Pratt truss optimization using

Pratt truss optimization using

1. Pratt Truss Optimization Using Genetic Algorithm By :- Harish Kant Soni Roll No:- 12CE31004

2. Use of Pratt truss Fig :- Gatton Railway Bridge, Queensland, Australia Image Source :- https://commons.wikimedia.org/wiki/File:Gatton_Railway_Bridge.JPG

3. Forces in P ratt truss Image source :-http://www.slideshare.net/sheikhjunaidyawar/trusses-28955458 F

4. 18 m 7 m

5. Loading Train’s engine has highest weight as compared to other coaches Indian locomotive class WAP-5 Length = 18.16 m Weight = 79251.7 kg Source :- https://en.wikipedia.org/wiki/Indian_locomotive_class_WAP-5

6. 18 m 7 m

7. 18 m 7 m Dead Load = 150 kN / meter/ side Total dead load = 150 x 18 = 2700 KN Live load = 800 KN 550 KN 550 KN 550 KN 550 KN 550 KN 1 2 3 4 5 6 7 12 11 10 9 8

8. Objective Function :- min. total Area = min A(1 )+A(2)+A(3)+A(4)+A(5)+A(6)+A(7)+A(8 ) + A(9)+A(10)+A(11 )+A(12 )+A(13 )+A(14 )+A(15)+ +A(16 )+A(17)+A(18)+A(19)+A(20)+A(21)+A(22 ) Constraints :- min. Area = 0.0010 m^2 = 10 cm^2 disp at any node < 50 mm

9. clc ; clear all; % initial cromosome having area in the range 0.002 to 0.02 m^2- C = 2e-3*[1 2 4 10 3 9 10 7 1 5 1 1 2 4 10 3 9 10 7 1 5 2; 9 3 7 9 4 7 5 2 4 9 1 9 3 7 9 4 7 5 2 4 9 3; 7 3 4 1 1 7 3 2 4 9 8 7 3 4 1 1 7 3 2 4 9 4; 1 5 7 9 4 9 5 2 4 9 6 1 5 7 9 4 9 5 2 4 9 5; 4 10 6 2 2 2 3 2 4 1 9 4 10 6 2 2 2 3 2 4 1 6; 9 3 5 9 5 7 5 1 4 9 1 9 3 5 9 5 7 5 1 4 9 7; 9 9 4 1 4 3 1 2 4 9 8 9 9 4 1 4 3 1 2 4 9 8; 1 3 7 9 1 7 5 5 4 4 1 1 3 7 9 1 7 5 5 4 4 9; 9 8 3 1 2 4 2 2 4 9 6 9 8 3 1 2 4 2 2 4 9 10; 2 3 7 9 3 7 5 9 4 3 1 2 3 7 9 3 7 5 9 4 3 1; 8 7 2 10 4 5 3 10 4 7 4 8 7 2 10 4 5 3 10 4 7 2; 1 2 4 10 3 9 10 7 1 5 1 1 2 4 10 3 9 10 7 1 5 3; 9 3 7 9 4 7 5 2 4 9 1 9 3 7 9 4 7 5 2 4 9 4; 7 3 4 1 1 7 3 2 4 9 8 7 3 4 1 1 7 3 2 4 9 5; 1 5 7 9 4 9 5 2 4 9 6 1 5 7 9 4 9 5 2 4 9 6; 4 10 6 2 2 2 3 2 4 1 9 4 10 6 2 2 2 3 2 4 1 7; 9 3 5 9 5 7 5 1 4 9 1 9 3 5 9 5 7 5 1 4 9 8; 9 9 4 1 4 3 1 2 4 9 8 9 9 4 1 4 3 1 2 4 9 9; 1 3 7 9 1 7 5 5 4 4 1 1 3 7 9 1 7 5 5 4 4 10; 9 8 3 1 2 4 2 2 4 9 6 9 8 3 1 2 4 2 2 4 9 1; 2 3 7 9 3 7 5 9 4 3 1 2 3 7 9 3 7 5 9 4 3 2; 2 3 7 9 3 7 5 9 4 3 1 2 3 7 9 3 7 5 9 4 3 3];

10. F_obj = sum(C,2); % return sum of rows in a column matrix of 22 X 1 %% selection Fitness = zeros(22,1); for a = 1:22 Fitness(a) = (1/(1+F_obj(a))) ; end S = sum(Fitness); Prob_of_cromosome = Fitness/S; roullet = zeros(22,1); roullet (1) = Prob_of_cromosome (1); for a = 2:22; roullet (a) = roullet (a-1) + Prob_of_cromosome (a ); %CDF end

11. %% new set of cromosome for a = 1 : 22 r = rand; if (r <= roullet (1)) new_cromosome_id = 1; else for b = 1 : 21 if (r > roullet (b) & r <= roullet (b+1)) new_cromosome_id = b+1; end end end C(a,:) = C ( new_cromosome_id ,:); end

12. %% Cross Over C_new = C; for a= 1:22 r_crossover = rand(); if( r_crossover < 0.7) r_location = 10*round(rand(),1); % generates random number between 0 to 10. It selects location for crossover for b = r_location+1 : 22 if (a==22) C_new ( a,b )= C(1,b); C_new (1,b) = C(22,b); else C_new ( a,b )= C(a+1,b); C_new (a+1,b) = C( a,b ); end end end end

