisions concerning such factors as the linearity or otherwise of
the structural behaviour are made at this stage. It is the most critical part of the whole finite element
analysis process as in a loose sense, the construction of an idealised world represents a transition
from a world “exterior” to the computer to an “interior” world.
Once the idealisation process has been performed a number of closely related representations are
constructed and are illustrated on the left hand side of Chart 7. These allow the generation of a
finite element model and, subsequently a finite element solution. Although they have a part to play
in the SAFESA Method they are not relevant to the description of the method as presented here.
The key aspects of the SAFESA are the identification of errors created in the idealisation process
and their treatment so that the eventual solution coming from the analysis corresponds in an error
controlled manner to the behaviour of the real world structure.
10
Catia V5.R20, FEA application of the SAFESA procedure to current work.
To perform an accurate finite element analysis of a structure a number of stages have to be passed
through during the construction of a suitable simulation model. In passing through these stages
several representations of the structural problem have to be crated and subsequently assessed
from an error viewpoint, these correspond to the various levels of abstraction which the stress
engineer has to consider in creating a finite element model.
The most important is the Idealised World which takes the real world model and turns it into a form
which can be analysed by the Finite Element Method. This is a very profound level of abstraction
which converts the structural model with its welds, rivets, bonded joints etc. into a smoothed model
in which each component, together with its boundary condition, loading situation etc. can be
mathematically defined. Thus, the decisions concerning such factors as the linearity or otherwise of
the structural behaviour are made at this stage. It is the most critical part of the whole finite element
analysis process as in a loose sense, the construction of an idealised world represents a transition
from a world “exterior” to the computer to an “interior” world.
Once the idealisation process has been performed a number of closely related representations are
constructed and are illustrated on the left hand side of Chart 7. These allow the generation of a
finite element model and, subsequently a finite element solution. Although they have a part to play
in the SAFESA Method they are not relevant to the description of the method as presented here.
The key aspects of the SAFESA are the identification of errors created in the idealisation process
and their treatment so that the eventual solution coming from the analysis corresponds in an error
controlled manner to the behaviour of the real world structure.
10
Catia V5.R20, FEA application of the SAFESA procedure to current work.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The SAFESA method is a systematic error control procedure which is used to support Finite
Element Modelling and ensures the total consistence of error control irrespective of the end users
level of experience. Errors are injected into an analysis through a number of individual causes
which can be categorised under a number of general headings: -
Mathematical model of the structure: The derivation of an appropriate mathematical model to
fit the description of the real structure employs physical laws, mathematical manipulation and
behavioural assumptions. The behaviour assumptions are needed so that the physical laws can
be manipulated mathematically to yield a useful set of expressions. Each behavioural
assumption introduces approximations and associated errors. In certain cases the model
reduces the dimensionality of the problem for example, from 3 to 2 dimensions.
Domain: Domain error relates to the geometrical region and the associated geometrical
simplification of the structures being analysed. The domain in most analysis is typically not
complete and may be limited to a portion of the total structure, with boundary conditions applied
explicitly at the interface with the rest of the structure. Often errors are generated by eliminating
or simplifying geometric detail. For example small cut - outs may be ignored or local stiffening
material might be „smeared‟ into adjacent structure.
Material: The structural model to be used for the analysis, the dimensional reduction and
associated mathematical manipulations fix the framework within which the material response is
described. This can involve significant approximation and is a potential source of error with
structural idealisation.
11
Section 2:- FEA application of the SAFESA procedure to ATDA project work.
The SAFESA method is a systematic error control procedure which is used to support Finite
Element Modelling and ensures the total consistence of error control irrespective of the end users
level of experience. Errors are injected into an analysis through a number of individual causes
which can be categorised under a number of general headings: -
Mathematical model of the structure: The derivation of an appropriate mathematical model to
fit the description of the real structure employs physical laws, mathematical manipulation and
behavioural assumptions. The behaviour assumptions are needed so that the physical laws can
be manipulated mathematically to yield a useful set of expressions. Each behavioural
assumption introduces approximations and associated errors. In certain cases the model
reduces the dimensionality of the problem for example, from 3 to 2 dimensions.
Domain: Domain error relates to the geometrical region and the associated geometrical
simplification of the structures being analysed. The domain in most analysis is typically not
complete and may be limited to a portion of the total structure, with boundary conditions applied
explicitly at the interface with the rest of the structure. Often errors are generated by eliminating
or simplifying geometric detail. For example small cut - outs may be ignored or local stiffening
material might be „smeared‟ into adjacent structure.
Material: The structural model to be used for the analysis, the dimensional reduction and
associated mathematical manipulations fix the framework within which the material response is
described. This can involve significant approximation and is a potential source of error with
structural idealisation.
11
Section 2:- FEA application of the SAFESA procedure to ATDA project work.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
12
Chart 1:- FEA modeling and SAFESA methods of error control.
SAFESA Error
Control
(1) Idealisation
(2) Discretisation
& Meshing
(3) Solving
(4) Post -
Processing
(5) Obtain
Qualification
Response
(6) Calculation of
Allowable
Response
(7) Comparison of
Qualification &
Allowable Response
(8) Validation
Review
(1.1) Global
Boundaries &
Loading Actions
(1.2) Global Load
Paths & Geometry
(1.3) Structural
Sub-Division
(1.4) Boundaries &
Loading Actions
for Features
(1.5) Load Paths &
Geometries for
Features
(1.6) Preliminary
Error Assessment
& Planning
(8.1) Follow Up
Error Assessment
(8.2) Test Program
(8.3) Experience
Data Key.
FEA Modeling
Start
End
12
Chart 1:- FEA modeling and SAFESA methods of error control.
SAFESA Error
Control
(1) Idealisation
(2) Discretisation
& Meshing
(3) Solving
(4) Post -
Processing
(5) Obtain
Qualification
Response
(6) Calculation of
Allowable
Response
(7) Comparison of
Qualification &
Allowable Response
(8) Validation
Review
(1.1) Global
Boundaries &
Loading Actions
(1.2) Global Load
Paths & Geometry
(1.3) Structural
Sub-Division
(1.4) Boundaries &
Loading Actions
for Features
(1.5) Load Paths &
Geometries for
Features
(1.6) Preliminary
Error Assessment
& Planning
(8.1) Follow Up
Error Assessment
(8.2) Test Program
(8.3) Experience
Data Key.
FEA Modeling
Start
End
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Boundary conditions and loading: The structural model also defines the form or type of the
boundary condition that can be applied and these are difficult to abstract from the physical
situation being analysed.
Error Treatment and Error Control: -In the preceding paragraphs the nature of the errors which
can occur in the analysis of a real world structure by the application of the Finite Element Method
has been highlighted. Realising that errors are present in a particular phase of the analysis process
is the beginning of the error control process, but methods required to treat and hopefully, bound
them. In performing this error control process there are two broad approaches adopted by
SAFESA. Firstly there are methods of error control which rely on a calculation process and which
often require exploiting the results from a finite element analysis. Essentially these are interior to
the analysis process and cannot supply objective error control but have a very important role to
play. Secondly there are exterior procedures which can be used to provide a measure of
objectivity, and these attempt to exploit information which is extracted from the real world problem.
These treatments are briefly outlined below: -
1)Interior Calculation Based Error Treatment Techniques: - Interior methods mainly employ
finite element models to check finite element models either by employing sequences of models
or by extracting the maximum information from a given model. Such a process is, essentially,
cyclic in nature with the analyst processing through a series of steps involving feedback loops.
Thus in an ideal situation the application of interior methods would begin with scoping
calculations, followed by hierarchical modelling and concluding with sensitivity studies.
13
Catia V5.R20, FEA application of the SAFESA procedure to current work.
Boundary conditions and loading: The structural model also defines the form or type of the
boundary condition that can be applied and these are difficult to abstract from the physical
situation being analysed.
Error Treatment and Error Control: -In the preceding paragraphs the nature of the errors which
can occur in the analysis of a real world structure by the application of the Finite Element Method
has been highlighted. Realising that errors are present in a particular phase of the analysis process
is the beginning of the error control process, but methods required to treat and hopefully, bound
them. In performing this error control process there are two broad approaches adopted by
SAFESA. Firstly there are methods of error control which rely on a calculation process and which
often require exploiting the results from a finite element analysis. Essentially these are interior to
the analysis process and cannot supply objective error control but have a very important role to
play. Secondly there are exterior procedures which can be used to provide a measure of
objectivity, and these attempt to exploit information which is extracted from the real world problem.
These treatments are briefly outlined below: -
1)Interior Calculation Based Error Treatment Techniques: - Interior methods mainly employ
finite element models to check finite element models either by employing sequences of models
or by extracting the maximum information from a given model. Such a process is, essentially,
cyclic in nature with the analyst processing through a series of steps involving feedback loops.
Thus in an ideal situation the application of interior methods would begin with scoping
calculations, followed by hierarchical modelling and concluding with sensitivity studies.
13
Catia V5.R20, FEA application of the SAFESA procedure to current work.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
2)Exterior Error Treatment Techniques: - As has already been discussed the interior methods
are not grounded in a reality which includes the real world. They represent a set of techniques
which, providing a datum point is available, are able to treat and control the additional errors
which are driving the analysis away from the datum. The datum being referred to in this case is
the finite element model which is directly related to a given real world structure together with
errors which cause the model to deviate from real world behaviour. In order to create a specific
datum structure it is necessary to characterise the structure in a unique manner.
The primary method for creating a starting point for the majority of analysts is to employ past
experience. Whilst this is an effective way to make progress it is not often done in a systematic
manner which allows a logical connection from the current problem to previously encountered
similar ones. Engineers rely on intuitive knowledge in deciding that one structure is sufficiently
close to a second example that the modelling procedures used in the first one, can be applied
to the second. Many years of experience in solving problems using finite element analysis
methods are a very valuable commodity in solving new structural analysis problems.
The question of how to relate one structure to another through a logical connection requires the
establishment of similarity rules. These, in turn, require that a set of parameters be identified
which uniquely define a given structure. A specific datum model for a given problem may be
either a complete model for a comparable problem or a model for a major sub component. In
the case of a complex structural design the error treatment process may therefore, require
several such models employed in a hierarchical sequence.
14
Catia V5.R20, FEA application of the SAFESA procedure to current work.
2)Exterior Error Treatment Techniques: - As has already been discussed the interior methods
are not grounded in a reality which includes the real world. They represent a set of techniques
which, providing a datum point is available, are able to treat and control the additional errors
which are driving the analysis away from the datum. The datum being referred to in this case is
the finite element model which is directly related to a given real world structure together with
errors which cause the model to deviate from real world behaviour. In order to create a specific
datum structure it is necessary to characterise the structure in a unique manner.
The primary method for creating a starting point for the majority of analysts is to employ past
experience. Whilst this is an effective way to make progress it is not often done in a systematic
manner which allows a logical connection from the current problem to previously encountered
similar ones. Engineers rely on intuitive knowledge in deciding that one structure is sufficiently
close to a second example that the modelling procedures used in the first one, can be applied
to the second. Many years of experience in solving problems using finite element analysis
methods are a very valuable commodity in solving new structural analysis problems.
The question of how to relate one structure to another through a logical connection requires the
establishment of similarity rules. These, in turn, require that a set of parameters be identified
which uniquely define a given structure. A specific datum model for a given problem may be
either a complete model for a comparable problem or a model for a major sub component. In
the case of a complex structural design the error treatment process may therefore, require
several such models employed in a hierarchical sequence.
14
Catia V5.R20, FEA application of the SAFESA procedure to current work.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The individual processes described above for treating errors need to be embedded in a routine
process if they are to be of any value to an analyst. This embedding process has resulted in the
creation of the SAFESA Method. It transforms the error treatment and control processes into an
applicable, quality control, step-wise procedure.
Each step within this process may itself be considered as a procedure with input data, a process or
action resulting in the generation of an output data set as outlined on the right hand side of Chart 1
in steps 1.1 through 1.6. Although these steps feed information from one step to the next in a linear
sequential manner, feedback loops are possible as indicated by the dotted lines. Indeed it is
unlikely that a simple pass through the structure will be satisfactory. Initial assumptions about
structural behaviour etc. are often incorrect and require revising. The process is decomposing the
structure in a step-wise manner to chase down errors. At each step the errors are identified and the
associated treatment procedures applied. A flagging process is used to identify that errors at a
specific stage in the Method have not been adequately treated and must be handled satisfactorily at
a later stage or during one of the feedback loops. If an error source cannot be treated this will
remain flagged as untreated and will be picked up at step 8.2 when a test programme is defined to
provide the analyst with the information to understand the nature and influence of the error.
The Method is therefore, an algorithm with a stopping criteria which requires that no error flags
remain set when the final step is completed. All the aspects relating to error sources and the control
of errors discussed above are incorporated, with the exception of the use of a datum and the
associated similarity rules. The latter is omitted due to the current incomplete state of this work. The
remaining parts of the Method are comprehensive and are applicable to the analysis of any
structure, and Table 1 error treatment techniques for identified errors.
15
Catia V5.R20, FEA application of the SAFESA procedure to current work.
The individual processes described above for treating errors need to be embedded in a routine
process if they are to be of any value to an analyst. This embedding process has resulted in the
creation of the SAFESA Method. It transforms the error treatment and control processes into an
applicable, quality control, step-wise procedure.
Each step within this process may itself be considered as a procedure with input data, a process or
action resulting in the generation of an output data set as outlined on the right hand side of Chart 1
in steps 1.1 through 1.6. Although these steps feed information from one step to the next in a linear
sequential manner, feedback loops are possible as indicated by the dotted lines. Indeed it is
unlikely that a simple pass through the structure will be satisfactory. Initial assumptions about
structural behaviour etc. are often incorrect and require revising. The process is decomposing the
structure in a step-wise manner to chase down errors. At each step the errors are identified and the
associated treatment procedures applied. A flagging process is used to identify that errors at a
specific stage in the Method have not been adequately treated and must be handled satisfactorily at
a later stage or during one of the feedback loops. If an error source cannot be treated this will
remain flagged as untreated and will be picked up at step 8.2 when a test programme is defined to
provide the analyst with the information to understand the nature and influence of the error.
The Method is therefore, an algorithm with a stopping criteria which requires that no error flags
remain set when the final step is completed. All the aspects relating to error sources and the control
of errors discussed above are incorporated, with the exception of the use of a datum and the
associated similarity rules. The latter is omitted due to the current incomplete state of this work. The
remaining parts of the Method are comprehensive and are applicable to the analysis of any
structure, and Table 1 error treatment techniques for identified errors.
15
Catia V5.R20, FEA application of the SAFESA procedure to current work.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
ERROR SOURCES.
ERROR TREATMENT.
First Stage. Second & Subsequent Stages.
Domain.
Experience / Simplification /
Calculations.
Model improvement.
Boundary conditions.
Experience / Existing test results /
Simple calculations.
Sensitivity analysis / Model
improvement.
Loading.
Experience / Existing test results /
Simple calculations.
Sensitivity analysis / Model
improvement.
Behaviour. Experience / Simple calculations.
Comparison with physical limits /
Model improvement.
Material. Experience / Simple calculations. Sensitivity analysis.
16
Table 1:- Error treatment techniques for the identified error sources.
ERROR SOURCES.
ERROR TREATMENT.
First Stage. Second & Subsequent Stages.
Domain.
Experience / Simplification /
Calculations.
Model improvement.
Boundary conditions.
Experience / Existing test results /
Simple calculations.
Sensitivity analysis / Model
improvement.
Loading.
Experience / Existing test results /
Simple calculations.
Sensitivity analysis / Model
improvement.
Behaviour. Experience / Simple calculations.
Comparison with physical limits /
Model improvement.
Material. Experience / Simple calculations. Sensitivity analysis.
16
Table 1:- Error treatment techniques for the identified error sources.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Aircraft structures fall into 3 categories which are as follows:-
Class 1:- structural component the failure of which will result in structural collapse; loss of control;
failure of motive power, injury or fatality (to any occupant); loss of safe operation of the aircraft.
Class 2:- Stresses components but not Class1.
Class 3:- Unstressed or lightly stresses component which is neither Class 1 or 2.
Structural integrity is defined as the capability of the structure to exceed applied design loading
throughout its operational life, and the selection of a design philosophy to achieve this from the start
of the design process is extremely important as this selection impacts on:- airframe weight;
maintainability; service life; and any future role change of the airframe. The approaches available to
the designer are:- Static Strength; Safe Life; Failsafe; Damage Tolerance; and Fatigue Life, the last
four of which, are expanded below (ref:-1). See tables 3 through 5 for ATDA candidate materials
selection.
(a)Safe Life:- The important criterion in this approach is the time before a „crack or flaw‟ is initiated
and the subsequent time before it grows to critical length. It can be seen from a typical S-N
curve that low levels of stress at high frequency of application theoretically do not cause any
fatigue damage. However it is necessary to allow for them, possibly by introducing a stress
factor such that effectively damage dose not occur.
(b)Fail-safe:- In this approach the dominate factors are the crack growth rate and the provision of
structural redundancy in conjunction with appropriate structural inspection provision.
17
Section 3:- Structural design philosophy of airframe structural components.
Aircraft structures fall into 3 categories which are as follows:-
Class 1:- structural component the failure of which will result in structural collapse; loss of control;
failure of motive power, injury or fatality (to any occupant); loss of safe operation of the aircraft.
Class 2:- Stresses components but not Class1.
Class 3:- Unstressed or lightly stresses component which is neither Class 1 or 2.
Structural integrity is defined as the capability of the structure to exceed applied design loading
throughout its operational life, and the selection of a design philosophy to achieve this from the start
of the design process is extremely important as this selection impacts on:- airframe weight;
maintainability; service life; and any future role change of the airframe. The approaches available to
the designer are:- Static Strength; Safe Life; Failsafe; Damage Tolerance; and Fatigue Life, the last
four of which, are expanded below (ref:-1). See tables 3 through 5 for ATDA candidate materials
selection.
(a)Safe Life:- The important criterion in this approach is the time before a „crack or flaw‟ is initiated
and the subsequent time before it grows to critical length. It can be seen from a typical S-N
curve that low levels of stress at high frequency of application theoretically do not cause any
fatigue damage. However it is necessary to allow for them, possibly by introducing a stress
factor such that effectively damage dose not occur.
(b)Fail-safe:- In this approach the dominate factors are the crack growth rate and the provision of
structural redundancy in conjunction with appropriate structural inspection provision.
17
Section 3:- Structural design philosophy of airframe structural components.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
There are several ways of ensuring that fail safety is achieved:-
i.By introducing secondary, stand-by components which only function is in the event of a
failure of the primary load path, to carry the load. This may consist of a tongue or a stop
which is normally just clear of the mating component. A mass penalty may be implied but in
same circumstances it is possible to use the secondary items in another role, for example
the need for a double pane assembly on cabin windows for thermal insulation purposes.
ii.By dividing a given load path into a number of separate members so that in the event of the
failure of one of them the rest can react the applied load. An example of this is the use of
several span wise planks in the tension surface of metallic wing boxes. When the load path
is designed to take advantage of the material strength the use of three separate items
enables any two remaining after one has failed to carry the full limit load under ultimate
stress. In some instances the „get home‟ consideration may enable a less severe approach
to be adopted.
iii.By design for slow crack growth such that in the event of crack initiation there is no danger
of a catastrophic failure before it is detected and repaired.
c)Damage tolerant:- With this philosophy it becomes necessary to distinguish between
components that can be inspected and those that cannot. Effectively either the fail-safe or
safe-life approaches are then applied, respectively, in conjunction with design for slow crack
growth and crack stopping (e.g. panel braking web stiffeners).
18
Structural design philosophy of airframe structural components.
There are several ways of ensuring that fail safety is achieved:-
i.By introducing secondary, stand-by components which only function is in the event of a
failure of the primary load path, to carry the load. This may consist of a tongue or a stop
which is normally just clear of the mating component. A mass penalty may be implied but in
same circumstances it is possible to use the secondary items in another role, for example
the need for a double pane assembly on cabin windows for thermal insulation purposes.
ii.By dividing a given load path into a number of separate members so that in the event of the
failure of one of them the rest can react the applied load. An example of this is the use of
several span wise planks in the tension surface of metallic wing boxes. When the load path
is designed to take advantage of the material strength the use of three separate items
enables any two remaining after one has failed to carry the full limit load under ultimate
stress. In some instances the „get home‟ consideration may enable a less severe approach
to be adopted.
iii.By design for slow crack growth such that in the event of crack initiation there is no danger
of a catastrophic failure before it is detected and repaired.
c)Damage tolerant:- With this philosophy it becomes necessary to distinguish between
components that can be inspected and those that cannot. Effectively either the fail-safe or
safe-life approaches are then applied, respectively, in conjunction with design for slow crack
growth and crack stopping (e.g. panel braking web stiffeners).
