Mechanical Engineering Assignment Help

Finite Element Analysis (FEA) is a powerful computational tool used in engineering to analyze and predict the behavior of structures and fluids under various conditions. In the context of "Finite Element Analysis of Solids and Fluids I," this presentation delves into a fundamental problem involving the analysis of a truss structure. The truss problem is a classic example used to illustrate the application of FEA in linear elastic analysis. By removing displacement boundary conditions and applying no external loads, the problem offers an opportunity to explore the inherent properties and responses of the structure. This analysis not only provides insights into the displacement and internal forces of the truss but also demonstrates the equilibrium conditions essential for structural integrity.

1. Mechanical Engineering Assignment Help Topic: Finite Element Analysis For any Assignment related queries, Call us at : - [phone]   You can mail us at : -   [email protected] Reach us at : - https://www.mechanicalengineeringassignmenthelp.com/

2. https://www.solidworksassignmenthelp.com/ Finite Element Analysis (FEA) is a powerful computational tool used in engineering to analyze and predict the behavior of structures and fluids under various conditions. In the context of "Finite Element Analysis of Solids and Fluids I," this presentation delves into a fundamental problem involving the analysis of a truss structure. The truss problem is a classic example used to illustrate the application of FEA in linear elastic analysis. By removing displacement boundary conditions and applying no external loads, the problem offers an opportunity to explore the inherent properties and responses of the structure. This analysis not only provides insights into the displacement and internal forces of the truss but also demonstrates the equilibrium conditions essential for structural integrity. Introduction

3. https://www.solidworksassignmenthelp.com/ Problem 1 Consider the truss problem already discussed in class, in linear elastic analysis, but with all displacement boundary conditions removed and no applied load. A ⎡ m ⎤ = cross-sectional area of each bar, E Y X

4. https://www.solidworksassignmenthelp.com/ a) Develop by the physical reasoning used in class that is “by inspection” the K matrix for b) Now assume U 1  U 2  U 4  U 7  U 8  and the external loads , R 3  , R 5  60 kN , and R 6  . Calculate the displacements, U 3 , U 5 , and U 6 and sketch the deflected shape of the structure.

5. https://www.solidworksassignmenthelp.com/ c) Calculate all internal element forces and the reactions corresponding to U 1 , U 2 , U 4 , U 7 and U 8 . d) Show explicitly that element 3 and joint (node) 3 are in equilibrium. Show that the complete structure is in equilibrium.

6. https://www.solidworksassignmenthelp.com/ Solution 2 The truss geometry is shown below. Bar mumbers are circled. Joint numbers are placed adjacent to their respective joints. For a linear static analysis, we have: K 8×8 U 8×1 =R 8×1

7. https://www.solidworksassignmenthelp.com/ a) The K matrix is calculated column by column. The i th column of the stiffness matrix represents the external force vector required to give the structure unit displacement about the i th degree of freedom and zero displacement about all other degree of freedom. Take a look at one example how to construct it. Calculate column 5: Imposing the following displacement pattern: U 5 =1, U 1 =U 2 =U 3 =U 4 =U 6 =U 7 =U 8 =0

8. https://www.solidworksassignmenthelp.com/ The resulting external force vector under this set of displacement conditions is equal to the 5 th column of the stiffness matrix K . In this case, the truss bar 1 changes length by 1, the truss bar 5 shrinks by , , and all other truss bars are fixed in length. Hence , the bar axial forces are as follows.

9. https://www.solidworksassignmenthelp.com/ Positive and negative signs of the axial forces imply tension and compression, respectively. Hence the reaction forces, the entries of the 5 th column, are obtained from the equilibrium equations at the joints.

10. https://www.solidworksassignmenthelp.com/ After assembling all columns, the following K is determined:

11. https://www.solidworksassignmenthelp.com/ b) Since U 1  U 2  U 4  U 7  U 8  , we can reduce K 8×8 U 8×1 =R 8×1 to K aa U a =R a as follows:

12. https://www.solidworksassignmenthelp.com/ The solution is

13. https://www.solidworksassignmenthelp.com/ c) Since we know the values of U 3 , U 5 , and U 6 , we can calculate the reaction forces from K ba U a = R b ,

14. https://www.solidworksassignmenthelp.com/ The undeformed and deformed meshes with applied boundary conditions and loads are plotted on the next page.

15. https://www.solidworksassignmenthelp.com/ To calculate all internal forces, let’s draw the equilibrium diagram for each joint. R=1.2426×10 4 N P=6×10 5 N

16. https://www.solidworksassignmenthelp.com/ Therefore, the internal forces are Element 1: tension 4.7572×10 4 N Element 2: no force Element 3: tension 1.2426×10 4 N Element 4: no force Element 5: Compression 1.7573×10 4 N

17. https://www.solidworksassignmenthelp.com/ and Reactions:

18. https://www.solidworksassignmenthelp.com/ d) We can make sure that element 3 and joint 3 are in equilibrium explicitly by the diagram below.

19. https://www.solidworksassignmenthelp.com/ External forces acting on structure.

20. https://www.solidworksassignmenthelp.com/ ∑ F x   12.4 kN  47.6 kN  60 kN  ∑ F y  12.4 kN  12.4 kN  ∑ M at 4   12.4 kN  a  47.6 kN  a  60 kN  a  Therefore, the structure is in equilibrium.

21. https://www.solidworksassignmenthelp.com/ Conclusion In conclusion, the truss problem presented in this session highlights the essential principles of Finite Element Analysis as applied to structural mechanics. By meticulously developing the stiffness matrix, imposing boundary conditions, and calculating displacements and internal forces, we gain a comprehensive understanding of the behavior of truss structures. This problem underscores the importance of equilibrium in ensuring the stability of structures. The methods and results discussed here are foundational to the broader applications of FEA in both solids and fluids, emphasizing its critical role in modern engineering analysis and design. Through such detailed studies, we pave the way for more complex and accurate simulations, ultimately leading to safer and more efficient engineering solutions.

22. https://www.solidworksassignmenthelp.com/ Thank You