13. %% Mutation Probability 0.1 for a=1:22 for b=1:22 if(rand < 0.1) C_new ( a,b )= round(((0.02-0.001)*rand+0.001),3); end end end

14. %% Truss code coordinate=[0 0 ;3 0 ;6 0;9 0; 12 0; 15 0; 18 0;15 7; 12 7; 9 7; 6 7; 3 7;]; connectivity=[1 2;2 3;3 4;4 5;5 6; 6 7; 7 8;8 9; 9 10;10 11; 11 12;1 12; 2 12;3 12;3 11; 4 11;4 9; 4 10; 5 9; 5 8;6 8; 7 8]; boundary=[1 1 ; 0 0 ; 0 0 ;0 0 ;0 0;0 0; 1 1;0 0; 0 0;0 0;0 0;0 0]; load=[0 0 0 -550e3 0 -550e3 0 -550e3 0 -550e3 0 -550e3 0 0 0 0 0 0 0 0 0 0 0 0]; Elasticity=2.E+11*[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1];

15. %% Penalty abs_unknown_displacement = abs( unknown_displacement ); count = 0; for k = 1 : 22 for l = 1:20 if( abs_unknown_displacement ( k,l )-0.050 > 0) count = count + 1; end C_new (k,:)= (1+0.05*count)* C_new (k,:); end end

16. Results

17. Results

18. member 1 2 3 4 5 6 7 8 9 10 11 0.019 0.004 0.016 0.015 0.019 0.008 0.005 0.008 0.012 0.014 0.019 0.019 0.015 0.016 0.003 0.009 0.015 0.005 0.008 0.003 0.014 0.003 0.019 0.015 0.016 0.017 0.009 0.008 0.005 0.006 0.01 0.008 0.019 0.019 0.015 0.016 0.003 0.005 0.014 0.005 0.011 0.003 0.014 0.003 0.019 0.004 0.016 0.015 0.019 0.019 0.005 0.006 0.01 0.008 0.015 0.019 0.015 0.016 0.003 0.005 0.016 0.013 0.008 0.003 0.014 0.003 0.019 0.011 0.016 0.003 0.005 0.016 0.009 0.008 0.003 0.014 0.003 0.019 0.004 0.016 0.003 0.005 0.016 0.013 0.017 0.003 0.003 0.003 0.019 0.015 0.016 0.015 0.019 0.008 0.005 0.008 0.012 0.014 0.003 0.019 0.004 0.016 0.019 0.011 0.008 0.005 0.006 0.01 0.008 0.005 0.008 0.015 0.016 0.015 0.019 0.008 0.005 0.008 0.016 0.014 0.003 0.019 0.015 0.016 0.009 0.005 0.016 0.013 0.008 0.003 0.014 0.003 0.006 0.004 0.016 0.015 0.019 0.008 0.005 0.008 0.012 0.014 0.016 0.019 0.015 0.016 0.003 0.005 0.016 0.013 0.008 0.003 0.014 0.016 0.019 0.015 0.016 0.007 0.019 0.014 0.019 0.008 0.019 0.014 0.003 0.019 0.002 0.016 0.015 0.005 0.016 0.013 0.008 0.003 0.014 0.003 0.019 0.004 0.016 0.015 0.019 0.014 0.005 0.008 0.019 0.014 0.003 0.019 0.015 0.016 0.003 0.005 0.015 0.005 0.008 0.003 0.016 0.003 0.019 0.015 0.006 0.003 0.009 0.016 0.013 0.008 0.003 0.014 0.003 0.019 0.015 0.009 0.017 0.009 0.002 0.009 0.009 0.01 0.015 0.016 0.019 0.015 0.016 0.014 0.005 0.016 0.013 0.008 0.003 0.014 0.003 0.019 0.015 0.016 0.003 0.005 0.016 0.013 0.008 0.003 0.014 0.003 value 0.019 0.015 0.016 0.003 0.005 0.015 0.005 0.008 0.003 0.014 0.003 times 20 14 20 9 6 14 10 16 12 17 15

19. 12 13 14 15 16 17 18 19 20 21 22 0.008 0.014 0.016 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.011 0.016 0.008 0.017 0.006 0.002 0.004 0.014 0.012 0.016 0.002 0.013 0.017 0.003 0.016 0.012 0.006 0.008 0.014 0.012 0.008 0.002 0.018 0.016 0.014 0.01 0.006 0.008 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.012 0.016 0.014 0.02 0.006 0.002 0.008 0.014 0.019 0.007 0.002 0.018 0.016 0.014 0.01 0.019 0.002 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.016 0.007 0.002 0.018 0.016 0.014 0.017 0.006 0.002 0.004 0.014 0.012 0.016 0.002 0.012 0.017 0.003 0.016 0.012 0.006 0.008 0.014 0.002 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.02 0.016 0.001 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.019 0.017 0.007 0.002 0.018 0.019 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.001 0.012 0.007 0.002 0.018 0.011 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.004 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.008 0.013 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.015 0.012 0.016 0.002 0.002 0.017 0.017 0.007 0.012 0.002 0.008 0.014 0.012 0.007 0.014 0.018 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.006 0.002 0.004 0.016 0.014 0.01 0.006 0.002 0.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.002 20 19 17 18 21 16 20 16 15 18 19