18
Structural design philosophy of airframe structural components.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
A.Safe-life and Fail–safe design processes (see Chart 2):- There is a commonality in the design
process for the safe –life and fail-safe concepts. The material to be used for the structure must
be selected with consideration of the critical requirements for crack initiation or crack growth
rate, as most relevant, together with the operating environment. A vital consideration for fail-
safe design is the provision of the alternative load paths, possibly together with crack
containment or crack arresting features. When these decisions have been made it is possible to
complete the design of the individual components of the structure and to define the
environmental protection necessary.
In the case of the safe-life concept the life inclusive of appropriate life factor follows directly
from the time taken initiation of the first crack to failure. Inspection is needed to monitor crack
growth. In the fail-safe concept the life is determined by the structure possessing adequate
residual strength subsequent to the development and growth of cracks.
In both cases it essential to demonstrate by testing, where possible on a complete specimen of
the airframe, that the design assumptions and calculations are justified. Further, in fail-safe
design it is necessary to inspect the structure at regular, appropriate intervals to ensure that any
developing cracks do not reach the critical length and are repaired before they do so.
As the design process is critically dependent upon assumed fatigue loading it is desirable, if not
essential, to carry out load monitoring throughout the operational life of the airframe. This is
used either to confirm the predicted life, or where necessary, to modify the allowable
operational life.
19
Structural design philosophy application processes.
A.Safe-life and Fail–safe design processes (see Chart 2):- There is a commonality in the design
process for the safe –life and fail-safe concepts. The material to be used for the structure must
be selected with consideration of the critical requirements for crack initiation or crack growth
rate, as most relevant, together with the operating environment. A vital consideration for fail-
safe design is the provision of the alternative load paths, possibly together with crack
containment or crack arresting features. When these decisions have been made it is possible to
complete the design of the individual components of the structure and to define the
environmental protection necessary.
In the case of the safe-life concept the life inclusive of appropriate life factor follows directly
from the time taken initiation of the first crack to failure. Inspection is needed to monitor crack
growth. In the fail-safe concept the life is determined by the structure possessing adequate
residual strength subsequent to the development and growth of cracks.
In both cases it essential to demonstrate by testing, where possible on a complete specimen of
the airframe, that the design assumptions and calculations are justified. Further, in fail-safe
design it is necessary to inspect the structure at regular, appropriate intervals to ensure that any
developing cracks do not reach the critical length and are repaired before they do so.
As the design process is critically dependent upon assumed fatigue loading it is desirable, if not
essential, to carry out load monitoring throughout the operational life of the airframe. This is
used either to confirm the predicted life, or where necessary, to modify the allowable
operational life.
19
Structural design philosophy application processes.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
20
Safe-Life.
Crack Initiation time.
Fail-Safe.
Crack growth rate.
Provision of redundancies.
Crack containment.
Environment.
Material: Component Design:
Corrosion protection: Testing.
Life. Residual strength.
In service load monitoring.
Chart 2:- Application of Safe-life and Fail-safe structural design philosophies.
20
Safe-Life.
Crack Initiation time.
Fail-Safe.
Crack growth rate.
Provision of redundancies.
Crack containment.
Environment.
Material: Component Design:
Corrosion protection: Testing.
Life. Residual strength.
In service load monitoring.
Chart 2:- Application of Safe-life and Fail-safe structural design philosophies.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
B.Damage Tolerant Design process (see Chart 3):- The damage tolerant approach commences
with the assumption that cracks or faults are present in the airframe as manufactured.
Experience suggests that these vary in length from 0.1mm to as much as 1.5mm.
Those items of the structure which may be readily inspected can be designed by selecting an
appropriate material and then applying essentially a fail-safe approach. The working stress
level must be selected and used in conjunction with crack stopping features to ensure that any
developing cracks grow slowly. Inspection periods must be established to give several
opportunities for a crack to be discovered before it attains a critical length.
When it is not possible to inspect a particular component it is essential to design for slow–crack
growth and ensure that the time for the initial length to reach its critical failure value is greater
than the required life of the whole structure. Since this approach is less satisfactory than that
applied to parts that can be inspected it is desirable to develop the design of the airframe such
that inspection is possible, wherever this can be arranged. As with safe-life and fail-safe
philosophies testing is needed to give confidence in the design calculations. Likewise, in-service
load monitoring is highly desirable for the same reason. This design philosophy is employed on
this project using techniques from ref:-1, JAR 25, and data sheets, MSc F&DT module notes.
C.Fatigue-life Design process (see Chart 4):- The first stage in the fatigue-life approach is the
definition of the relevant fatigue loads and the determination of the response of the aircraft
structure to these loads. The analysis for this follows that for limit load conditions, which
enables the loading on individual components of the airframe to be determined, and the
airframe structural response to be assed and the best design philosophy to be applied.
21
Structural design philosophy application processes.
B.Damage Tolerant Design process (see Chart 3):- The damage tolerant approach commences
with the assumption that cracks or faults are present in the airframe as manufactured.
Experience suggests that these vary in length from 0.1mm to as much as 1.5mm.
Those items of the structure which may be readily inspected can be designed by selecting an
appropriate material and then applying essentially a fail-safe approach. The working stress
level must be selected and used in conjunction with crack stopping features to ensure that any
developing cracks grow slowly. Inspection periods must be established to give several
opportunities for a crack to be discovered before it attains a critical length.
When it is not possible to inspect a particular component it is essential to design for slow–crack
growth and ensure that the time for the initial length to reach its critical failure value is greater
than the required life of the whole structure. Since this approach is less satisfactory than that
applied to parts that can be inspected it is desirable to develop the design of the airframe such
that inspection is possible, wherever this can be arranged. As with safe-life and fail-safe
philosophies testing is needed to give confidence in the design calculations. Likewise, in-service
load monitoring is highly desirable for the same reason. This design philosophy is employed on
this project using techniques from ref:-1, JAR 25, and data sheets, MSc F&DT module notes.
C.Fatigue-life Design process (see Chart 4):- The first stage in the fatigue-life approach is the
definition of the relevant fatigue loads and the determination of the response of the aircraft
structure to these loads. The analysis for this follows that for limit load conditions, which
enables the loading on individual components of the airframe to be determined, and the
airframe structural response to be assed and the best design philosophy to be applied.
21
Structural design philosophy application processes.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Chart 3:- Application of the Damage Tolerance structural design philosophy.
Damage Tolerant.
Crack in structure as manufactured.
Is the component inspectable?
Yes. No.
Fail-safe approach.
Slow crack growth.
Crack arrest features.
Inspection periods.
Crack growth to initiate
failure to be more than
service life.
Testing.
In service load monitoring (FTI / G monitors / SHM).
22
Chart 3:- Application of the Damage Tolerance structural design philosophy.
Damage Tolerant.
Crack in structure as manufactured.
Is the component inspectable?
Yes. No.
Fail-safe approach.
Slow crack growth.
Crack arrest features.
Inspection periods.
Crack growth to initiate
failure to be more than
service life.
Testing.
In service load monitoring (FTI / G monitors / SHM).
22
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
23
Chart 4:- Application of the Fatigue-life structural design philosophy.
Fatigue-life.
Aircraft structural response.
Fatigue load spectra.
Design philosophy selection.
Damage Tolerant. Safe-Life. Fail-Safe.
23
Chart 4:- Application of the Fatigue-life structural design philosophy.
Fatigue-life.
Aircraft structural response.
Fatigue load spectra.
Design philosophy selection.
Damage Tolerant. Safe-Life. Fail-Safe.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Fatigue Design Requirements:- The emphasis of the requirements specified to ensure the integrity
of the airframe design under fatigue loading is on the methods of analysis and the means of
determination of a satisfactory fatigue life. Only in the United States military code is there a
specification of a magnitude and frequency of repeated loading and this is outlined below. Loading
conditions for all categories of aircraft are discussed below.
1)Civil transport aircraft JAR 25.571:- This standard outlines the basic requirements for fatigue
evaluation and damage tolerance design of transport aircraft. The paragraph outlines the
general requirements for the analysis and the extent of the calculations. Amplification of the
details is given in the associated „acceptable methods of compliance‟ given in JAR 25.ACJ
25.571.
2)UK Military Aircraft:- The basic requirements for fatigue analysis and life evaluation are
specified in Def Stan 00970 Chapter 201. This covers techniques for allowing for variances in
the data as well as overall requirements and the philosophy to be adopted. Detail requirements
of the frequency and magnitude of the repeated loading are given in the particular specification
for the aircraft.
3)US Military Aircraft:- The United States military aircraft stipulations are to be found in three
separate documents:- In MIL-A-8866A the emphasis is on the detail of the required magnitude
and frequency of the repeated loading rather than on analysis the data covers;- maneuver;
gust; ground and pressurization conditions for fighter, attack, trainer, bomber, patrol, utility and
transport aircraft.
24
Structural design fatigue requirements for design philosophy application.
Fatigue Design Requirements:- The emphasis of the requirements specified to ensure the integrity
of the airframe design under fatigue loading is on the methods of analysis and the means of
determination of a satisfactory fatigue life. Only in the United States military code is there a
specification of a magnitude and frequency of repeated loading and this is outlined below. Loading
conditions for all categories of aircraft are discussed below.
1)Civil transport aircraft JAR 25.571:- This standard outlines the basic requirements for fatigue
evaluation and damage tolerance design of transport aircraft. The paragraph outlines the
general requirements for the analysis and the extent of the calculations. Amplification of the
details is given in the associated „acceptable methods of compliance‟ given in JAR 25.ACJ
25.571.
2)UK Military Aircraft:- The basic requirements for fatigue analysis and life evaluation are
specified in Def Stan 00970 Chapter 201. This covers techniques for allowing for variances in
the data as well as overall requirements and the philosophy to be adopted. Detail requirements
of the frequency and magnitude of the repeated loading are given in the particular specification
for the aircraft.
3)US Military Aircraft:- The United States military aircraft stipulations are to be found in three
separate documents:- In MIL-A-8866A the emphasis is on the detail of the required magnitude
and frequency of the repeated loading rather than on analysis the data covers;- maneuver;
gust; ground and pressurization conditions for fighter, attack, trainer, bomber, patrol, utility and
transport aircraft.
24
Structural design fatigue requirements for design philosophy application.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
MIL-A-8867 prescribes the ground testing to be undertaken as part of the demonstration of the
life of the airframe. The final document the is MIL-8868 paragraph 3.4 and 3.5 which stipulate
the information to be provided in the form of reports outlining the analysis and testing
undertaken to substantiate the life of the airframe.
The types of repeated airframe load data required for design against fatigue and to apply in the
selected component design philosophy are outlined below.
1)Symmetric manoeuvre case:- Extensive information is available in relation to symmetric
manoeuvres of both military and civil aircraft, e.g. Van Dijk and Jonge‟s work which outlines a
fatigue spectrum obtained from flying experience of fighter / attack aircraft which is known as
the FALSTAFF spectrum, based on the maximum value of peak stress (s) and loading
frequency (n) the peak stress selected being the Input Parameter.
2)Asymmetric manoeuvre case:- Fatigue loading data for asymmetric manoeuvre loading is
sparse, and these originate from the roll and yaw controls, the texts of Taylor derives data from
early jet fighter experience. As for civil aircraft it has been determined that atmospheric
turbulence is of much greater significance.
3)Atmospheric turbulence:- Fatigue loading due to encounters with discrete gusting or the effect
of continuous turbulence is of importance for all classes of aircraft, but especially for those
where operational role does not demand substantial manoeuvring in flight. ESDU data sheets
69023 (Average gust frequency for Subsonic Transport Aircraft (ESDU International plc. May
1989) is used in this study.
25
Structural design fatigue requirements for design philosophy application.
MIL-A-8867 prescribes the ground testing to be undertaken as part of the demonstration of the
life of the airframe. The final document the is MIL-8868 paragraph 3.4 and 3.5 which stipulate
the information to be provided in the form of reports outlining the analysis and testing
undertaken to substantiate the life of the airframe.
The types of repeated airframe load data required for design against fatigue and to apply in the
selected component design philosophy are outlined below.
1)Symmetric manoeuvre case:- Extensive information is available in relation to symmetric
manoeuvres of both military and civil aircraft, e.g. Van Dijk and Jonge‟s work which outlines a
fatigue spectrum obtained from flying experience of fighter / attack aircraft which is known as
the FALSTAFF spectrum, based on the maximum value of peak stress (s) and loading
frequency (n) the peak stress selected being the Input Parameter.
2)Asymmetric manoeuvre case:- Fatigue loading data for asymmetric manoeuvre loading is
sparse, and these originate from the roll and yaw controls, the texts of Taylor derives data from
early jet fighter experience. As for civil aircraft it has been determined that atmospheric
turbulence is of much greater significance.
3)Atmospheric turbulence:- Fatigue loading due to encounters with discrete gusting or the effect
of continuous turbulence is of importance for all classes of aircraft, but especially for those
where operational role does not demand substantial manoeuvring in flight. ESDU data sheets
69023 (Average gust frequency for Subsonic Transport Aircraft (ESDU International plc. May
1989) is used in this study.
25
Structural design fatigue requirements for design philosophy application.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
There are two main types of turbulence which are:- (a)Symmetric Vertical Turbulence, and
(b)Lateral Turbulence.
a)Symmetric Vertical Turbulence:- where gust magnitude is a function of both flight altitude and
terrain over which the aircraft is flying, e.g. low level penetration bombing missions B-1B,
Tornado, and B-52H, where there are more up gusts than down, these are allowed for by
using correction factors.
b)Lateral Turbulence:- there is less information on the frequency and magnitude of lateral
turbulence for aircraft but it has been suggested that at altitudes below about 3km the
frequency of a given magnitude is some 10-15% greater than those of the corresponding
vertical condition.
4)Landing gear loads:- these fall into three categories;- (a) loads due to ground manoeuvring e.g.
taxiing; (b) the effects of the unevenness of the ground surface e.g. unpaved runways, rough
field poor condition runways, major consideration in troop / cargo military transports, and
forward based CAS aircraft; (c) landing impact conditions. The texts of Howe (ref:-1): Niu: and
MIL-A-8866A are employed in this project.
5)Buffeting Turbulence:- Flow over the aircraft may break down at local points and give rise to
buffeting. This induces a relatively high – frequency variation in the aerodynamic loads,
possibly resulting in the fatigue of local airframe components such as metallic skin panels.
6)Acoustic Noise Turbulence:- local high frequency vibration or flow field loading, and ESDU Data
sheets 75021 and 89041 were used in this project.
26
Structural design fatigue requirements for design philosophy application.
There are two main types of turbulence which are:- (a)Symmetric Vertical Turbulence, and
(b)Lateral Turbulence.
a)Symmetric Vertical Turbulence:- where gust magnitude is a function of both flight altitude and
terrain over which the aircraft is flying, e.g. low level penetration bombing missions B-1B,
Tornado, and B-52H, where there are more up gusts than down, these are allowed for by
using correction factors.
b)Lateral Turbulence:- there is less information on the frequency and magnitude of lateral
turbulence for aircraft but it has been suggested that at altitudes below about 3km the
frequency of a given magnitude is some 10-15% greater than those of the corresponding
vertical condition.
4)Landing gear loads:- these fall into three categories;- (a) loads due to ground manoeuvring e.g.
taxiing; (b) the effects of the unevenness of the ground surface e.g. unpaved runways, rough
field poor condition runways, major consideration in troop / cargo military transports, and
forward based CAS aircraft; (c) landing impact conditions. The texts of Howe (ref:-1): Niu: and
MIL-A-8866A are employed in this project.
5)Buffeting Turbulence:- Flow over the aircraft may break down at local points and give rise to
buffeting. This induces a relatively high – frequency variation in the aerodynamic loads,
possibly resulting in the fatigue of local airframe components such as metallic skin panels.
6)Acoustic Noise Turbulence:- local high frequency vibration or flow field loading, and ESDU Data
sheets 75021 and 89041 were used in this project.
26
Structural design fatigue requirements for design philosophy application.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Materials Code
ρ
Kg/m
E
GPa
σe
MPa
kht khc kdt kdc kθ
Carbon /
Epoxy.
3501/6 QI 1605.44 67 736 0.61 0.65 0.55 0.38 0.83
Carbon /
Epoxy.
3501/6 O 1605.44 80 880 0.55 0.62 0.55 0.38 0.83
Ti Alloy Ti6Al4V 4428.8 110 902 0.94 0.94 0.20 0.94 1.00
Al/Li Alloy 8090 T3X 2530 80 329 0.94 0.94 0.39 0.94 0.90
Al Alloy 7075 T76 2768 72 483 0.94 0.94 0.29 0.94 0.90
Al Alloy 2024 T3 2768 72 325 0.94 0.94 0.31 0.94 0.90
27
3
Table 2(a):- Materials Properties for ATDA wing empennage materials (Ref.3).
Materials Code
ρ
Kg/m
E
GPa
σe
MPa
kht khc kdt kdc kθ
Carbon /
Epoxy.
3501/6 QI 1605.44 67 736 0.61 0.65 0.55 0.38 0.83
Carbon /
Epoxy.
3501/6 O 1605.44 80 880 0.55 0.62 0.55 0.38 0.83
Ti Alloy Ti6Al4V 4428.8 110 902 0.94 0.94 0.20 0.94 1.00
Al/Li Alloy 8090 T3X 2530 80 329 0.94 0.94 0.39 0.94 0.90
Al Alloy 7075 T76 2768 72 483 0.94 0.94 0.29 0.94 0.90
Al Alloy 2024 T3 2768 72 325 0.94 0.94 0.31 0.94 0.90
27
3
Table 2(a):- Materials Properties for ATDA wing empennage materials (Ref.3).
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Table 2(b):- Materials Properties for ATDA fuselage materials (Ref‟s. 4&5).
Property. Unidirectional Tape /Slit Tape. Plain Weave Fabric.
Thickness per ply 0.15mm 0.25mm
Density (ρ) 1790kg/m 1570kg/m
Longitudinal modulus E1 (GPa) 137.3 62.6
Transverse modulus E2 (GPa) 7.8 59.3
In-plain Shear modulus G12 (GPa) 5.23 4.6
Poisson's ratio V12 0.36 0.062
Longitudinal tensile strength F1t (MPa) 2057 621
Transverse tensile strength F2t (MPa) 46.9 594
Longitudinal compressive strength F1c (MPa) 1610 760
Transference compressive strength F2c (MPa) 207 707
In-plain shear strength F6 (MPa) 135 125
Standard Width ATL* 460mm / AFP* 12.5mm 1600 mm
28
*ATL= Automated Tape Laying : AFP = Automated Fibre Placement.
3 3
Table 2(b):- Materials Properties for ATDA fuselage materials (Ref‟s. 4&5).
Property. Unidirectional Tape /Slit Tape. Plain Weave Fabric.
Thickness per ply 0.15mm 0.25mm
Density (ρ) 1790kg/m 1570kg/m
Longitudinal modulus E1 (GPa) 137.3 62.6
Transverse modulus E2 (GPa) 7.8 59.3
In-plain Shear modulus G12 (GPa) 5.23 4.6
Poisson's ratio V12 0.36 0.062
Longitudinal tensile strength F1t (MPa) 2057 621
Transverse tensile strength F2t (MPa) 46.9 594
Longitudinal compressive strength F1c (MPa) 1610 760
Transference compressive strength F2c (MPa) 207 707
In-plain shear strength F6 (MPa) 135 125
Standard Width ATL* 460mm / AFP* 12.5mm 1600 mm
28
*ATL= Automated Tape Laying : AFP = Automated Fibre Placement.
3 3
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Category. Failure Mode. Weight Ratio (W2 / W1)
1 Tensile strength. ρ2 / ρ1 σe1/σe2 [kth1/ kth2 kθ1/kθ2]
2 Compressive strength. ρ2 /ρ1 σe1/σe2 [kch1/kch2 kθ1/kθ2]
3 Crippling ρ2 / ρ1 [Es1 σe1 / Es2 σe2]
4 Compression surface column and crippling ρ2/ρ1 [Es1 Et1 σe1/Es2 Et2 σe2]
5 Buckling compression and shear ρ2 /ρ1 [E1 / E2]
6 Aeroelastic stiffness ρ2/ρ1 E1/E2
7 Durability and damage tolerance ρ2/ρ1 [kd1kθ1/kd2kθ2]
29
Table 3:- Weight Ratio Equations for Various Failure Categories (based on Ref.3).
0.25
0.2
1/3
Category. Failure Mode. Weight Ratio (W2 / W1)
1 Tensile strength. ρ2 / ρ1 σe1/σe2 [kth1/ kth2 kθ1/kθ2]
2 Compressive strength. ρ2 /ρ1 σe1/σe2 [kch1/kch2 kθ1/kθ2]
3 Crippling ρ2 / ρ1 [Es1 σe1 / Es2 σe2]
4 Compression surface column and crippling ρ2/ρ1 [Es1 Et1 σe1/Es2 Et2 σe2]
5 Buckling compression and shear ρ2 /ρ1 [E1 / E2]
6 Aeroelastic stiffness ρ2/ρ1 E1/E2
7 Durability and damage tolerance ρ2/ρ1 [kd1kθ1/kd2kθ2]
29
Table 3:- Weight Ratio Equations for Various Failure Categories (based on Ref.3).
0.25
0.2
1/3
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Material Code
Weight Ratio (S1/S2) (ρ2/ρ1)
Cat 1 Cat 2 Cat 3 Cat 5 Cat 6 Cat 7(a) Cat 7(b)
Carbon /
epoxy
3501/6QI 0.4 0.4 0.5 0.4 0.6 0.2 0.7
Carbon /
epoxy
3501/6O 0.4 0.3 0.4 0.4 0.5 0.1 0.6
Titanium Ti6Al4V 0.5 0.5 1.1 1.0 1.0 0.8 0.5
Aluminium /
Lithium
8090T3X 0.9 0.9 0.9 0.9 0.8 0.7 0.9
Aluminium
alloy
7075 T76 0.7 0.7 0.9 0.9 1.0 0.7 0.7
Aluminium
alloy
2024 T3 1.0 1.0 1.0 1.0 1.0 1.0 1.0
30
Table 4:- Weight Ratios for Airframe Materials for Various Failure Categories (Ref.3).
n
Material Code
Weight Ratio (S1/S2) (ρ2/ρ1)
Cat 1 Cat 2 Cat 3 Cat 5 Cat 6 Cat 7(a) Cat 7(b)
Carbon /
epoxy
3501/6QI 0.4 0.4 0.5 0.4 0.6 0.2 0.7
Carbon /
epoxy
3501/6O 0.4 0.3 0.4 0.4 0.5 0.1 0.6
Titanium Ti6Al4V 0.5 0.5 1.1 1.0 1.0 0.8 0.5
Aluminium /
Lithium
8090T3X 0.9 0.9 0.9 0.9 0.8 0.7 0.9
Aluminium
alloy
7075 T76 0.7 0.7 0.9 0.9 1.0 0.7 0.7
Aluminium
alloy
2024 T3 1.0 1.0 1.0 1.0 1.0 1.0 1.0
30
Table 4:- Weight Ratios for Airframe Materials for Various Failure Categories (Ref.3).
n
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
31
Table 5:- Structural Analysis Reserve Factors
Discipline Design Objective Load Case Criteria Parameters
Static Strength
Ultimate Strength Ultimate Loads Failure
Fracture: Instability: Barely
Visible Impact Damage.
Deformation Limit Loads
Detrimental of
Deformation
Plasticity: Instability: Barely
Visible Impact Damage.
Fatigue and
Damage
Tolerance
Fatigue Life: Durability Operational Loads Crack Initiation Design Service Goal.
Crack Growth Operational Loads
Critical Crack
Length
Inspection Threshold &
Intervals no Growth Policies
and Barely Visible Impact
Damage.
Residual Strength &
Damage Capability
Limit Loads Failure
Two Bay Crack Visible Impact
Damage.
In order to develop a successful structural analysis the following primary data is required :-
(1) The applied loading for each load case: (2) Allowable loading for each design objective: (3) The Reserve factor for
each load case and each design objective.
Design allowable
Design load x Design Factor x Safety Factor
RF =
MS = RF-1 ….. Margin of safety
31
Table 5:- Structural Analysis Reserve Factors
Discipline Design Objective Load Case Criteria Parameters
Static Strength
Ultimate Strength Ultimate Loads Failure
Fracture: Instability: Barely
Visible Impact Damage.
Deformation Limit Loads
Detrimental of
Deformation
Plasticity: Instability: Barely
Visible Impact Damage.
Fatigue and
Damage
Tolerance
Fatigue Life: Durability Operational Loads Crack Initiation Design Service Goal.
Crack Growth Operational Loads
Critical Crack
Length
Inspection Threshold &
Intervals no Growth Policies
and Barely Visible Impact
Damage.
Residual Strength &
Damage Capability
Limit Loads Failure
Two Bay Crack Visible Impact
Damage.
In order to develop a successful structural analysis the following primary data is required :-
(1) The applied loading for each load case: (2) Allowable loading for each design objective: (3) The Reserve factor for
each load case and each design objective.
Design allowable
Design load x Design Factor x Safety Factor
RF =
MS = RF-1 ….. Margin of safety
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
32
Section 5:- My CATIA V5.R20 FEA capability metallic analysis examples.
See references (2), (5), and (6) for all methodologies used in this section.
32
Section 5:- My CATIA V5.R20 FEA capability metallic analysis examples.
See references (2), (5), and (6) for all methodologies used in this section.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Four examples of these ongoing studies are given here:-
1)Bearing Shaft Assembly using Analysis Connections:- Problem statement:- The assembly
shown in figure 2 consist of a shaft of 1” diameter and length 6”, and two bearings with dimensions
as shown. All parts are made of aluminum with E=10.15E7 psi and v = 0.346. The bottom faces of
the bearings are clamped and the shaft is subjected to a total downward load of 100lb distributed
on its surface. The objective of this analysis was to predict stresses and deflections in the structure.
Full stress report was produced the results are shown in figures 3(a) and 3(b).
2)Tensile Test Specimen Assembly:- Problem statement:- The assembly consisted of two steel
pins (1”diam x 3” long) and an aluminum block (10”x 4”x1”). The constrained and loaded assembly
is shown in figure 4. The end faces of the bottom pin are clamped, and the end faces of the top pin
are given a displacement of 0.01” (0.254mm) causing the block to stretch. The objective was to
determine the force necessary to cause this deflection and predict the stresses in the structure, for
this analysis Parabolic Tetrahedron elements were used for this analysis. A full stress report was
produced, the results are shown in figures 5(a) and 5(b).
3)Spot Weld Analysis:- Two sheets of made of steel having a thickness of 0.03” are spot welded
together at four dotted points as shown in figure 6. The edge AB of the bottom plate is clamped and
the edge CD of the top L section is loaded with a 10lb force. All the dimensions shown are in
inches. The objective was to use Catia V5.R20 Generative Structural Analysis to predict the
stresses in these parts. Linear Triangular elements were used for this analysis. A full stress report
was produced, the results are shown in figures 6 to 8.
33
Catia V5.R20, FEA Skills toolset enhancement worked examples.
Four examples of these ongoing studies are given here:-
1)Bearing Shaft Assembly using Analysis Connections:- Problem statement:- The assembly
shown in figure 2 consist of a shaft of 1” diameter and length 6”, and two bearings with dimensions
as shown. All parts are made of aluminum with E=10.15E7 psi and v = 0.346. The bottom faces of
the bearings are clamped and the shaft is subjected to a total downward load of 100lb distributed
on its surface. The objective of this analysis was to predict stresses and deflections in the structure.
Full stress report was produced the results are shown in figures 3(a) and 3(b).
2)Tensile Test Specimen Assembly:- Problem statement:- The assembly consisted of two steel
pins (1”diam x 3” long) and an aluminum block (10”x 4”x1”). The constrained and loaded assembly
is shown in figure 4. The end faces of the bottom pin are clamped, and the end faces of the top pin
are given a displacement of 0.01” (0.254mm) causing the block to stretch. The objective was to
determine the force necessary to cause this deflection and predict the stresses in the structure, for
this analysis Parabolic Tetrahedron elements were used for this analysis. A full stress report was
produced, the results are shown in figures 5(a) and 5(b).
3)Spot Weld Analysis:- Two sheets of made of steel having a thickness of 0.03” are spot welded
together at four dotted points as shown in figure 6. The edge AB of the bottom plate is clamped and
the edge CD of the top L section is loaded with a 10lb force. All the dimensions shown are in
inches. The objective was to use Catia V5.R20 Generative Structural Analysis to predict the
stresses in these parts. Linear Triangular elements were used for this analysis. A full stress report
was produced, the results are shown in figures 6 to 8.
33
Catia V5.R20, FEA Skills toolset enhancement worked examples.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
34
Figure 2:- Example my Catia V5.R20 FEA:- bearing assembly exercise load and constraints.
2 inch
1 inch
34
Figure 2:- Example my Catia V5.R20 FEA:- bearing assembly exercise load and constraints.
2 inch
1 inch
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Figure 3:- My Catia V5.R20 aluminum bearing beam assembly analysis.
Figure 3(a) :- Total displacement magnitude
analysis of the bearing beam assembly.
Maximum deflection = 0.000881691”
Minimum = 0”
35
Figure 3(b) :- Von Mises Stress (nodal values)
analysis of the same bearing beam assembly.
Maximum stress = 1902.12 psi, Minimum
stress = 17.7862 psi.
Figure 3:- My Catia V5.R20 aluminum bearing beam assembly analysis.
Figure 3(a) :- Total displacement magnitude
analysis of the bearing beam assembly.
Maximum deflection = 0.000881691”
Minimum = 0”
35
Figure 3(b) :- Von Mises Stress (nodal values)
analysis of the same bearing beam assembly.
Maximum stress = 1902.12 psi, Minimum
stress = 17.7862 psi.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
36
Figure 4:- Example my Catia V5.R20 FEA:- tensile specimen exercise load and constraints.
36
Figure 4:- Example my Catia V5.R20 FEA:- tensile specimen exercise load and constraints.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
37
Figure 46:- My Catia V5.R20 two material tensile test specimen assembly analysis.
Figure 5(a) :- Total displacement magnitude
analysis of the tensile specimen assembly.
Maximum deflection = 0.01” Minimum = 0”in
the pins and Maximum deflection of 0.00851”
Minimum = 0.00148” in the test block.
Figure 5(b) :- Von Mises Stress (nodal values)
analysis of the same tensile specimen
assembly. Maximum stress = 50732.6 psi, in the
top pin Minimum stress = 51.8327 psi in the
test block.
37
Figure 46:- My Catia V5.R20 two material tensile test specimen assembly analysis.
Figure 5(a) :- Total displacement magnitude
analysis of the tensile specimen assembly.
Maximum deflection = 0.01” Minimum = 0”in
the pins and Maximum deflection of 0.00851”
Minimum = 0.00148” in the test block.
Figure 5(b) :- Von Mises Stress (nodal values)
analysis of the same tensile specimen
assembly. Maximum stress = 50732.6 psi, in the
top pin Minimum stress = 51.8327 psi in the
test block.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
38
Figure 6:- My Catia V5.R20 FEA Spot welded sheet assembly problem structure.
C
D
A
B
5 in
12 in
3 in
4 in
2 in
2 in
2 in
2 in
2 in
C
D
A
B
5 in
12 in
3 in
4 in
2 in
2 in
2 in
2 in
2 in
1in
10 in
Sheet Material = Steel:
Sheet Thickness = 0.03 inch:
Top L section loaded edge C-D:
Bottom plate clamped edge A-B.
38
Figure 6:- My Catia V5.R20 FEA Spot welded sheet assembly problem structure.
C
D
A
B
5 in
12 in
3 in
4 in
2 in
2 in
2 in
2 in
2 in
C
D
A
B
5 in
12 in
3 in
4 in
2 in
2 in
2 in
2 in
2 in
1in
10 in
Sheet Material = Steel:
Sheet Thickness = 0.03 inch:
Top L section loaded edge C-D:
Bottom plate clamped edge A-B.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
39
Figure 7:- Example my Catia V5.R20 FEA:- Spot welded sheet exercise load and constraints.
39
Figure 7:- Example my Catia V5.R20 FEA:- Spot welded sheet exercise load and constraints.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
40
Figure 8(a) :- Total displacement magnitude
analysis of the spot welded sheet assembly.
Maximum deflection = 1.38369” Minimum = 0”.
Figure 8(b) :- Von Mises Stress (nodal values)
analysis of the spot welded sheet assembly.
Maximum stress = 35325.8psi, Minimum
stress = 265.515psi. Maximum stress was in
the weld line as expected.
Figure 8:- My Catia V5.R20 Sheet steel spot welded assembly analysis.
40
Figure 8(a) :- Total displacement magnitude
analysis of the spot welded sheet assembly.
Maximum deflection = 1.38369” Minimum = 0”.
Figure 8(b) :- Von Mises Stress (nodal values)
analysis of the spot welded sheet assembly.
Maximum stress = 35325.8psi, Minimum
stress = 265.515psi. Maximum stress was in
the weld line as expected.
Figure 8:- My Catia V5.R20 Sheet steel spot welded assembly analysis.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
4)Analysis of a fastened assembly:- This assembly consisted of two plates, clamped together
with a preloaded steel bolt. One plate was loaded causing the bending of the entire structure.
The objective of this analysis was to predict the stresses and deflections to which the assembly
was subjected. The top plate was 1” by 1” square with a thickness of 0.125”: the bottom plate
was 1” by 2” with a thickness of 0.125” each had a 0.125” radius hole 0.5” from the trailing edge
as shown in figure 9. The bolt had a shaft radius of 0.125” and length 0.4”, and a head radius of
0.2” and thickness of 0.1”. The assembly was constructed using Coincidence constraint's and
the material steel was applied. The resultant assembly being meshed, restrained, and contact
connected as shown in figure 10, then a tightening force of 50lbs was applied to the bolt
tightening connection, analysis was then undertaken of displacement, and Von Mises stress in
the assembly, the results are shown in figures 11(a) and (b). Subsequently a distributed load of
100lbf was applied to the leading edge of the lower plate as shown in figure 12 in the Z direction
as a distributed force, and the assembly was re-analysed for displacement and Von Mises
stress values, the results are shown in figures 13(a) and (b).
The final outcome of this research will be the analysis of metallic and composite airframe structures
in support of my FATA airframe research program.
41
Catia V5.R20, FEA Skills toolset enhancement worked examples.
4)Analysis of a fastened assembly:- This assembly consisted of two plates, clamped together
with a preloaded steel bolt. One plate was loaded causing the bending of the entire structure.
The objective of this analysis was to predict the stresses and deflections to which the assembly
was subjected. The top plate was 1” by 1” square with a thickness of 0.125”: the bottom plate
was 1” by 2” with a thickness of 0.125” each had a 0.125” radius hole 0.5” from the trailing edge
as shown in figure 9. The bolt had a shaft radius of 0.125” and length 0.4”, and a head radius of
0.2” and thickness of 0.1”. The assembly was constructed using Coincidence constraint's and
the material steel was applied. The resultant assembly being meshed, restrained, and contact
connected as shown in figure 10, then a tightening force of 50lbs was applied to the bolt
tightening connection, analysis was then undertaken of displacement, and Von Mises stress in
the assembly, the results are shown in figures 11(a) and (b). Subsequently a distributed load of
100lbf was applied to the leading edge of the lower plate as shown in figure 12 in the Z direction
as a distributed force, and the assembly was re-analysed for displacement and Von Mises
stress values, the results are shown in figures 13(a) and (b).
The final outcome of this research will be the analysis of metallic and composite airframe structures
in support of my FATA airframe research program.
41
Catia V5.R20, FEA Skills toolset enhancement worked examples.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
42
Figure 9:- Example my Catia V5.R20 Bolted assembly components for analysis.
42
Figure 9:- Example my Catia V5.R20 Bolted assembly components for analysis.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
43
Figure 10:- Example my Catia V5.R20 Bolted assembly constrained and preload for analysis.
43
Figure 10:- Example my Catia V5.R20 Bolted assembly constrained and preload for analysis.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
44
Figure 11:- My Catia V5.R20 Bolted assembly preload analysis.
Figure 11(b) :- Von Mises Stress (nodal
values) analysis of preloaded bolted
assembly. Maximum stress = 1818.98psi,
Minimum stress = 0.149288psi. Maximum
stress the bolt as expected.
Figure 11(a):- Total displacement magnitude
analysis of the preloaded bolted plate
assembly. Maximum deflection = 3.35588e-
005” Minimum =1.0” the max value being in
the bolt as expected.
44
Figure 11:- My Catia V5.R20 Bolted assembly preload analysis.
Figure 11(b) :- Von Mises Stress (nodal
values) analysis of preloaded bolted
assembly. Maximum stress = 1818.98psi,
Minimum stress = 0.149288psi. Maximum
stress the bolt as expected.
Figure 11(a):- Total displacement magnitude
analysis of the preloaded bolted plate
assembly. Maximum deflection = 3.35588e-
005” Minimum =1.0” the max value being in
the bolt as expected.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
45
Figure 12:- Example my Catia V5.R20 Bolted assembly constrained meshed with distributed load.
45
Figure 12:- Example my Catia V5.R20 Bolted assembly constrained meshed with distributed load.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
46
Figure 13:- My Catia V5.R20 Bolted assembly preload with added end load analysis.
Figure 13(a) :- Total displacement
magnitude analysis of the loaded
bolted plate assembly. Maximum
deflection = 0.0448786” Minimum =
1.0” the max value being in the lower
plate edge as expected.
Figure 13(b) :- Von Mises Stress (nodal
values) analysis of preloaded bolted
assembly. Maximum stress = 39003.4psi,
Minimum stress = 82.218psi. Maximum
stress the bolt region as expected.
46
Figure 13:- My Catia V5.R20 Bolted assembly preload with added end load analysis.
Figure 13(a) :- Total displacement
magnitude analysis of the loaded
bolted plate assembly. Maximum
deflection = 0.0448786” Minimum =
1.0” the max value being in the lower
plate edge as expected.
Figure 13(b) :- Von Mises Stress (nodal
values) analysis of preloaded bolted
assembly. Maximum stress = 39003.4psi,
Minimum stress = 82.218psi. Maximum
stress the bolt region as expected.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The application of hexahedral elements in Catia V5.R20
In addition to the elements covered above in Section 1 an other element type is available namely
the Hexahedral element, however its capabilities are very limited and do not have all of the
functionalities of the tetrahedral elements used in the above examples. These elements are
obtained by dragging shell elements in a prescribed direction.
1)Problem Statement and model creation:- This modelling exercises examined a steel rectangular
block with a central hole of 2in diameter which was being pulled from both ends as shown in
figure 14(a), which gives the dimensions 6in x 4in x 2in and end loads of 100 psi. In the
Mechanical Design workbench block was modelled in Part Design, as shown in figure 14,
subsequently in the Mechanical Design workbench surfaces were extracted in Wireframe and
Surface Design as shown in figure 14(b). Subsequently Line 2 was created between points (A)
and (B) which was used to define the direction of mesh extrusion as shown in figure 14(b). The
material was then applied using the apply material icon, and Steel was selected from the
material library and the view mode was changed to Shading with Material, as shown in figure
15.
2)Mesh generation:- The model was then opened in the Analysis and Simulation workbench and
entering Advanced Meshing Tools toolset, upon which the New Analysis Case dialogue box
appeared and „Static Analysis‟ was selected N.B. unlike in the previous GSA toolset
representative “size” and “sag” are not visible in the display, and therefore no mesh was
present. The Meshing Methods toolbar has sub-toolset Surface Mesher (see figure 16(a))
from which the Advanced Surface Mesher icon was selected, and the Global Parameters box
appeared, in this case the default Mesh size was used.
47
The application of hexahedral elements in Catia V5.R20
In addition to the elements covered above in Section 1 an other element type is available namely
the Hexahedral element, however its capabilities are very limited and do not have all of the
functionalities of the tetrahedral elements used in the above examples. These elements are
obtained by dragging shell elements in a prescribed direction.
1)Problem Statement and model creation:- This modelling exercises examined a steel rectangular
block with a central hole of 2in diameter which was being pulled from both ends as shown in
figure 14(a), which gives the dimensions 6in x 4in x 2in and end loads of 100 psi. In the
Mechanical Design workbench block was modelled in Part Design, as shown in figure 14,
subsequently in the Mechanical Design workbench surfaces were extracted in Wireframe and
Surface Design as shown in figure 14(b). Subsequently Line 2 was created between points (A)
and (B) which was used to define the direction of mesh extrusion as shown in figure 14(b). The
material was then applied using the apply material icon, and Steel was selected from the
material library and the view mode was changed to Shading with Material, as shown in figure
15.
2)Mesh generation:- The model was then opened in the Analysis and Simulation workbench and
entering Advanced Meshing Tools toolset, upon which the New Analysis Case dialogue box
appeared and „Static Analysis‟ was selected N.B. unlike in the previous GSA toolset
representative “size” and “sag” are not visible in the display, and therefore no mesh was
present. The Meshing Methods toolbar has sub-toolset Surface Mesher (see figure 16(a))
from which the Advanced Surface Mesher icon was selected, and the Global Parameters box
appeared, in this case the default Mesh size was used.
47
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
48
Figure 14(a):- Hexahedral Catia V5.R20 analysis problem statement.
48
Figure 14(a):- Hexahedral Catia V5.R20 analysis problem statement.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
In order to see the mesh whilst in this workbench, the Mesh Part icon was selected from the
Mesh / Unmesh toolbar (see figure 16(b)). This created the mesh visualisation on Extraction 5,
with a mesh summary box. This toolbar was then exited and Extrude Mesher with Translation
icon was selected in the Extrude Transformation toolbar was selected to complete the
operation with the parameters selected as shown on figure 16(d). In order to view the generated
mesh the cursor was used to select Nodes and Elements in the tree right-click and select
Mesh Visualization selecting Mesh.1 in the tree and right–click again and select Activate /
Deactivate as shown in figure 16(e).
3)Surface Grouping:-The key to working with the Hexahedral Mesh is the application of the
concept of Surface Group by Neighbourhood and two such groups were defined for in this
exercise by the following method:- The Surface Group by Neighbourhood icon was selected
(figure 17(a)): followed by selection of Extraction 7 as support 1: a small Tolerance value of
0.001 was set in the dialogue box. This method was then repeated selecting Extraction 8 as
support 2 with the same tolerance value.
4)Defining the 3D property:- The 3D Property associated with the Hexahedral Mesh was now
defined selecting the 3D Property icon (see figure 17(a)) from the model manager toolbar, and
selecting Extrusion Mesh with Transition.1 as the support from the tree.
5)Applying Restraints:- Restraints were applied using the Isostactic icon from the Advanced
Restraint toolbar, which is automatically applied without requiring the selection of an entity.
49
The application of hexahedral elements in Catia V5.R20 (continued).
In order to see the mesh whilst in this workbench, the Mesh Part icon was selected from the
Mesh / Unmesh toolbar (see figure 16(b)). This created the mesh visualisation on Extraction 5,
with a mesh summary box. This toolbar was then exited and Extrude Mesher with Translation
icon was selected in the Extrude Transformation toolbar was selected to complete the
operation with the parameters selected as shown on figure 16(d). In order to view the generated
mesh the cursor was used to select Nodes and Elements in the tree right-click and select
Mesh Visualization selecting Mesh.1 in the tree and right–click again and select Activate /
Deactivate as shown in figure 16(e).
3)Surface Grouping:-The key to working with the Hexahedral Mesh is the application of the
concept of Surface Group by Neighbourhood and two such groups were defined for in this
exercise by the following method:- The Surface Group by Neighbourhood icon was selected
(figure 17(a)): followed by selection of Extraction 7 as support 1: a small Tolerance value of
0.001 was set in the dialogue box. This method was then repeated selecting Extraction 8 as
support 2 with the same tolerance value.
4)Defining the 3D property:- The 3D Property associated with the Hexahedral Mesh was now
defined selecting the 3D Property icon (see figure 17(a)) from the model manager toolbar, and
selecting Extrusion Mesh with Transition.1 as the support from the tree.
5)Applying Restraints:- Restraints were applied using the Isostactic icon from the Advanced
Restraint toolbar, which is automatically applied without requiring the selection of an entity.
49
The application of hexahedral elements in Catia V5.R20 (continued).
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
50
Figure 14(a):- Hexahedral Catia V5.R20 analysis extracted surfaces.
Extraction 5
Extraction 7
Extraction 6 Extraction 8
Line 2
(A)
(B)
50
Figure 14(a):- Hexahedral Catia V5.R20 analysis extracted surfaces.
Extraction 5
Extraction 7
Extraction 6 Extraction 8
Line 2
(A)
(B)
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
51
Figure 15:- Hexahedral Catia V5.R20 analysis surface extraction after material applied.
51
Figure 15:- Hexahedral Catia V5.R20 analysis surface extraction after material applied.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
52
Figure 16(a):- Hexahedral Catia V5.R20 analysis mesh application .
Meshing Methods tool
Advanced Surface Mesher Parameter input interface.
52
Figure 16(a):- Hexahedral Catia V5.R20 analysis mesh application .
Meshing Methods tool
Advanced Surface Mesher Parameter input interface.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
53
Figure 16(b):- Hexahedral Catia V5.R20 analysis mesh application .
Mesh Part icon
Mesh Part
Summary
Exit toolbar icon
53
Figure 16(b):- Hexahedral Catia V5.R20 analysis mesh application .
Mesh Part icon
Mesh Part
Summary
Exit toolbar icon
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
54
Figure 16(d):- Hexahedral Catia V5.R20 analysis mesh application .
Mesh Extrusion with Translation icon
Mesh Extrusion axis
Mesh Part
54
Figure 16(d):- Hexahedral Catia V5.R20 analysis mesh application .
Mesh Extrusion with Translation icon
Mesh Extrusion axis
Mesh Part
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
55
Figure 16(e):- Hexahedral Catia V5.R20 analysis complete mesh application .
Surface Mesh 1
Activated.
55
Figure 16(e):- Hexahedral Catia V5.R20 analysis complete mesh application .
Surface Mesh 1
Activated.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
56
Figure 17(a):- Hexahedral Catia V5.R20 analysis constraint and load case application .
Surface Group by
Neighbourhood icon
Surface by
Neighbourhood Group 2
(support)
Surface by
Neighbourhood Group 1
(support)
3D Property icon
Pressure icon
Isostactic icon
3D Property and
Support
56
Figure 17(a):- Hexahedral Catia V5.R20 analysis constraint and load case application .
Surface Group by
Neighbourhood icon
Surface by
Neighbourhood Group 2
(support)
Surface by
Neighbourhood Group 1
(support)
3D Property icon
Pressure icon
Isostactic icon
3D Property and
Support
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
5)Applying the Loading:- For Pressure.1 the Pressure icon was selected (see figure 17(b)), and
for support Surface Group by Neighborhood.1 was selected and a pressure input of -100psi
was applied. For Pressure.2 the Pressure icon was selected (see figure 17(b)), and for support
Surface Group by Neighborhood.2 was selected and a pressure input of -100psi was applied,
the resulting tree is shown in figure 17(b) below.
6)Launching the Solver:- To run the analysis the Compute toolbar is used accessed through the
Compute icon shown in figure 18, for this analysis the default All was used meaning everything
was computed, closing this box prompted the Computation Resources Estimation information
box to be displayed giving:- the CPU run time: memory usage: disc space: and data library, this
the same as with my previous analysis examples using Generative Structural Analysis
workbench meshing.
7)Postprocessing:- The Image postprocessing toolbar was used to view the deformed shape
using the Deformation icon (see figure 18), again this follows the same process as all of the
previous analysis examples. Final postprocessing step was to plot the contours of the von
Mises stresses using the von Mises Stress icon as shown in figure 19, in the Image toolbar.
The analysis contour plots for the von Mises stress are shown in figure 19 below.
This example was specifically to demonstrate the methodology employed to generate a hexahedral
element mesh in Catia V5.R20 FEA toolset, and this may be applied to some FATA project
component analysis, however GSA using solid tetrahedron, and sheet triangular shell elements are
the preferred options.
57
The application of hexahedral elements in Catia V5.R20 (continued).
5)Applying the Loading:- For Pressure.1 the Pressure icon was selected (see figure 17(b)), and
for support Surface Group by Neighborhood.1 was selected and a pressure input of -100psi
was applied. For Pressure.2 the Pressure icon was selected (see figure 17(b)), and for support
Surface Group by Neighborhood.2 was selected and a pressure input of -100psi was applied,
the resulting tree is shown in figure 17(b) below.
6)Launching the Solver:- To run the analysis the Compute toolbar is used accessed through the
Compute icon shown in figure 18, for this analysis the default All was used meaning everything
was computed, closing this box prompted the Computation Resources Estimation information
box to be displayed giving:- the CPU run time: memory usage: disc space: and data library, this
the same as with my previous analysis examples using Generative Structural Analysis
workbench meshing.
7)Postprocessing:- The Image postprocessing toolbar was used to view the deformed shape
using the Deformation icon (see figure 18), again this follows the same process as all of the
previous analysis examples. Final postprocessing step was to plot the contours of the von
Mises stresses using the von Mises Stress icon as shown in figure 19, in the Image toolbar.
The analysis contour plots for the von Mises stress are shown in figure 19 below.
This example was specifically to demonstrate the methodology employed to generate a hexahedral
element mesh in Catia V5.R20 FEA toolset, and this may be applied to some FATA project
component analysis, however GSA using solid tetrahedron, and sheet triangular shell elements are
the preferred options.
57
The application of hexahedral elements in Catia V5.R20 (continued).
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
58
Figure 17(b):- Hexahedral Catia V5.R20 analysis constraint and load case application .
Surface by
Neighbourhood Group 2
(support)
Surface by
Neighbourhood Group 1
(support)
Pressure Loads
Pressure icon
Pressure Load
Supports
58
Figure 17(b):- Hexahedral Catia V5.R20 analysis constraint and load case application .
Surface by
Neighbourhood Group 2
(support)
Surface by
Neighbourhood Group 1
(support)
Pressure Loads
Pressure icon
Pressure Load
Supports
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
59
Figure 18:- Hexahedral Catia V5.R20 analysis displacement analysis.
Deformation icon
Compute icon
59
Figure 18:- Hexahedral Catia V5.R20 analysis displacement analysis.
Deformation icon
Compute icon
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
60
Figure 19:- Hexahedral Catia V5.R20 analysis Von Mises stress analysis.
Von Mises stresses icon
60
Figure 19:- Hexahedral Catia V5.R20 analysis Von Mises stress analysis.
Von Mises stresses icon
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
61
Section 6:- Patran/Nastran FEA methodology and ATDA capability examples.
61
Section 6:- Patran/Nastran FEA methodology and ATDA capability examples.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
General Background:- The idealisation of the real structure into the NASTRAN model should only
be undertaken when the full purpose and scope of the analysis has been determined and what
should be known is the following:-
The size of the grid:
The position of the major load paths:
The interface points to other components or between frames and shell etc.:
The loading and support requirements. (Additional points may have to be created.).
NASTRAN is a displacement method program which solves for displacements at grid points.
Thus the general aim in the idealisation process is to model the CORRECT STIFFNESS. This
normally requires the specification of the correct thickness and area of the items, but in many
instances these are modified due to a compromise in the selection of the geometry.
If a single element represents several items with different area or materials, the calculation of the
idealised size will be linked to the selected idealised material stiffness, and the subsequent
interpretation of the results will have to use the same relationships to obtain the real structural
loads.
NASTRAN element forces and stresses balance the applied loading, however STRESSES are only
accurate for the real structure in the instance where the GEOMETRY is at the centroid of the item
and the element SIZE is correct. Thus in most instances the element FORCES are used in
subsequent interpretation of the real structure. Therefore the element and real structural forces
must be kept in balance when correcting for geometry and size idealisation methods (or changes to
the structure.
62
ATDA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
General Background:- The idealisation of the real structure into the NASTRAN model should only
be undertaken when the full purpose and scope of the analysis has been determined and what
should be known is the following:-
The size of the grid:
The position of the major load paths:
The interface points to other components or between frames and shell etc.:
The loading and support requirements. (Additional points may have to be created.).
NASTRAN is a displacement method program which solves for displacements at grid points.
Thus the general aim in the idealisation process is to model the CORRECT STIFFNESS. This
normally requires the specification of the correct thickness and area of the items, but in many
instances these are modified due to a compromise in the selection of the geometry.
If a single element represents several items with different area or materials, the calculation of the
idealised size will be linked to the selected idealised material stiffness, and the subsequent
interpretation of the results will have to use the same relationships to obtain the real structural
loads.
NASTRAN element forces and stresses balance the applied loading, however STRESSES are only
accurate for the real structure in the instance where the GEOMETRY is at the centroid of the item
and the element SIZE is correct. Thus in most instances the element FORCES are used in
subsequent interpretation of the real structure. Therefore the element and real structural forces
must be kept in balance when correcting for geometry and size idealisation methods (or changes to
the structure.
62
ATDA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
NASTRAN / PATRAN modelling:- The idealisation of all of these real structures into an acceptable
geometrical grid, set of elements, sizes, constraints, materials and there method of processing,
loading, etc. had one objective, i.e. to enable the REAL structural loads, stresses, and deflections to
be calculated. In the above test article cases individual parts were modelled to determine if and
where additional stiffening was required. The idealisations therefore had to represent all of the load
paths and realistic loading distributions set up.
The overall accuracy of the idealisations was linked to the quality of the source geometry created in
PATRAN based on Catia V5.R20 data for the ATDA project enabled direct geometry transfer at the
preliminary design stage. Materials selections for metallic components were Al Li 8090 T3X rolled
plate and Ti alloy Ti6Al4V. Composite skins, ribs, spars, and frames, in Carbon / Epoxy CFC
3501/6 QI and 3501/6 O. The initial design being based on hand calculations, and was
progressively refined based on structural analysis / manufacturing / aero / and weights derived
data. The analysis methodologies applied is shown in subsequent slides.
The ATDA baseline and PRSEUS development aircraft are designed in Catia V5.R20, and
structurally analysed using NASTRAN 2000, the geometry could be directly imported from Catia V5
without remodelling in PATRAN the current plan for metallic structures is to analyse components
first in NASTRAN and compare with the same component analysed in Catia V5.R20 GSA package,
as a first comparison I will use an analysis from my Cranfield University MSc Aircraft Engineering
post graduate degree. Also the GSA within Catia V5.R20 with solid elements will allow through
thickness comparative component modelling studies to be undertaken which are covered in this
presentation.
63
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
NASTRAN / PATRAN modelling:- The idealisation of all of these real structures into an acceptable
geometrical grid, set of elements, sizes, constraints, materials and there method of processing,
loading, etc. had one objective, i.e. to enable the REAL structural loads, stresses, and deflections to
be calculated. In the above test article cases individual parts were modelled to determine if and
where additional stiffening was required. The idealisations therefore had to represent all of the load
paths and realistic loading distributions set up.
The overall accuracy of the idealisations was linked to the quality of the source geometry created in
PATRAN based on Catia V5.R20 data for the ATDA project enabled direct geometry transfer at the
preliminary design stage. Materials selections for metallic components were Al Li 8090 T3X rolled
plate and Ti alloy Ti6Al4V. Composite skins, ribs, spars, and frames, in Carbon / Epoxy CFC
3501/6 QI and 3501/6 O. The initial design being based on hand calculations, and was
progressively refined based on structural analysis / manufacturing / aero / and weights derived
data. The analysis methodologies applied is shown in subsequent slides.
The ATDA baseline and PRSEUS development aircraft are designed in Catia V5.R20, and
structurally analysed using NASTRAN 2000, the geometry could be directly imported from Catia V5
without remodelling in PATRAN the current plan for metallic structures is to analyse components
first in NASTRAN and compare with the same component analysed in Catia V5.R20 GSA package,
as a first comparison I will use an analysis from my Cranfield University MSc Aircraft Engineering
post graduate degree. Also the GSA within Catia V5.R20 with solid elements will allow through
thickness comparative component modelling studies to be undertaken which are covered in this
presentation.
63
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
64
1
1
2
3
4
4
5
MSC Software toolset simulation of the complete aircraft engineering process.
1 WINGS
2 FUSELAGE
3 ENGINES
4 LANDING GEAR
5 AVIONICS
64
1
1
2
3
4
4
5
MSC Software toolset simulation of the complete aircraft engineering process.
1 WINGS
2 FUSELAGE
3 ENGINES
4 LANDING GEAR
5 AVIONICS
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
No Component MSC Software Toolset Simulation capability
1 Wing
Static & Dynamic Aeroelastic & Trim Advanced and Explicit Linear and Non-linear: Fluid
Structural Interactions: Durability & Fatigue: Materials: Manufacturing Process: Thermal:
Multibody Dynamics: modelling, simulation, analysis & optimisation.
2 Fuselage
FEA: Explicit FEA Linear & Non-linear VibroAcoustics: Durability & Fatigue: Materials:
Manufacturing Process: Thermal: modelling, simulation, analysis & optimisation. External
Superelement (ES) capability.
3 Engines
Rotor Dynamics: Thermal: Explicit Non-linear: Acoustics: NVH: Explicit Dynamics & Fluid
Structural Interactions: Durability & Fatigue: Materials: modelling, simulation, analysis &
optimisation.
4 Landing Gear
Multibody Dynamics: Non-linear: Durability & Fatigue: modelling, simulation, analysis &
optimisation.
5 Avionics
Control System Analysis: Structural Dynamics & Impact Analysis: Thermal Durability: Joule
Heating: Coupled Thermal-Structural.
(a) Aircraft Eng Complete Aircraft Analysis.
(b) Aircraft Eng Integrated Multiphysics.
(c) Aircraft Eng Composite Virtual Allowables.
(d) Aircraft Eng Engineering Lifecycle Management.
65
Table 6:- Aircraft Engineering Simulated by MSC Software.
No Component MSC Software Toolset Simulation capability
1 Wing
Static & Dynamic Aeroelastic & Trim Advanced and Explicit Linear and Non-linear: Fluid
Structural Interactions: Durability & Fatigue: Materials: Manufacturing Process: Thermal:
Multibody Dynamics: modelling, simulation, analysis & optimisation.
2 Fuselage
FEA: Explicit FEA Linear & Non-linear VibroAcoustics: Durability & Fatigue: Materials:
Manufacturing Process: Thermal: modelling, simulation, analysis & optimisation. External
Superelement (ES) capability.
3 Engines
Rotor Dynamics: Thermal: Explicit Non-linear: Acoustics: NVH: Explicit Dynamics & Fluid
Structural Interactions: Durability & Fatigue: Materials: modelling, simulation, analysis &
optimisation.
4 Landing Gear
Multibody Dynamics: Non-linear: Durability & Fatigue: modelling, simulation, analysis &
optimisation.
5 Avionics
Control System Analysis: Structural Dynamics & Impact Analysis: Thermal Durability: Joule
Heating: Coupled Thermal-Structural.
(a) Aircraft Eng Complete Aircraft Analysis.
(b) Aircraft Eng Integrated Multiphysics.
(c) Aircraft Eng Composite Virtual Allowables.
(d) Aircraft Eng Engineering Lifecycle Management.
65
Table 6:- Aircraft Engineering Simulated by MSC Software.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Idealisation:- Structural Idealisation involved a number of formal operations to determine the
structural equivalence which are REVERSED to provide correct results on the REAL structure.
GEOMETRY
ELEMENT TYPE
SIZE (Area, Thickness)
BALANCE
Selection of Geometry:- There are two stages in determining the model geometry:- (1) Locating the
source of the geometry: (2) The application of the geometry to the model. Both of these stages
have several options.
1)Source of geometry:- The source can play a vital part in the scope of an analysis, not only in the
accuracy but in the elapsed time to definition. The ATDA project wing analysis, for example,
would have required a greatly extended time scale if the surface geometry had not been
created based on AeroDYNAMIC™ analysis. Where Key Datum models for a structure are not
available a complex analysis should not be undertaken since by implication the results would be
approximate.
i.Defined explicitly e.g. Catia V5 models with all the required geometry. This may be used as
direct input into Nastran as a DFX format file, or for model creation in Patran.
ii.Scale drawings, these may be interpreted in several ways, hand measurement, or using a
digitiser to produce the model for meshing in Patran.
66
All Related
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Idealisation:- Structural Idealisation involved a number of formal operations to determine the
structural equivalence which are REVERSED to provide correct results on the REAL structure.
GEOMETRY
ELEMENT TYPE
SIZE (Area, Thickness)
BALANCE
Selection of Geometry:- There are two stages in determining the model geometry:- (1) Locating the
source of the geometry: (2) The application of the geometry to the model. Both of these stages
have several options.
1)Source of geometry:- The source can play a vital part in the scope of an analysis, not only in the
accuracy but in the elapsed time to definition. The ATDA project wing analysis, for example,
would have required a greatly extended time scale if the surface geometry had not been
created based on AeroDYNAMIC™ analysis. Where Key Datum models for a structure are not
available a complex analysis should not be undertaken since by implication the results would be
approximate.
i.Defined explicitly e.g. Catia V5 models with all the required geometry. This may be used as
direct input into Nastran as a DFX format file, or for model creation in Patran.
ii.Scale drawings, these may be interpreted in several ways, hand measurement, or using a
digitiser to produce the model for meshing in Patran.
66
All Related
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
iii.Key diagram giving the intersection points of major items, ribs / spars etc. The mesh may be
created by importing into Patran from Catia V5.R20 and refined.
iv.Surfaces available in Catia V5 can be used to form up the basic model using intersects as
patch boundaries which are then put into Patran for further refinement, or to generate profile
geometry by projecting a previously defined 2-D mesh of points onto the surface.
v.Solid geometry Catia V5 items, these can be imported directly into Nastran / Patran 2000 as
DFX format models for conversion into Patran models, this geometry source is used for
metal components in the ATDA project.
2.Application of geometry to the FE model:- The geometry may be used directly in some cases,
but in other cases should be modified to represent the best interests of accuracy and
expediency of analysis.
a)Flying surfaces, wings, empennage, winglets, and control surfaces, are relatively thin
structures and thus in order to keep the skin membrane loading and stiffness correct, the mid
skin thickness geometry should be used. There is a procedure within the Optimisation
routines which will carry this out automatically.
b)Fuselage shells, requires a decision to be made on the geometry profile, which should be
consistent, i.e. at the OML (Outer Mould Line), the IML (Inner Mould Line), or the Mid Skin
Point (MSP). Rules for calculating frame flange areas etc. can thus be fixed. Because of the
relative size errors are small whichever approach is applied for ATDA OML is used.
67
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
iii.Key diagram giving the intersection points of major items, ribs / spars etc. The mesh may be
created by importing into Patran from Catia V5.R20 and refined.
iv.Surfaces available in Catia V5 can be used to form up the basic model using intersects as
patch boundaries which are then put into Patran for further refinement, or to generate profile
geometry by projecting a previously defined 2-D mesh of points onto the surface.
v.Solid geometry Catia V5 items, these can be imported directly into Nastran / Patran 2000 as
DFX format models for conversion into Patran models, this geometry source is used for
metal components in the ATDA project.
2.Application of geometry to the FE model:- The geometry may be used directly in some cases,
but in other cases should be modified to represent the best interests of accuracy and
expediency of analysis.
a)Flying surfaces, wings, empennage, winglets, and control surfaces, are relatively thin
structures and thus in order to keep the skin membrane loading and stiffness correct, the mid
skin thickness geometry should be used. There is a procedure within the Optimisation
routines which will carry this out automatically.
b)Fuselage shells, requires a decision to be made on the geometry profile, which should be
consistent, i.e. at the OML (Outer Mould Line), the IML (Inner Mould Line), or the Mid Skin
Point (MSP). Rules for calculating frame flange areas etc. can thus be fixed. Because of the
relative size errors are small whichever approach is applied for ATDA OML is used.
67
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
c)Fuselage frames sloping frames should be converted to local axes so that the in plane
stiffness is not lost due to small kinks. PPS offers an automatic conversion of co-ordinate
systems.
d)Fuselage floors, shear webs, etc. one must ensure that the geometry is planar, and the
local axis should be converted where necessary.
e)Ring frames, should be modelled as shear webs and rods, geometry at skin points and
internal points modelled as bar elements, and use offset vectors to section neutral axis N/A.
f)Longerons / spars, one needs to ensure that these follow correct (straight) lines. Geometry
errors which create kinks both reduce the effective stiffness and impose unreal loads on
support points.
g)Offset joints, one needs to beware of setting up joints involving offsets from the main load
paths unless the offset has been modelled correctly and the local structure is capable of
reacting the kink loads. It is better to put the joint coincident with a skin / frame / longeron
junction. The joint loads can be re-calculated and offsets taken to account in subsequent
detailed stressing work.
h)Hinge lines, the geometry of the hinge points must be set up co-linear in order to avoid
„locking up‟. Us a coordinate system with the hinge line axis nearest to the basic x,y, or z
direction. This is covered in detail in the modelling of hinges section, later in this
presentation.
68
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
c)Fuselage frames sloping frames should be converted to local axes so that the in plane
stiffness is not lost due to small kinks. PPS offers an automatic conversion of co-ordinate
systems.
d)Fuselage floors, shear webs, etc. one must ensure that the geometry is planar, and the
local axis should be converted where necessary.
e)Ring frames, should be modelled as shear webs and rods, geometry at skin points and
internal points modelled as bar elements, and use offset vectors to section neutral axis N/A.
f)Longerons / spars, one needs to ensure that these follow correct (straight) lines. Geometry
errors which create kinks both reduce the effective stiffness and impose unreal loads on
support points.
g)Offset joints, one needs to beware of setting up joints involving offsets from the main load
paths unless the offset has been modelled correctly and the local structure is capable of
reacting the kink loads. It is better to put the joint coincident with a skin / frame / longeron
junction. The joint loads can be re-calculated and offsets taken to account in subsequent
detailed stressing work.
h)Hinge lines, the geometry of the hinge points must be set up co-linear in order to avoid
„locking up‟. Us a coordinate system with the hinge line axis nearest to the basic x,y, or z
direction. This is covered in detail in the modelling of hinges section, later in this
presentation.
68
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
69
Figure 20:- Geometry application to PATRAN/NASTRAN model.
Fig 20(d):- RING FRAMES:-
FRAME
SKIN
CHOICE
(SHEAR PANEL / BOOM
IDEALISATION.)
Fig 20(a):- WINGS: EMENNAGE: WING TIP FENCES:-
Geometry at Mid Skin Depth: – Preserves
Skin Loading and Section Stiffness.
Fig 20(c):- FUSELAGE SHELLS:- SKIN
CHOICE
FRAME
Fig 20(b):- OFFSET JOINTS:-
Use Grid at Nearest Skin Point.
Prevent Longeron or Skin Kink
Load as Detail Stress will cover this.
TRANSPORT TYPE JOINTS.
69
Figure 20:- Geometry application to PATRAN/NASTRAN model.
Fig 20(d):- RING FRAMES:-
FRAME
SKIN
CHOICE
(SHEAR PANEL / BOOM
IDEALISATION.)
Fig 20(a):- WINGS: EMENNAGE: WING TIP FENCES:-
Geometry at Mid Skin Depth: – Preserves
Skin Loading and Section Stiffness.
Fig 20(c):- FUSELAGE SHELLS:- SKIN
CHOICE
FRAME
Fig 20(b):- OFFSET JOINTS:-
Use Grid at Nearest Skin Point.
Prevent Longeron or Skin Kink
Load as Detail Stress will cover this.
TRANSPORT TYPE JOINTS.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
70
Figure 21:- Geometry application to PATRAN/NASTRAN model.
Fig 21(a):- RING FRAMES:-
(BAR IDEALISATION.)
FRAME SKIN
OFFSET VECTOR FROM SKIN POINT.
Neutral Axis.
SLOPING FRAME
FRAME
FRAME
Fig 21(b):- SLOPING FRAMES FLOORS SHEAR WEBS:-
SLOPING FLOOR
z
Cld =
z = CONSTANT
x
Cld =
KINKS can lead to MAJOR loss of in-plane
stiffness, therefore avoid kinks in geometry –
put into LOCAL axes making one co-ordinate
constant.
70
Figure 21:- Geometry application to PATRAN/NASTRAN model.
Fig 21(a):- RING FRAMES:-
(BAR IDEALISATION.)
FRAME SKIN
OFFSET VECTOR FROM SKIN POINT.
Neutral Axis.
SLOPING FRAME
FRAME
FRAME
Fig 21(b):- SLOPING FRAMES FLOORS SHEAR WEBS:-
SLOPING FLOOR
z
Cld =
z = CONSTANT
x
Cld =
KINKS can lead to MAJOR loss of in-plane
stiffness, therefore avoid kinks in geometry –
put into LOCAL axes making one co-ordinate
constant.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
71
Figure 22:- Geometry application to PATRAN/NASTRAN model.
LONGERONS, SPARS, ETC : -
LONGERON
FRAME
FRAME
FRAME
FRAME
FRAME
ERROR.
UNREAL Load due to Geometry Error,
PLUS Loss of stiffness in the longeron.
CL
FRAME / RIB Loads which are due
to LONGERON / SPAR curvature etc.
71
Figure 22:- Geometry application to PATRAN/NASTRAN model.
LONGERONS, SPARS, ETC : -
LONGERON
FRAME
FRAME
FRAME
FRAME
FRAME
ERROR.
UNREAL Load due to Geometry Error,
PLUS Loss of stiffness in the longeron.
CL
FRAME / RIB Loads which are due
to LONGERON / SPAR curvature etc.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
72
Figure 23:- Direct Area Relationship Idealisation in NASTRAN.
ROOF SKIN
SIDE SKIN
LONGERON
Fig 23(a):- REAL WORLD DIRECT AREA RELATIONSHIP:-
CSHEAR
CSHEAR
CROD
ROD AREA = Area of Longeron + Effective areas of Skins.
If materials are different scale areas by Ratio of:- Actual E Before adding.
CROD E
Fig 32(b):- FEA IDEALISED DIRECT AREA RELATIONSHIP:-
72
Figure 23:- Direct Area Relationship Idealisation in NASTRAN.
ROOF SKIN
SIDE SKIN
LONGERON
Fig 23(a):- REAL WORLD DIRECT AREA RELATIONSHIP:-
CSHEAR
CSHEAR
CROD
ROD AREA = Area of Longeron + Effective areas of Skins.
If materials are different scale areas by Ratio of:- Actual E Before adding.
CROD E
Fig 32(b):- FEA IDEALISED DIRECT AREA RELATIONSHIP:-
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
73
Figure 24:- Direct Area Relationship NASTRAN model output.
E
Fig24(a):- FORCES.
End Load in CROD and Edge Shear Flows.
Other
Connections
Other
Connections
Fig24(b):- GP FORCES.
Since GP FORCES are in Global System they must be
resolved into CROD axis.
73
Figure 24:- Direct Area Relationship NASTRAN model output.
E
Fig24(a):- FORCES.
End Load in CROD and Edge Shear Flows.
Other
Connections
Other
Connections
Fig24(b):- GP FORCES.
Since GP FORCES are in Global System they must be
resolved into CROD axis.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
LOAD IN CROD:-
End Load Known at 3 points:-
Load in Longeron = P . AL
ATOT
End Load in Panels = P . AP
ATOT
If Materials are Different :-
Stress is given by σ = P.AP . EP
ATOT ECROD
74
ɭ
E
P
CROD
P = End Loads at positions
along the rod
E + (q1+q2) l/2
E - (q1+q2) l/2
Constant Stress in Items:- σ = P
ATOT
Direct Area Relationship NASTRAN model output loads in CROD.
LOAD IN CROD:-
End Load Known at 3 points:-
Load in Longeron = P . AL
ATOT
End Load in Panels = P . AP
ATOT
If Materials are Different :-
Stress is given by σ = P.AP . EP
ATOT ECROD
74
ɭ
E
P
CROD
P = End Loads at positions
along the rod
E + (q1+q2) l/2
E - (q1+q2) l/2
Constant Stress in Items:- σ = P
ATOT
Direct Area Relationship NASTRAN model output loads in CROD.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
PANEL LOADS:- Shear loads are obtained from force output on edges. End loads are obtained
from effective area as above. Stresses obtained from End Loads and Shear Flows and ratio of
Idealised to Actual thickness i.e.
σ = q . t I
ATOT t ACT
FASTENER LOADS:- Rivet or bolt shear loads = q ɭ
N
or
q x Pitch
Pitch
Where:-
q = Edge Shear:
ɭ = Panel length:
N = Number of Fasteners:
Pitch = Fastener Pitch.
75
Direct Area Relationship NASTRAN output Panel Loads and Fastener Loads .
PANEL LOADS:- Shear loads are obtained from force output on edges. End loads are obtained
from effective area as above. Stresses obtained from End Loads and Shear Flows and ratio of
Idealised to Actual thickness i.e.
σ = q . t I
ATOT t ACT
FASTENER LOADS:- Rivet or bolt shear loads = q ɭ
N
or
q x Pitch
Pitch
Where:-
q = Edge Shear:
ɭ = Panel length:
N = Number of Fasteners:
Pitch = Fastener Pitch.
75
Direct Area Relationship NASTRAN output Panel Loads and Fastener Loads .
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Apart from the later comments regarding the use of coarse and fine mesh fuselage panels, the
following general rules apply to any situation where a choice of mesh size is required.
A coarse mesh idealisation, where a structural bay / panel is modelled by a single element, can
only recover element forces at the centre of the element. Corner or end forces have to be
calculated using the G.P.F.B. data, which is a time consuming process. The force variation is
linear in each element and thus this dictates the accuracy expected from the model. If element
forces alone are used, there is a danger of over / under designing an area (see figure 25(a)).
A fine mesh idealisation will split a bay / panel into several elements. Element forces will now
indicate the panel loading variation over its length, and this should be sufficient for design. Also
shear lag effects will be improved (see figure 25(b)).
The different basic element types are shown in figure 26, and their application to a real airframe
idealisation is shown in figure 27 where the following elements are use in the idealisation of an
Airbus A340-600 global airframe model:-
Fuselage Stringers = Rod elements:
Fuselage Skin = QUAD elements:
Fuselage Frames = Beam elements.
These element types will be discussed in detail in the following descriptive methodology slides.
76
FATA Project FEA Structural Design Analysis Coarse mesh v Fine Mesh.
Apart from the later comments regarding the use of coarse and fine mesh fuselage panels, the
following general rules apply to any situation where a choice of mesh size is required.
A coarse mesh idealisation, where a structural bay / panel is modelled by a single element, can
only recover element forces at the centre of the element. Corner or end forces have to be
calculated using the G.P.F.B. data, which is a time consuming process. The force variation is
linear in each element and thus this dictates the accuracy expected from the model. If element
forces alone are used, there is a danger of over / under designing an area (see figure 25(a)).
A fine mesh idealisation will split a bay / panel into several elements. Element forces will now
indicate the panel loading variation over its length, and this should be sufficient for design. Also
shear lag effects will be improved (see figure 25(b)).
The different basic element types are shown in figure 26, and their application to a real airframe
idealisation is shown in figure 27 where the following elements are use in the idealisation of an
Airbus A340-600 global airframe model:-
Fuselage Stringers = Rod elements:
Fuselage Skin = QUAD elements:
Fuselage Frames = Beam elements.
These element types will be discussed in detail in the following descriptive methodology slides.
76
FATA Project FEA Structural Design Analysis Coarse mesh v Fine Mesh.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
77
Figure 25(a):- Coarse Mesh v Fine Mesh in PATRAN/NASTRAN models.
Element Forces given
at Centre of Elements.
Real World Assembly.
Coarse Mesh Idealisation of the Assembly:-
Single Element Per Real Panel:
Load variation is Linear in Element:
Use G.P.F.B. to determine edge conditions.
Bay 1
Bay 2
Bay 3
1 2 3
Bay number.
Load in Flange or Skin.
These Areas Over - designed if element forces are used.
These Areas Under - designed
if element forces are used.
77
Figure 25(a):- Coarse Mesh v Fine Mesh in PATRAN/NASTRAN models.
Element Forces given
at Centre of Elements.
Real World Assembly.
Coarse Mesh Idealisation of the Assembly:-
Single Element Per Real Panel:
Load variation is Linear in Element:
Use G.P.F.B. to determine edge conditions.
Bay 1
Bay 2
Bay 3
1 2 3
Bay number.
Load in Flange or Skin.
These Areas Over - designed if element forces are used.
These Areas Under - designed
if element forces are used.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
78
Figure 25(b)(c):- Coarse Mesh v Fine Mesh in PATRAN/NASTRAN models.
Undercarriage bay area fine
mesh fig 25(b)i.
COARSE MESH OF F/A-24
WING DESIGN OPTION (D).
FINE MESH OF F/A-24 OPTION (D)
UNERCARRIAGE BAY TORSION
BOX UPPER SKIN REMOVED.
Figure 25(b):- Application of coarse and fine meshing to wing box design study Cranfield University ©.
Fine Mesh Idealisation of the Assembly:-
Several Element Per Real Panel:
Element force will usually be sufficient to design panel:
Shear lag effects improved.
1 2 3
Bay number.
Load in Flange or Skin.
Figure 25(c):- Plot of Loading in Flange or Skin for fine mesh
of the bay assembly in figure 25(a) previous slide.
78
Figure 25(b)(c):- Coarse Mesh v Fine Mesh in PATRAN/NASTRAN models.
Undercarriage bay area fine
mesh fig 25(b)i.
COARSE MESH OF F/A-24
WING DESIGN OPTION (D).
FINE MESH OF F/A-24 OPTION (D)
UNERCARRIAGE BAY TORSION
BOX UPPER SKIN REMOVED.
Figure 25(b):- Application of coarse and fine meshing to wing box design study Cranfield University ©.
Fine Mesh Idealisation of the Assembly:-
Several Element Per Real Panel:
Element force will usually be sufficient to design panel:
Shear lag effects improved.
1 2 3
Bay number.
Load in Flange or Skin.
Figure 25(c):- Plot of Loading in Flange or Skin for fine mesh
of the bay assembly in figure 25(a) previous slide.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
79
Figure 26:- Basic Element Types in PATRAN/NASTRAN models.
Simple Rod or Truss
Element:- 2 D.o.F
Bar Element:-
6 D.o.F
Shear Element:-
2 D.o.F
Membrane and Bending
Element:- 2 D.o.F
Solid Element:-
3 D.o.F only
79
Figure 26:- Basic Element Types in PATRAN/NASTRAN models.
Simple Rod or Truss
Element:- 2 D.o.F
Bar Element:-
6 D.o.F
Shear Element:-
2 D.o.F
Membrane and Bending
Element:- 2 D.o.F
Solid Element:-
3 D.o.F only
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
80
Figure 27(a):- Full FE Model Meshing and element selection for A340-600.
Z
X
Y
80
Figure 27(a):- Full FE Model Meshing and element selection for A340-600.
Z
X
Y
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
81
Figure 27(b):- Combined load cases applied to an Airbus A340-600 Model.
Z
X
Y
81
Figure 27(b):- Combined load cases applied to an Airbus A340-600 Model.
Z
X
Y
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
NASTRAN Methodology for Wings / Empennage – Ribs, Spars, Skins. Wings, Horizontal (HT) and
Vertical Tails (VT), (empennage) are thin structures dominated by bending loading for the skin
design and shear loading for the internal spar / rib construction as is the case with the ATDA
Project aircraft, VT, HT, and wing major structural components. Therefore the idealisation of these
components aimed at providing the correct stiffness for these components. The geometry was set
up at the mid depth of the skins, therefore the loading and stiffness would be correct. The spar / rib
idealisation aimed at obtaining the correct moment of inertia, in a similar way to that recommended
in the TSM for heavy ring frames (to be employed on my ATDA Airframe Research Project). For the
current FATA Project wing and empennage studies, the skins were idealised as QUAD4 elements,
the spar / rib webs as SHEARs and the flanges as RODs. As the CSHEAR element only has ROD
elements along the skin edges, a degree of stiffness has to be given in the through thickness
direction, thus the appropriate F factor had to be applied on the PSHEAR card. Although
alternatively the use of RRODs, linking only the through thickness Degrees Of Freedom between
top and bottom skin grid points can be as effective. If neither of these methods is employed
excessive displacements are generated since the webs will be near singular. Figure 28 gives a
representation of the REAL and IDEALISATION geometry to represent section stiffness, and the
derivation of the flange stresses. The geometry is set up at the skin mid depth – QUAD4 Loads are
accurate providing the component sizing is correct.
Idealised ROD areas are calculated from:-
A1 y1² + A2 y2² = I SPAR / RIB MOMENT OF INERTIA.
A1 y1 = A2 y2 MAINTAINING N.A. POSITION.
Hence A1 and A2 .
82
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
NASTRAN Methodology for Wings / Empennage – Ribs, Spars, Skins. Wings, Horizontal (HT) and
Vertical Tails (VT), (empennage) are thin structures dominated by bending loading for the skin
design and shear loading for the internal spar / rib construction as is the case with the ATDA
Project aircraft, VT, HT, and wing major structural components. Therefore the idealisation of these
components aimed at providing the correct stiffness for these components. The geometry was set
up at the mid depth of the skins, therefore the loading and stiffness would be correct. The spar / rib
idealisation aimed at obtaining the correct moment of inertia, in a similar way to that recommended
in the TSM for heavy ring frames (to be employed on my ATDA Airframe Research Project). For the
current FATA Project wing and empennage studies, the skins were idealised as QUAD4 elements,
the spar / rib webs as SHEARs and the flanges as RODs. As the CSHEAR element only has ROD
elements along the skin edges, a degree of stiffness has to be given in the through thickness
direction, thus the appropriate F factor had to be applied on the PSHEAR card. Although
alternatively the use of RRODs, linking only the through thickness Degrees Of Freedom between
top and bottom skin grid points can be as effective. If neither of these methods is employed
excessive displacements are generated since the webs will be near singular. Figure 28 gives a
representation of the REAL and IDEALISATION geometry to represent section stiffness, and the
derivation of the flange stresses. The geometry is set up at the skin mid depth – QUAD4 Loads are
accurate providing the component sizing is correct.
Idealised ROD areas are calculated from:-
A1 y1² + A2 y2² = I SPAR / RIB MOMENT OF INERTIA.
A1 y1 = A2 y2 MAINTAINING N.A. POSITION.
Hence A1 and A2 .
82
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
83
Figure 28:- Wing / Empennage FEA PATRAN / NASTRAN Idealisation mythology.
Flanges
Skin
Skin
Web
Web
Flanges
y
N A
ẏ
tw
y1
y2
GRID POINTS
REAL WORLD ASSEMBLY
QUAD4
QUAD4
SHEAR
SHEAR
ROD
IDEALISED ASSEMBLY
QUAD4
QUAD4
QUAD4
QUAD4
CSHEAR
t
A1
A2
CROD
CROD
t is Effective
shear
thickness
C ROD Areas are calculated
to give correct Moment of
inertia of the spar
83
Figure 28:- Wing / Empennage FEA PATRAN / NASTRAN Idealisation mythology.
Flanges
Skin
Skin
Web
Web
Flanges
y
N A
ẏ
tw
y1
y2
GRID POINTS
REAL WORLD ASSEMBLY
QUAD4
QUAD4
SHEAR
SHEAR
ROD
IDEALISED ASSEMBLY
QUAD4
QUAD4
QUAD4
QUAD4
CSHEAR
t
A1
A2
CROD
CROD
t is Effective
shear
thickness
C ROD Areas are calculated
to give correct Moment of
inertia of the spar
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
STRESS in the UPPER FLANGE is given by σu = σA1 / y1. (y-ẏ)
and in the LOWER FLANGE by σL= σA2. (y-ẏ)
Note the use of PSHEAR F1 or F2 Factor to give through thickness Spar / Rib End load stiffness.
NASTRAN Methodology for Trailing Edge Idealisation. The Idealisation of trailing edges has in the
past been of minor concern since for purely stressing purposes local pressure design has been
critical. However with the advent of optimisation methods using aeroelastic data the trailing edge
displacements are of interest, and for flutter the T/E stiffness and mass can be critical.
In reality most trailing edges do not meet at a point and it is vital to represent the real finite depth.
The usual method is to include a slender QUAD4 closing element with a thickness representing the
closing material as shown in figure 29(a). The skin elements are thus separated at the T/E and now
represent the correct stiffness. For example on the Experimental Aircraft Program the wing T/E
thickness varied from 6mm at the tip to over 25mm at the root, and on the Tornado the fin T/E was
made blunt to gain stiffness.
In the case where a trailing edge is manufactured to meet at a point, for example in a Super
Plastically Formed / Diffusion Bonded (SPF/DB) Ti alloy structure, the most accurate Idealisation
would be with a single T/E point. In this case the T/E stiffness will be greater since it acts as a
triangular framework, as shown in figure 29(b).
If a T/E is unsupported by honeycomb or foam, the shear path is through the skins as transverse
shear (if bending elements are used for the skins) together with any finite depth T/E element
spanwise path. If a single point is used the majority of the shear will be carried as differential loads
in the skins.
84
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
STRESS in the UPPER FLANGE is given by σu = σA1 / y1. (y-ẏ)
and in the LOWER FLANGE by σL= σA2. (y-ẏ)
Note the use of PSHEAR F1 or F2 Factor to give through thickness Spar / Rib End load stiffness.
NASTRAN Methodology for Trailing Edge Idealisation. The Idealisation of trailing edges has in the
past been of minor concern since for purely stressing purposes local pressure design has been
critical. However with the advent of optimisation methods using aeroelastic data the trailing edge
displacements are of interest, and for flutter the T/E stiffness and mass can be critical.
In reality most trailing edges do not meet at a point and it is vital to represent the real finite depth.
The usual method is to include a slender QUAD4 closing element with a thickness representing the
closing material as shown in figure 29(a). The skin elements are thus separated at the T/E and now
represent the correct stiffness. For example on the Experimental Aircraft Program the wing T/E
thickness varied from 6mm at the tip to over 25mm at the root, and on the Tornado the fin T/E was
made blunt to gain stiffness.
In the case where a trailing edge is manufactured to meet at a point, for example in a Super
Plastically Formed / Diffusion Bonded (SPF/DB) Ti alloy structure, the most accurate Idealisation
would be with a single T/E point. In this case the T/E stiffness will be greater since it acts as a
triangular framework, as shown in figure 29(b).
If a T/E is unsupported by honeycomb or foam, the shear path is through the skins as transverse
shear (if bending elements are used for the skins) together with any finite depth T/E element
spanwise path. If a single point is used the majority of the shear will be carried as differential loads
in the skins.
84
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
85
Figure 29(a)/(b):- Trailing Edge FEA PATRAN / NASTRAN Idealisation mythology.
Skin
Skin
t1
t2
t3
dAK
Figure 29(a):- REAL WORLD OPEN TE STRUCTURE IDEALISATION OF OPEN TE STRUCTURE
d
QUAD4 T= t3
Figure 29(b):- REAL WORLD CLOSED TE STRUCTURE
t2
t1
IDEALISATION OF CLOSED TE STRUCTURE
85
Figure 29(a)/(b):- Trailing Edge FEA PATRAN / NASTRAN Idealisation mythology.
Skin
Skin
t1
t2
t3
dAK
Figure 29(a):- REAL WORLD OPEN TE STRUCTURE IDEALISATION OF OPEN TE STRUCTURE
d
QUAD4 T= t3
Figure 29(b):- REAL WORLD CLOSED TE STRUCTURE
t2
t1
IDEALISATION OF CLOSED TE STRUCTURE
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
86
The above is a description of the recommended modeling techniques applied in the FATA Project
Preliminary FEA wing structural design work as used to support wing component structural
optimization studies. The following are recommended modeling techniques which can be applied to
separately to the following aircraft structural components. The element sizing is linked to the
selection of the geometry and the types of element chosen, thus in the examples that follow the
sizing method is shown explicitly. Interpretation of the results is linked to the method of idealization
and therefore guidelines from experience are included where convenient.
NASTRAN Methodology for Fuselage Frames:- These can be in various forms:- Ring Frames (light
or heavy): Machined (part /full) frames: or Pressure Bulkheads.
a)Light Ring Frames:- Two methods for idealization can be applied which are described below.
1)Shear web and boom method:- where the frame is represented as a shear web and boom
using CSHEAR and CROD elements and sized to combine the effective web and flange areas.
The geometry should be set at the average depth between the flanges and flange efficiency
factors should be used in determining the CROD areas. Stressing method:- use the bending
moment calculated from the boom end loads and shear values to carry out detailed stressing
round the frame. It is assumed that the fuselage skin efficiency area is modelled as a separate
CROD and thus the frame loading can be readily found. If the outer CROD includes the
effective skin, some load shearing is necessary before the outer flange load can be
determined and thus the frame bending moment (see figure 30).
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
86
The above is a description of the recommended modeling techniques applied in the FATA Project
Preliminary FEA wing structural design work as used to support wing component structural
optimization studies. The following are recommended modeling techniques which can be applied to
separately to the following aircraft structural components. The element sizing is linked to the
selection of the geometry and the types of element chosen, thus in the examples that follow the
sizing method is shown explicitly. Interpretation of the results is linked to the method of idealization
and therefore guidelines from experience are included where convenient.
NASTRAN Methodology for Fuselage Frames:- These can be in various forms:- Ring Frames (light
or heavy): Machined (part /full) frames: or Pressure Bulkheads.
a)Light Ring Frames:- Two methods for idealization can be applied which are described below.
1)Shear web and boom method:- where the frame is represented as a shear web and boom
using CSHEAR and CROD elements and sized to combine the effective web and flange areas.
The geometry should be set at the average depth between the flanges and flange efficiency
factors should be used in determining the CROD areas. Stressing method:- use the bending
moment calculated from the boom end loads and shear values to carry out detailed stressing
round the frame. It is assumed that the fuselage skin efficiency area is modelled as a separate
CROD and thus the frame loading can be readily found. If the outer CROD includes the
effective skin, some load shearing is necessary before the outer flange load can be
determined and thus the frame bending moment (see figure 30).
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
2.Bar representation method:- CBAR elements are specified using the outer geometry and offset
vectors to the N/A (neutral / axis) of the section. The frame bending moment and shear values
are direct output. The analyst must make sure that the bars are co-planer (e.g. X = const) and
if not supply all properties A, I1, I2, J etc. Remember the default for shear flexibility is ZERO
(infinitely stiff). Note that additional D.O.F. are required for this method. Stressing method:-
Some interpolation is required since the skin shears are applied at the grid points and thus
steps appear in the BM (Bending Moment) at the grid points so use the average. The
moments at the centre of the elements will be correct (see figure 31).
b)Heavy Ring Frames:- The idealisation is calculated to maintain the correct moment of inertia
and N/A position, the geometry being dictated by the fuselage skin and internal skin if present.
The stresses in the real structure can then be calculated using E.B.T. and the analysis stress
levels (see figure 32).
c)Machined Frames:- The idealisation should follow the stiffener pattern as close as possible,
using CRODS for the stiffeners and CSHEAR‟s for thin (non end load effective) panels and
CQUAD4‟s for thick end load carrying panels. Provided the areas and thicknesses are accurate
no corrections it the real structure are necessary.
CSHEAR‟s will give the panel edge shears directly whilst QUAD4 elements quote the centre of
the panel values (in element axes). Using the GPFB for a QUAD 4 panel will enable the edge
shears and loads to be calculated – remember to resolve the loads into the axis of the edge
concerned - GPFB‟s are produced in GLOBAL axes (see figure 33).
87
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
2.Bar representation method:- CBAR elements are specified using the outer geometry and offset
vectors to the N/A (neutral / axis) of the section. The frame bending moment and shear values
are direct output. The analyst must make sure that the bars are co-planer (e.g. X = const) and
if not supply all properties A, I1, I2, J etc. Remember the default for shear flexibility is ZERO
(infinitely stiff). Note that additional D.O.F. are required for this method. Stressing method:-
Some interpolation is required since the skin shears are applied at the grid points and thus
steps appear in the BM (Bending Moment) at the grid points so use the average. The
moments at the centre of the elements will be correct (see figure 31).
b)Heavy Ring Frames:- The idealisation is calculated to maintain the correct moment of inertia
and N/A position, the geometry being dictated by the fuselage skin and internal skin if present.
The stresses in the real structure can then be calculated using E.B.T. and the analysis stress
levels (see figure 32).
c)Machined Frames:- The idealisation should follow the stiffener pattern as close as possible,
using CRODS for the stiffeners and CSHEAR‟s for thin (non end load effective) panels and
CQUAD4‟s for thick end load carrying panels. Provided the areas and thicknesses are accurate
no corrections it the real structure are necessary.
CSHEAR‟s will give the panel edge shears directly whilst QUAD4 elements quote the centre of
the panel values (in element axes). Using the GPFB for a QUAD 4 panel will enable the edge
shears and loads to be calculated – remember to resolve the loads into the axis of the edge
concerned - GPFB‟s are produced in GLOBAL axes (see figure 33).
87
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
88
Figure 30(a)/(b):- Ring Frames Light Section Sear and Boom Idealisation mythology.
Skin
Frame
Figure 30(a):- REAL WORLD LIGHT RING FRAME Figure 30(b):- IDEALISED LIGHT RING FRAME
Geometry set at average height „h‟.
CROD areas need no correction.
ACROD = Flange Area x Efficiency + Web Area / 6
Stressing Method:-
Use analysis geometry and CROD forces to produce bending moment distribution around
frame:
CSHEAR loads for SHEARS:
Skin Effective area is a separate CROD element if not load in outer flange element must be
shared to determine frame loading.
88
Figure 30(a)/(b):- Ring Frames Light Section Sear and Boom Idealisation mythology.
Skin
Frame
Figure 30(a):- REAL WORLD LIGHT RING FRAME Figure 30(b):- IDEALISED LIGHT RING FRAME
Geometry set at average height „h‟.
CROD areas need no correction.
ACROD = Flange Area x Efficiency + Web Area / 6
Stressing Method:-
Use analysis geometry and CROD forces to produce bending moment distribution around
frame:
CSHEAR loads for SHEARS:
Skin Effective area is a separate CROD element if not load in outer flange element must be
shared to determine frame loading.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
89
Figure 31(a)/(b):- Ring Frames Light Section Bar Element Idealisation mythology.
Skin
Frame
Figure 31(a):- REAL WORLD LIGHT RING FRAME Figure 31(b):- BAR IDEALISATION LIGHT RING FRAME
Requires:- Calculation of the Offset
Vectors: Section Properties:
and Additional Rotational
D.O.F in the model.
Note:- Use CBARɸ Card to request
outputs at points along the Bar.
Stressing Method:- NASTRAN output is:- End load; Moment; and Shear around the frame. The
Moment at element ends is an input from skin shears and thus is stepped so use average value.
M1
M2
M3
Moments Due To Offsets. Bending Moments.
M1
M2
M3
Interpolated.
Mid Points.
89
Figure 31(a)/(b):- Ring Frames Light Section Bar Element Idealisation mythology.
Skin
Frame
Figure 31(a):- REAL WORLD LIGHT RING FRAME Figure 31(b):- BAR IDEALISATION LIGHT RING FRAME
Requires:- Calculation of the Offset
Vectors: Section Properties:
and Additional Rotational
D.O.F in the model.
Note:- Use CBARɸ Card to request
outputs at points along the Bar.
Stressing Method:- NASTRAN output is:- End load; Moment; and Shear around the frame. The
Moment at element ends is an input from skin shears and thus is stepped so use average value.
M1
M2
M3
Moments Due To Offsets. Bending Moments.
M1
M2
M3
Interpolated.
Mid Points.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
d)Pressure Bulkhead Frames:- For an initial simple idealisation of a fuselage model the
pressure bulkheads are usually modelled for in plane loading only, the pressure loading effects
being taken into account in the detailed stressing. Therefore all stiffeners have the correct area
but are not subject to bending loading. This enables the model to be kept simple and does not
involve any additional rotational D.O.F.
However, for more detailed work the bending effects should be modelled and pressure loading
supplied as part of the loading case definitions. The stiffeners should then be modelled using
CBAR‟s see figure 34.
The CBAR‟s should be used with offsets to their correct N/A position - in which case the
bending moments will be correct at the centre of the elements and need averaging at the ends.
Idealisations without offsets would require re-calculation of the bar loads to take into account
the offset shear loads.
Notes on the use of CSHEAR elements.
The CSHEAR element normally carries shear loads only and thus should be surrounded by ROD
elements to carry end loads in the equivalent areas. If this extensional stiffness is not present the
panel will be singular and would probably lead to a FATAL error or excessive displacements.
A facility to give the shear element extensional stiffness in either direction exists using the F1 and
or F2 factors. (see slide 87)
90
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
d)Pressure Bulkhead Frames:- For an initial simple idealisation of a fuselage model the
pressure bulkheads are usually modelled for in plane loading only, the pressure loading effects
being taken into account in the detailed stressing. Therefore all stiffeners have the correct area
but are not subject to bending loading. This enables the model to be kept simple and does not
involve any additional rotational D.O.F.
However, for more detailed work the bending effects should be modelled and pressure loading
supplied as part of the loading case definitions. The stiffeners should then be modelled using
CBAR‟s see figure 34.
The CBAR‟s should be used with offsets to their correct N/A position - in which case the
bending moments will be correct at the centre of the elements and need averaging at the ends.
Idealisations without offsets would require re-calculation of the bar loads to take into account
the offset shear loads.
Notes on the use of CSHEAR elements.
The CSHEAR element normally carries shear loads only and thus should be surrounded by ROD
elements to carry end loads in the equivalent areas. If this extensional stiffness is not present the
panel will be singular and would probably lead to a FATAL error or excessive displacements.
A facility to give the shear element extensional stiffness in either direction exists using the F1 and
or F2 factors. (see slide 87)
90
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
91
Figure 32(a)/(b):- Heavy Ring Frame Idealisation mythology.
Outer Skin
Inner Skin
Frame
Figure 32(a):- REAL WORLD HEAVY RING FRAME
N/A
A1
A2
CROD
CROD
y2
y1
CSHEAR t = Equivalent for shear
stiffness.
Figure 32(b):- IDEALISATION HEAVY RING FRAME
91
Figure 32(a)/(b):- Heavy Ring Frame Idealisation mythology.
Outer Skin
Inner Skin
Frame
Figure 32(a):- REAL WORLD HEAVY RING FRAME
N/A
A1
A2
CROD
CROD
y2
y1
CSHEAR t = Equivalent for shear
stiffness.
Figure 32(b):- IDEALISATION HEAVY RING FRAME
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
92
Figure 32(c):- Heavy Ring Frame Stressing mythology.
Calculation of CROD areas A1 and A2:-
1)Find the FLANGE EFFICIENCY FACTORS from ESDU 71004 data sheets.
2)Calculate SECTION I and position of N/A, and reduce Flange Areas by FLANGE EFFICENCY
FACTORS, and Flange Widths for calculation of local I‟s:-
A1y1² + A2y2² = I
Hence A1 and A2
A1y1 = A2y2
Stressing Method:-
Using Nastran stresses in CROD‟s σ1 and σ2 calculate stress using Linear Interpolation or E.B.T.
σ2
N/A N/A
σ1
≡
N/A N/A
+
N/A N/A
MAX UPPER
MAX LOWER
92
Figure 32(c):- Heavy Ring Frame Stressing mythology.
Calculation of CROD areas A1 and A2:-
1)Find the FLANGE EFFICIENCY FACTORS from ESDU 71004 data sheets.
2)Calculate SECTION I and position of N/A, and reduce Flange Areas by FLANGE EFFICENCY
FACTORS, and Flange Widths for calculation of local I‟s:-
A1y1² + A2y2² = I
Hence A1 and A2
A1y1 = A2y2
Stressing Method:-
Using Nastran stresses in CROD‟s σ1 and σ2 calculate stress using Linear Interpolation or E.B.T.
σ2
N/A N/A
σ1
≡
N/A N/A
+
N/A N/A
MAX UPPER
MAX LOWER
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
93
Figure 33(a):- Machined Frame Patran / Nastran Idealisation mythology.
CROD
CSHEAR (Thin)
CQUAD4 (Thick)
GRIDS at Internal Stiffener Interfaces
GRIDS at Skin Line
Provided Rod Areas and Panel Thicknesses are correct no corrections are necessary.
CSHEAR Forces in Panels:-
CQUAD4 Forces in Panels:-
1 2
3 4
Edge Shears Given
1 2
3 4
ﺤ
ﮮ
Fxy
93
Figure 33(a):- Machined Frame Patran / Nastran Idealisation mythology.
CROD
CSHEAR (Thin)
CQUAD4 (Thick)
GRIDS at Internal Stiffener Interfaces
GRIDS at Skin Line
Provided Rod Areas and Panel Thicknesses are correct no corrections are necessary.
CSHEAR Forces in Panels:-
CQUAD4 Forces in Panels:-
1 2
3 4
Edge Shears Given
1 2
3 4
ﺤ
ﮮ
Fxy
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
94
Figure 33(b):- Machined Frame Patran / Nastran analysis mythology.
Use G.P. Force Output resolved into the Panel Edge Directions to obtain Edge Shears and End
Loads for Rectangular Panels.
F x a/2
ɋ b/2
F x a/2
ɋ b/2
F x a/2 F x a/2
ɋ b/2 ɋ b/2
X- Direction Loads.
Average Shear stress σx y
Shear Flow ɋ = σx y / t
b
a
F y
F x
ɋⁿ
94
Figure 33(b):- Machined Frame Patran / Nastran analysis mythology.
Use G.P. Force Output resolved into the Panel Edge Directions to obtain Edge Shears and End
Loads for Rectangular Panels.
F x a/2
ɋ b/2
F x a/2
ɋ b/2
F x a/2 F x a/2
ɋ b/2 ɋ b/2
X- Direction Loads.
Average Shear stress σx y
Shear Flow ɋ = σx y / t
b
a
F y
F x
ɋⁿ
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
95
Figure 34(a)/(b):- Pressure Bulkhead Patran / Nastran Idealisation mythology.
Figure 34(a):- REAL WORLD PRESSURE BULKHEAD
Figure 34(b):- IDEALISATION OF PRESSURE BULKHEAD
USING CBAR‟s and CSHEAR‟s or CQUAD 4‟s
CSHEAR‟s or
CQUAD4‟s.
CBAR‟s to react
Pressure loading.
Point Loads from
Pressure loading.
Pressure loading.
CBAR End Load, Moments and Shears enable the stiffener stresses to be calculated making
corrections for BAR offsets.
95
Figure 34(a)/(b):- Pressure Bulkhead Patran / Nastran Idealisation mythology.
Figure 34(a):- REAL WORLD PRESSURE BULKHEAD
Figure 34(b):- IDEALISATION OF PRESSURE BULKHEAD
USING CBAR‟s and CSHEAR‟s or CQUAD 4‟s
CSHEAR‟s or
CQUAD4‟s.
CBAR‟s to react
Pressure loading.
Point Loads from
Pressure loading.
Pressure loading.
CBAR End Load, Moments and Shears enable the stiffener stresses to be calculated making
corrections for BAR offsets.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
96
Figure 34(c):- Pressure Bulkhead Patran / Nastran Idealisation mythology.
Normal CBAR output does not give Mid Length output therefore use CBAR O card to define
additional points.
Figure 34(c):- IDEALISATION OF PRESSURE BULKHEAD USING CBAR‟s With Offset Vectors
CBAR‟s to react
Pressure loading.
ALTERNATIVE METHOD: - Using CBAR‟s with offset Vectors.
Offset Vectors in Global Displacement
system at bar ends.
BENDING MOMENTS.
Steps are due to shear loads being inputs at
Grid Points only: – Use averages and correct
values at BAR centres.
96
Figure 34(c):- Pressure Bulkhead Patran / Nastran Idealisation mythology.
Normal CBAR output does not give Mid Length output therefore use CBAR O card to define
additional points.
Figure 34(c):- IDEALISATION OF PRESSURE BULKHEAD USING CBAR‟s With Offset Vectors
CBAR‟s to react
Pressure loading.
ALTERNATIVE METHOD: - Using CBAR‟s with offset Vectors.
Offset Vectors in Global Displacement
system at bar ends.
BENDING MOMENTS.
Steps are due to shear loads being inputs at
Grid Points only: – Use averages and correct
values at BAR centres.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Notes on the use of CSHEAR elements (continued).
If F1 or F2 are set to 1.0 the equivalent rods would be set to areas of ½.t.w1 or ½.t.w2….ie,
fully effective for end load.
If the panel is less than fully effective, two methods of approach are possible.
a) F < 1.01, the areas are set to ½.F1.t.w1 or ½.F2.t.w2…a function of the panel WITH.
b)F > 1.01, the areas are set to ½.F1.t².w1 or ½.F2.t².w2…a function of the panel
THICKNESS.
97
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
w1
w2
1 2
3 4
F1 rods
F2 rods
F1 = factor for areas on sides 1,2 and 3,4
F2 = factor for areas on sides 1,4 and 2,3
Notes on the use of CSHEAR elements (continued).
If F1 or F2 are set to 1.0 the equivalent rods would be set to areas of ½.t.w1 or ½.t.w2….ie,
fully effective for end load.
If the panel is less than fully effective, two methods of approach are possible.
a) F < 1.01, the areas are set to ½.F1.t.w1 or ½.F2.t.w2…a function of the panel WITH.
b)F > 1.01, the areas are set to ½.F1.t².w1 or ½.F2.t².w2…a function of the panel
THICKNESS.
97
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
w1
w2
1 2
3 4
F1 rods
F2 rods
F1 = factor for areas on sides 1,2 and 3,4
F2 = factor for areas on sides 1,4 and 2,3
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Notes on the use of CSHEAR elements (continued).
USE:- These factors can be used to remove the singularity for ring frames across the frame depth.
AND:- In calculating flange area the web thickness component Aw/6 can be included using the F
factors by setting the required F factor to 1/3. N.B. Using F1 or F2 = 1.0 will lead to an over stiff
bending section.
Direct Loads in panels:- The only method of determining the end loads carried in the SHEAR panel
when an F factor is used is to look at the corner forces F-FROM-4, F-FROM-2 etc. Without F
factors the corner forces are of equal magnitude and amount to shear loading on the edges.
98
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Use F1 or F2 to create equivalent
rods across the frame.
Flange rods.
Notes on the use of CSHEAR elements (continued).
USE:- These factors can be used to remove the singularity for ring frames across the frame depth.
AND:- In calculating flange area the web thickness component Aw/6 can be included using the F
factors by setting the required F factor to 1/3. N.B. Using F1 or F2 = 1.0 will lead to an over stiff
bending section.
Direct Loads in panels:- The only method of determining the end loads carried in the SHEAR panel
when an F factor is used is to look at the corner forces F-FROM-4, F-FROM-2 etc. Without F
factors the corner forces are of equal magnitude and amount to shear loading on the edges.
98
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Use F1 or F2 to create equivalent
rods across the frame.
Flange rods.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Notes on the use of CSHEAR elements (continued).
With F factors the corner forces will be different and the shear contribution should be removed to
determine the end loads in the panel. For rectangular panels orthogonal to the global axes the
corner forces are identical to the GPFB values.
For rectangular panels the GPBS output can be easily used to calculate the shear and end load
components of the panel loading, and these will be identical to the panel FORCE output for both
CSHEAR and CQUAD4 panels.
For non-rectangular panels the GPFB output can be used to calculate the edge loads provided the
output is transformed into the edge directions and components from adjacent edges are removed.
This will be covered in more detail latter in this presentation.
e)Floor analysis:- Usually these can be regarded as being fully effective in end load and shear,
and may be required to carry pressure loading. The normal idealisation is by using ROD and
SHEAR elements, the ROD elements represent any stiffener areas plus the effective panel
areas (see figure 35(a)).
If the panel has any significant stiffener offsets and / or is subject to pressure loading, BAR‟s
should be used with offset vectors, leaving the ROD‟s only for the panel end load paths (see
figure 35(b)).
For initial project work the pressure effects can be added in the detail stressing, the model
reduced to in plane effects only and thus no rotational D.o.F. are needed (see figure 35(c)).
99
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Notes on the use of CSHEAR elements (continued).
With F factors the corner forces will be different and the shear contribution should be removed to
determine the end loads in the panel. For rectangular panels orthogonal to the global axes the
corner forces are identical to the GPFB values.
For rectangular panels the GPBS output can be easily used to calculate the shear and end load
components of the panel loading, and these will be identical to the panel FORCE output for both
CSHEAR and CQUAD4 panels.
For non-rectangular panels the GPFB output can be used to calculate the edge loads provided the
output is transformed into the edge directions and components from adjacent edges are removed.
This will be covered in more detail latter in this presentation.
e)Floor analysis:- Usually these can be regarded as being fully effective in end load and shear,
and may be required to carry pressure loading. The normal idealisation is by using ROD and
SHEAR elements, the ROD elements represent any stiffener areas plus the effective panel
areas (see figure 35(a)).
If the panel has any significant stiffener offsets and / or is subject to pressure loading, BAR‟s
should be used with offset vectors, leaving the ROD‟s only for the panel end load paths (see
figure 35(b)).
For initial project work the pressure effects can be added in the detail stressing, the model
reduced to in plane effects only and thus no rotational D.o.F. are needed (see figure 35(c)).
99
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
100
Figure 35:- Airframe Floor Patran / Nastran Idealisation and analysis mythology.
≡
≡
Figure 35(a):- REAL WORLD STIFFENED AL ALLOY FLOOR
Figure 35(b):- IDEALISED STIFFENED AL ALLOY FLOOR
CSHEAR‟s
CROD‟s for effective panel areas
Offset BAR‟s for stiffness
Figure 35(c):- IDEALISED STIFFENED AL ALLOY FLOOR FOR INITIAL PROJECT WORK
CROD‟s
CSHEAR‟s
100
Figure 35:- Airframe Floor Patran / Nastran Idealisation and analysis mythology.
≡
≡
Figure 35(a):- REAL WORLD STIFFENED AL ALLOY FLOOR
Figure 35(b):- IDEALISED STIFFENED AL ALLOY FLOOR
CSHEAR‟s
CROD‟s for effective panel areas
Offset BAR‟s for stiffness
Figure 35(c):- IDEALISED STIFFENED AL ALLOY FLOOR FOR INITIAL PROJECT WORK
CROD‟s
CSHEAR‟s
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The panel effective end load areas can be set up automatically by setting F1 and F2 = 1.0 on
the PSHEAR card, in which case each effective rod area will be ½ the panel width x thickness.
GEOMTRY...make sure the floors are planar, put into local axis system if necessary. A slight out
of plane kink in any of the grids will destroy the load carrying capability.
f)Fuselage skin analysis:- The idealisation of fuselage skins is probably the most difficult to
model correctly in that the modelling is dependant on several factors:-
The size of the mesh:
The frame support:
The skin thickness:
The design condition, buckled / unbuckled etc.
However it is possible to divide the methods into two groups, coarse mesh and fine mesh.
1)Coarse Mesh Fuselages:- In the coarse mesh idealisation the skin between the modelled
frames is represented by single elements. It is not possible to represent any skin bending
(pressure loading will load the frame grids only) or hoop tension effects, these must be
taken into account in the detail stressing work. The skins are thus represented by SHEAR
elements and the effective end loads areas by ROD elements.
Longitudinally the skin will be fully effective and thus the F factor on the PSHEAR card may
be used to provide this, in which case longitudinal CROD‟s will represent any longeron or
stringer areas. Alternatively if the F factor is not used the CROD areas should represent the
sum of the effective end load and longeron / stringer areas.
101
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
The panel effective end load areas can be set up automatically by setting F1 and F2 = 1.0 on
the PSHEAR card, in which case each effective rod area will be ½ the panel width x thickness.
GEOMTRY...make sure the floors are planar, put into local axis system if necessary. A slight out
of plane kink in any of the grids will destroy the load carrying capability.
f)Fuselage skin analysis:- The idealisation of fuselage skins is probably the most difficult to
model correctly in that the modelling is dependant on several factors:-
The size of the mesh:
The frame support:
The skin thickness:
The design condition, buckled / unbuckled etc.
However it is possible to divide the methods into two groups, coarse mesh and fine mesh.
1)Coarse Mesh Fuselages:- In the coarse mesh idealisation the skin between the modelled
frames is represented by single elements. It is not possible to represent any skin bending
(pressure loading will load the frame grids only) or hoop tension effects, these must be
taken into account in the detail stressing work. The skins are thus represented by SHEAR
elements and the effective end loads areas by ROD elements.
Longitudinally the skin will be fully effective and thus the F factor on the PSHEAR card may
be used to provide this, in which case longitudinal CROD‟s will represent any longeron or
stringer areas. Alternatively if the F factor is not used the CROD areas should represent the
sum of the effective end load and longeron / stringer areas.
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FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
The CROD‟s along the panel edges bounded by the frames will be sized depending upon
the effective area of the skins in the circumferential direction. ESDU 71004 data sheet gives
formula for the effective areas for single and multiple frame attachment lines. The CROD‟s
will be independent of any frame flange areas, which should have been modelled
separately.
For thick skins the effective areas may approach 100% (intake ducts etc.), and in the case
of the CSHEAR‟s may be replaced by CQUAD4s, i.e. fully end load effective . In this case
CROD‟s would be required only for the longerons etc. (see figure 36).
The design condition will dictate the material stiffness used i.e. a reduced E for a bulkhead
structure.
Warning N.B.:- If QUAD4‟s are used for skin elements globally the structure could / will be
significantly over – stiff, which would lead to incorrect load paths and deflections.
2)Fine Mesh Fuselage:- In a fine mesh situation the skins between the frames are modelled
in sufficient detail to enable skin bending and hoop tension effects to be predicted. This
forces the model to have rotational D.o.F. and this increases the running time of the solver
considerably. The mesh should be sufficiently fine (minimum 4 panels) so that the skin
effects can be seen in the output.
The panels should be bending QUAD4‟s and any longerons or stringers should be CBAR‟s.
Pressure loading should now load the mid-bay points (see figure 37).
102
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
The CROD‟s along the panel edges bounded by the frames will be sized depending upon
the effective area of the skins in the circumferential direction. ESDU 71004 data sheet gives
formula for the effective areas for single and multiple frame attachment lines. The CROD‟s
will be independent of any frame flange areas, which should have been modelled
separately.
For thick skins the effective areas may approach 100% (intake ducts etc.), and in the case
of the CSHEAR‟s may be replaced by CQUAD4s, i.e. fully end load effective . In this case
CROD‟s would be required only for the longerons etc. (see figure 36).
The design condition will dictate the material stiffness used i.e. a reduced E for a bulkhead
structure.
Warning N.B.:- If QUAD4‟s are used for skin elements globally the structure could / will be
significantly over – stiff, which would lead to incorrect load paths and deflections.
2)Fine Mesh Fuselage:- In a fine mesh situation the skins between the frames are modelled
in sufficient detail to enable skin bending and hoop tension effects to be predicted. This
forces the model to have rotational D.o.F. and this increases the running time of the solver
considerably. The mesh should be sufficiently fine (minimum 4 panels) so that the skin
effects can be seen in the output.
The panels should be bending QUAD4‟s and any longerons or stringers should be CBAR‟s.
Pressure loading should now load the mid-bay points (see figure 37).
102
FATA Project FEA Structural Design Analysis using PATRAN/NASTRAN Toolset.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
103
Figure 36:- Fuselage Skin Coarse Mesh Patran / Nastran Idealisation.
Single panel between frames.
For Thin Skins:-
CSHEAR thickness = t : average panel width = ω
(between fastener lines) : CROD‟s on edges 1-2
and 4-3 represent full end load capability of the
skins:
CROD‟s on edges 1-4 and 2-3 represent effective
area of the attached skin use E.S.D.U. 71004
data sheet (see below).
1-4 and 2-3 ROD areas – where the skin is
attached by a single fastener line:-
Area along edge 1-4 = 0.39⃰ √R1 t³
Area along edge 2-3 = 0.39√R2 t³
(See E.S.D.U. data sheet for correct values for
application). If PSHEAR F2 factor is used,
F2 = 0.39 (√R1 t³ + √R2 t³)
ω t
Skin attached by >1 line of fasteners:- Add W t
2
Where W is the width between the outer most
fasteners.
For Thick Skins:- Intake ducts etc. effective skin
area may approach 100% so replace CSHEAR
with CQUAD4‟s i.e. fully end load effective.
Frames
Skin Idealisation
W t
Pressure Loading:- Pressure on panels load Frame Grid Only detail
stressing should cover skin bending and Hoop tension effects.
103
Figure 36:- Fuselage Skin Coarse Mesh Patran / Nastran Idealisation.
Single panel between frames.
For Thin Skins:-
CSHEAR thickness = t : average panel width = ω
(between fastener lines) : CROD‟s on edges 1-2
and 4-3 represent full end load capability of the
skins:
CROD‟s on edges 1-4 and 2-3 represent effective
area of the attached skin use E.S.D.U. 71004
data sheet (see below).
1-4 and 2-3 ROD areas – where the skin is
attached by a single fastener line:-
Area along edge 1-4 = 0.39⃰ √R1 t³
Area along edge 2-3 = 0.39√R2 t³
(See E.S.D.U. data sheet for correct values for
application). If PSHEAR F2 factor is used,
F2 = 0.39 (√R1 t³ + √R2 t³)
ω t
Skin attached by >1 line of fasteners:- Add W t
2
Where W is the width between the outer most
fasteners.
For Thick Skins:- Intake ducts etc. effective skin
area may approach 100% so replace CSHEAR
with CQUAD4‟s i.e. fully end load effective.
Frames
Skin Idealisation
W t
Pressure Loading:- Pressure on panels load Frame Grid Only detail
stressing should cover skin bending and Hoop tension effects.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
104
Figure 37:- Fuselage Skin Fine Mesh Patran / Nastran Idealisation.
Deflected Shape
Pressure Loading
QUAD4 Bending Panels Fully Effective.
CBAR‟s For any Longerons or Stringers.
Pressure Loads now load Mid-Bay Points.
Curved Skin Effects seen –Hoop Tension etc.
Stringer / Longeron loads in CBAR‟s correct.
Idealisation needs additional rotational D.o.F.
Running time increased.
104
Figure 37:- Fuselage Skin Fine Mesh Patran / Nastran Idealisation.
Deflected Shape
Pressure Loading
QUAD4 Bending Panels Fully Effective.
CBAR‟s For any Longerons or Stringers.
Pressure Loads now load Mid-Bay Points.
Curved Skin Effects seen –Hoop Tension etc.
Stringer / Longeron loads in CBAR‟s correct.
Idealisation needs additional rotational D.o.F.
Running time increased.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Composite Panels can be represented by one of the following methods:-
a)Single QUAD4 Anisotropic panel:
b)Multiple QUAD4 Anisotropic panel:
c)NASTRAN PCOM Facility:
d)Through the thickness modelling using 2-D elements.
N.B. Both (a) and (c) can represent bending effects.
a)SINGLE QUAD4 PANEL METHOD:-
Create MAT2 data.
105
ATDA Project PATRAN/NASTRAN Toolset Composite Panel Idealisation Overview.
MEMBRANE ONLY MEMBRANE +BENDING
Use CF02 with % Layers for Unit thickness.
Stiffness Matrix Gives terms for MAT2
Card.
Membrane MAT2 Data.
Use CF02 with Full layup for Unit Thickness.
Rigidity (Bending) Stiffness MATRIX ⃰12.0 gives
terms for bending MAT2 Data.
Use actual thickness on PSHELL Card, separate materials for Membrane and bending,
and 12I/T³=1.0. Add material for Transverse Shear based on Matrix (Glue) stiffness.
Use actual thickness on PSHELL card.
Composite Panels can be represented by one of the following methods:-
a)Single QUAD4 Anisotropic panel:
b)Multiple QUAD4 Anisotropic panel:
c)NASTRAN PCOM Facility:
d)Through the thickness modelling using 2-D elements.
N.B. Both (a) and (c) can represent bending effects.
a)SINGLE QUAD4 PANEL METHOD:-
Create MAT2 data.
105
ATDA Project PATRAN/NASTRAN Toolset Composite Panel Idealisation Overview.
MEMBRANE ONLY MEMBRANE +BENDING
Use CF02 with % Layers for Unit thickness.
Stiffness Matrix Gives terms for MAT2
Card.
Membrane MAT2 Data.
Use CF02 with Full layup for Unit Thickness.
Rigidity (Bending) Stiffness MATRIX ⃰12.0 gives
terms for bending MAT2 Data.
Use actual thickness on PSHELL Card, separate materials for Membrane and bending,
and 12I/T³=1.0. Add material for Transverse Shear based on Matrix (Glue) stiffness.
Use actual thickness on PSHELL card.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
b)MULTIPLE QUAD4 ANISOTROPIC PANELS: -
Overlapping QUAD4 panels:
One panel per ply orientation:
Panel element data contains material layer direction for Unidirectional (U.D.) material:
Can represent membrane only:
Normally used for optimisation.
Create a Stiffness Matrix using CF02 for U.D. material at 0º …….unit thickness, and refer each
layer to this material.
Post processing can check bending effects of combined panel………using typical layup stacking.
c)NASTRAN PCOM Facility:-
Any combination of layer material, orientation, and thickness can be represented.
Automatically produces PSHELL and material data for;- MEMBRANE; BENDING; and
TRANSVERSE SHEAR.
Create a Stiffness Matrix using CF02 for each U.D. material at 0º for unit thickness. Write
NASTRAN PCOM data.
106
ATDA Project PATRAN/NASTRAN Toolset Composite Panel Idealisation Overview.
b)MULTIPLE QUAD4 ANISOTROPIC PANELS: -
Overlapping QUAD4 panels:
One panel per ply orientation:
Panel element data contains material layer direction for Unidirectional (U.D.) material:
Can represent membrane only:
Normally used for optimisation.
Create a Stiffness Matrix using CF02 for U.D. material at 0º …….unit thickness, and refer each
layer to this material.
Post processing can check bending effects of combined panel………using typical layup stacking.
c)NASTRAN PCOM Facility:-
Any combination of layer material, orientation, and thickness can be represented.
Automatically produces PSHELL and material data for;- MEMBRANE; BENDING; and
TRANSVERSE SHEAR.
Create a Stiffness Matrix using CF02 for each U.D. material at 0º for unit thickness. Write
NASTRAN PCOM data.
106
ATDA Project PATRAN/NASTRAN Toolset Composite Panel Idealisation Overview.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
107
ATDA Project PATRAN/NASTRAN Toolset Composite Panel Idealisation Overview.
d)Through Thickness Modelling:-
≡
QUAD4‟s
y
x
SLICE
LAMINATE
SLICE
2-D ELEMENTS
Requires 2 Stage use of CF02:-
1) To calculate compliance matrix in the x-direction, this gives „Ex‟ values for x-direction.
2)Using known values of the through thickness material „Ey‟ and „G‟, use Ex, Ey, G and ʋ
(0.3) to form up stiffness matrix via CF02.
If slice is from the centre of the model Poisson's Ratio constraints should modify basic
materials properties.
This thickness reduces for Ex load.
This direction should be constrained if the
slice is at centre of the model.
107
ATDA Project PATRAN/NASTRAN Toolset Composite Panel Idealisation Overview.
d)Through Thickness Modelling:-
≡
QUAD4‟s
y
x
SLICE
LAMINATE
SLICE
2-D ELEMENTS
Requires 2 Stage use of CF02:-
1) To calculate compliance matrix in the x-direction, this gives „Ex‟ values for x-direction.
2)Using known values of the through thickness material „Ey‟ and „G‟, use Ex, Ey, G and ʋ
(0.3) to form up stiffness matrix via CF02.
If slice is from the centre of the model Poisson's Ratio constraints should modify basic
materials properties.
This thickness reduces for Ex load.
This direction should be constrained if the
slice is at centre of the model.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Problem Statement:- A panel has three parallel integrally machined stiffeners on one side, as
shown in figure 38. The panel is loaded on the opposite side to the stiffeners by a uniform pressure,
and it is simply supported around its entire periphery by rigid supports. The material and geometric
data are given in figures 38 (a) and (b) and Table 7.
Analysis Specification:- The panel was analysed using different idealisations. Each idealisation
was intended to be modelled using different meshes (see later).
a)Both panel and stiffeners to be modelled using shell idealisations.
b)Panel modelled as a shell and stiffeners modelled as beam idealisations.
In both cases the pressure load is applied to the panel only on the side opposite from the stiffeners.
The panel is simply supported around all of its periphery. Sufficient additional constraints are
required at the corners of the panel to prevent all remaining possible rigid body motions. However
care was taken not to over-constrain the panel. In the building of the Finite Element mesh, the
Mapped (Iso-) meshing approach was used (i.e. not automatic or paved mesh).
Results required from each analysis:-
1)Maximum out-of plane deflection of the panel / stiffener structure:
2)Maximum Stress in the panel:
3)Maximum Stress in the centre stiffener of the structure.
4)Plots were made of the deformed shape of the structure, and the stress distribution in the panel
and stiffeners. (a) using “smoothed contours”: (b) using “element fill” display.
108
FATA Project PATRAN/NASTRAN Toolset Exercise 3 example application.
Problem Statement:- A panel has three parallel integrally machined stiffeners on one side, as
shown in figure 38. The panel is loaded on the opposite side to the stiffeners by a uniform pressure,
and it is simply supported around its entire periphery by rigid supports. The material and geometric
data are given in figures 38 (a) and (b) and Table 7.
Analysis Specification:- The panel was analysed using different idealisations. Each idealisation
was intended to be modelled using different meshes (see later).
a)Both panel and stiffeners to be modelled using shell idealisations.
b)Panel modelled as a shell and stiffeners modelled as beam idealisations.
In both cases the pressure load is applied to the panel only on the side opposite from the stiffeners.
The panel is simply supported around all of its periphery. Sufficient additional constraints are
required at the corners of the panel to prevent all remaining possible rigid body motions. However
care was taken not to over-constrain the panel. In the building of the Finite Element mesh, the
Mapped (Iso-) meshing approach was used (i.e. not automatic or paved mesh).
Results required from each analysis:-
1)Maximum out-of plane deflection of the panel / stiffener structure:
2)Maximum Stress in the panel:
3)Maximum Stress in the centre stiffener of the structure.
4)Plots were made of the deformed shape of the structure, and the stress distribution in the panel
and stiffeners. (a) using “smoothed contours”: (b) using “element fill” display.
108
FATA Project PATRAN/NASTRAN Toolset Exercise 3 example application.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
109
500mm
500mm
(a) Plan View
(b) Front View
(c) Side View
125mm 125mm 125mm
Figure 38(a):- Exercise 3,The layout of the test panel with three equidistant stiffeners.
109
500mm
500mm
(a) Plan View
(b) Front View
(c) Side View
125mm 125mm 125mm
Figure 38(a):- Exercise 3,The layout of the test panel with three equidistant stiffeners.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
110
Stiffeners Panel simply supported around all
Four Edges (i.e. all translation is
prevented normal to the panel).
Uniform Pressure applied to face
opposite to the stiffeners.
2 mm
2 mm
Figure 38(b):- Exercise 3,The layout of the test panel with three equidistant stiffeners.
110
Stiffeners Panel simply supported around all
Four Edges (i.e. all translation is
prevented normal to the panel).
Uniform Pressure applied to face
opposite to the stiffeners.
2 mm
2 mm
Figure 38(b):- Exercise 3,The layout of the test panel with three equidistant stiffeners.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Property Symbol Value Units
Young‟s Modulus. E 80,000 N/mm²
Poisson Ratio. ʋ 0.33
Pressure. ρ 0.1 N/mm²
Stiffener Section
Height.
h 50 mm
Stiffener Section
Width.
b 2 mm
Panel Through
Thickness
t 2 mm
111
Table 7:- Exercise 3 Panel Properties.
Property Symbol Value Units
Young‟s Modulus. E 80,000 N/mm²
Poisson Ratio. ʋ 0.33
Pressure. ρ 0.1 N/mm²
Stiffener Section
Height.
h 50 mm
Stiffener Section
Width.
b 2 mm
Panel Through
Thickness
t 2 mm
111
Table 7:- Exercise 3 Panel Properties.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
a)Panel Modelled using Shell Idealisation:- For this case, NASTRAN QUAD4 elements were
used to model both the panel and stiffeners, this required the production of two Finite Element
Models for the idealisation:
1)Stiffeners modelled using one layer of QUAD4 elements over their height (figure 39(a)):
2)Stiffeners modelled with two layers of QUAD4 elements over their height (figure 39(b)):
Figures 39(a) and 39(b) are representations and the meshes shown are for information only the
actual meshing is shown in figure 41. Mapped (Iso-) meshing was used and care was taken to
prevent excessive distortions of the QUAD4 shell elements, for example not allowing element
aspect ratios to exceed 3.
a)Panel Modelled using Beam and Shell Idealisation:- For this case, NASTRAN QUAD4
elements were used to model the panel but the stiffeners were modelled using NASTRAN
BAR2 and later BEAM elements. Two Finite Element models were required for this idealisation:-
1)Stiffeners modelled using NASTRAN CBAR elements (referred to as BAR2 in PATRAN)
with no axis offset, i.e. BAR neutral axis coincides with panel neutral axis (figure 40(a)):
2)Stiffeners modelled using CBAR elements with axis offset, i.e. stiffener neutral axis offset
from panel neutral axis to allow for the fact that the stiffeners are on one side of the panel
only (figure 40(b)).
112
FATA Project PATRAN/NASTRAN Toolset Exercise 3 example application.
a)Panel Modelled using Shell Idealisation:- For this case, NASTRAN QUAD4 elements were
used to model both the panel and stiffeners, this required the production of two Finite Element
Models for the idealisation:
1)Stiffeners modelled using one layer of QUAD4 elements over their height (figure 39(a)):
2)Stiffeners modelled with two layers of QUAD4 elements over their height (figure 39(b)):
Figures 39(a) and 39(b) are representations and the meshes shown are for information only the
actual meshing is shown in figure 41. Mapped (Iso-) meshing was used and care was taken to
prevent excessive distortions of the QUAD4 shell elements, for example not allowing element
aspect ratios to exceed 3.
a)Panel Modelled using Beam and Shell Idealisation:- For this case, NASTRAN QUAD4
elements were used to model the panel but the stiffeners were modelled using NASTRAN
BAR2 and later BEAM elements. Two Finite Element models were required for this idealisation:-
1)Stiffeners modelled using NASTRAN CBAR elements (referred to as BAR2 in PATRAN)
with no axis offset, i.e. BAR neutral axis coincides with panel neutral axis (figure 40(a)):
2)Stiffeners modelled using CBAR elements with axis offset, i.e. stiffener neutral axis offset
from panel neutral axis to allow for the fact that the stiffeners are on one side of the panel
only (figure 40(b)).
112
FATA Project PATRAN/NASTRAN Toolset Exercise 3 example application.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
113
Figure 39:- Exercise 3 test panel idealisation with Shell QUAD4 elements only.
Figure 39(a) One layer of QUAD4 Elements in Stiffeners.
Figure 39(b) Two layers of QUAD4 Elements in Stiffeners.
113
Figure 39:- Exercise 3 test panel idealisation with Shell QUAD4 elements only.
Figure 39(a) One layer of QUAD4 Elements in Stiffeners.
Figure 39(b) Two layers of QUAD4 Elements in Stiffeners.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
114
Figure 40:- Exercise 3 test panel idealisation with Shell and Beam elements.
Figure 40(b) Axis Offset in Stiffener BAR Elements.
N.B. The Axis Offset is in the Formulation of the
BAR element. It is included by modifying the
BAR element properties.
NODE
Offsets for BAR Element 1
Offsets for BAR Element 2
NODE
NODE
Figure 40(a) No Offset in Stiffener BAR Elements.
114
Figure 40:- Exercise 3 test panel idealisation with Shell and Beam elements.
Figure 40(b) Axis Offset in Stiffener BAR Elements.
N.B. The Axis Offset is in the Formulation of the
BAR element. It is included by modifying the
BAR element properties.
NODE
Offsets for BAR Element 1
Offsets for BAR Element 2
NODE
NODE
Figure 40(a) No Offset in Stiffener BAR Elements.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Again mapped (Iso-) meshing was used (i.e. not automatic or paved mesh). Care was exercise to
prevent excessive distortions of the QUAD4 shell elements (e.g. element aspect ratio‟s less than 3
as for the shell only idealisation), but one advantage of the combined shell and bar element
idealisation is that larger shell elements can be used in the panel. The CBAR local axis were
orientated using the vector method.
Displayed here are the exercise results obtained from my original application of this exercise as
part of my Cranfield University MSc in Aircraft Engineering FEA module, problems with the printer
meant that only the results from the Shell modelling portion of the exercise could be printed and are
given in figures 41(a) through 41(e).
Currently I am in the process of reproducing this exercise with my own NATRAN 2000 package and
will incorporate the results in this presentation update, further I intend to repeat the all-shell
analyses (Part (a)) using “higher order” elements (e.g. QUAD8), and repeating both parts of the
analysis using different constraints, particularly on the ends of the stiffeners. I also intend to explore
the implications of modelling the stiffeners using solid (HEX8) elements, and comparative complete
solid modelling for comparison with analysis of the identical panel created and idealised in Catia
V5.R20 Finite Element Analysis toolset. As a prelude to applying the airframe component
idealisation methodologies to the FATA airframe structural analysis. Table 8 gives the results
obtained from the original analysis.
115
ATDA Project PATRAN/NASTRAN Toolset Exercise 3 example application.
Again mapped (Iso-) meshing was used (i.e. not automatic or paved mesh). Care was exercise to
prevent excessive distortions of the QUAD4 shell elements (e.g. element aspect ratio‟s less than 3
as for the shell only idealisation), but one advantage of the combined shell and bar element
idealisation is that larger shell elements can be used in the panel. The CBAR local axis were
orientated using the vector method.
Displayed here are the exercise results obtained from my original application of this exercise as
part of my Cranfield University MSc in Aircraft Engineering FEA module, problems with the printer
meant that only the results from the Shell modelling portion of the exercise could be printed and are
given in figures 41(a) through 41(e).
Currently I am in the process of reproducing this exercise with my own NATRAN 2000 package and
will incorporate the results in this presentation update, further I intend to repeat the all-shell
analyses (Part (a)) using “higher order” elements (e.g. QUAD8), and repeating both parts of the
analysis using different constraints, particularly on the ends of the stiffeners. I also intend to explore
the implications of modelling the stiffeners using solid (HEX8) elements, and comparative complete
solid modelling for comparison with analysis of the identical panel created and idealised in Catia
V5.R20 Finite Element Analysis toolset. As a prelude to applying the airframe component
idealisation methodologies to the FATA airframe structural analysis. Table 8 gives the results
obtained from the original analysis.
115
ATDA Project PATRAN/NASTRAN Toolset Exercise 3 example application.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
116
Figure 41(a):- Exercise 3 test panel with one layer of QUAD4 stiffener elements.
116
Figure 41(a):- Exercise 3 test panel with one layer of QUAD4 stiffener elements.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
117
Figure 41(b):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Deformed shape “Smoothed Contours”.
117
Figure 41(b):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Deformed shape “Smoothed Contours”.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
118
Figure 41(c):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Deformed shape “element fit”.
118
Figure 41(c):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Deformed shape “element fit”.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
119
Figure 41(d):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Stress distribution “Smoothed Contours”.
119
Figure 41(d):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Stress distribution “Smoothed Contours”.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
120
Figure 41(e):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Stress distribution “element fit”.
120
Figure 41(e):- Exercise 3 test panel with two layers of QUAD4 stiffener elements.
Stress distribution “element fit”.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
Name of
analysis run.
Stiffener
model.
Plate. Stiffener.
Max Deflection
(mm).
Stress N/mm² on
Pressure side.
Stress N/mm² on
Stiffener side.
Max Stress
(Combined)
N/mm²
Plate 4
2 Layers of shell
elements.
1.532 -68.40 76.030 195.000
Plate 3
1 layer of shell
elements.
1.530 -65.40 76.123 124.128
Plate 2
BAR elements
with offset.
1.490 -67.50 75.190 270.400
Plate 1
BAR elements
without offset.
2.941 -77.24 72.240 493.000
121
Table 8:- Exercise 3 Initial panel analysis results.
Name of
analysis run.
Stiffener
model.
Plate. Stiffener.
Max Deflection
(mm).
Stress N/mm² on
Pressure side.
Stress N/mm² on
Stiffener side.
Max Stress
(Combined)
N/mm²
Plate 4
2 Layers of shell
elements.
1.532 -68.40 76.030 195.000
Plate 3
1 layer of shell
elements.
1.530 -65.40 76.123 124.128
Plate 2
BAR elements
with offset.
1.490 -67.50 75.190 270.400
Plate 1
BAR elements
without offset.
2.941 -77.24 72.240 493.000
121
Table 8:- Exercise 3 Initial panel analysis results.
Mr. Geoffrey Allen Wardle MSc. MSc. C.Eng. MRAeS.
1)Aircraft Loading and Structural Layout: Professional Engineering Publishing: by Prof Denis
Howe: 2004: ISBN 186058432 2.
2)Catia V5.R20 FEA in Airframe Design Workbook 2: Private Study 2014: Mr. Geoffrey Wardle
(not a published document).
3)Composite Materials for Aircraft Structures second edition: AIAA Education Series: by Alan
Baker et al: 2004: ISBN 1-56347-540-5.
4)Design and Analysis of a Composite Fuselage: 3
rd
CTA-DRL Workshop on Design Analysis and
Flight Control September 14-16, 2009: S.J. Campos. SP, Brazil: by Marco Aurelio Rossi and
Sergio Frascion Muller de Almdeida ITA Mechanical Engineering Department.
5)Damage Tolerance in Aircraft: by Prof P.E. Irving Damage Tolerance Group School of
Engineering Cranfield University: Published by Cranfield University 2003 / 2004.
6)Cranfield University MSc Aircraft Engineering FEA module course notes 2003.
7)Patran / Nastran Introduction: J. C. Brown: Published by Cranfield University College of
Aeronautics 2001.
8)Rules for Modeling Structures and Interpretation of Results using Nastran / Patran Toolset FEA
Workbook 1 based on collected data, Cranfield University FEA module, and personnel
research: by Mr. Geoffrey Wardle MSc. MSc. Snr MAIAA: not yet published in full completed
20013.
9)Some Aspects of Practical Finite Element Modeling: J. C. Brown: Published by Cranfield
University 2001.
122
Current reference material in use for this presentation list will be extended.
1)Aircraft Loading and Structural Layout: Professional Engineering Publishing: by Prof Denis
Howe: 2004: ISBN 186058432 2.
2)Catia V5.R20 FEA in Airframe Design Workbook 2: Private Study 2014: Mr. Geoffrey Wardle
(not a published document).
3)Composite Materials for Aircraft Structures second edition: AIAA Education Series: by Alan
Baker et al: 2004: ISBN 1-56347-540-5.
4)Design and Analysis of a Composite Fuselage: 3
rd
CTA-DRL Workshop on Design Analysis and
Flight Control September 14-16, 2009: S.J. Campos. SP, Brazil: by Marco Aurelio Rossi and
Sergio Frascion Muller de Almdeida ITA Mechanical Engineering Department.
5)Damage Tolerance in Aircraft: by Prof P.E. Irving Damage Tolerance Group School of
Engineering Cranfield University: Published by Cranfield University 2003 / 2004.
6)Cranfield University MSc Aircraft Engineering FEA module course notes 2003.
7)Patran / Nastran Introduction: J. C. Brown: Published by Cranfield University College of
Aeronautics 2001.
8)Rules for Modeling Structures and Interpretation of Results using Nastran / Patran Toolset FEA
Workbook 1 based on collected data, Cranfield University FEA module, and personnel
research: by Mr. Geoffrey Wardle MSc. MSc. Snr MAIAA: not yet published in full completed
20013.
9)Some Aspects of Practical Finite Element Modeling: J. C. Brown: Published by Cranfield
University 2001.
122
Current reference material in use for this presentation list will be extended.
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