Pratt Truss Optimization Using Genetic Algorithm

By :- Harish Kant SoniRoll No:- 12CE31004

Use of Pratt truss

Fig :- Gatton Railway Bridge, Queensland, Australia

Image Source :- https://commons.wikimedia.org/wiki/File:Gatton_Railway_Bridge.JPG

Forces in Pratt truss

Image source :-http://www.slideshare.net/sheikhjunaidyawar/trusses-28955458

F

18 m

7 m

LoadingTrain’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

18 m

7 m

18 m

7 m

Dead Load = 150 kN/ meter/ sideTotal dead load = 150 x 18 = 2700 KN

Live load = 800 KN

550 KN550 KN

550 KN 550 KN 550 KN

12 3 4 5 6 7

12 11 10 9 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^2disp at any node < 50 mm

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];

F_obj= sum(C,2); % return sum of rows in a column matrix of 22 X 1

%% selectionFitness = 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); %CDFend

%% 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

%% 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 endend

%% Mutation Probability 0.1for 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 endend

%% Truss codecoordinate=[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];

%% 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

Results

Results

member 1 2 3 4 5 6 7 8 9 10 110.019 0.004 0.016 0.015 0.019 0.008 0.005 0.008 0.012 0.014 0.0190.019 0.015 0.016 0.003 0.009 0.015 0.005 0.008 0.003 0.014 0.0030.019 0.015 0.016 0.017 0.009 0.008 0.005 0.006 0.01 0.008 0.0190.019 0.015 0.016 0.003 0.005 0.014 0.005 0.011 0.003 0.014 0.0030.019 0.004 0.016 0.015 0.019 0.019 0.005 0.006 0.01 0.008 0.0150.019 0.015 0.016 0.003 0.005 0.016 0.013 0.008 0.003 0.014 0.0030.019 0.011 0.016 0.003 0.005 0.016 0.009 0.008 0.003 0.014 0.0030.019 0.004 0.016 0.003 0.005 0.016 0.013 0.017 0.003 0.003 0.0030.019 0.015 0.016 0.015 0.019 0.008 0.005 0.008 0.012 0.014 0.0030.019 0.004 0.016 0.019 0.011 0.008 0.005 0.006 0.01 0.008 0.0050.008 0.015 0.016 0.015 0.019 0.008 0.005 0.008 0.016 0.014 0.0030.019 0.015 0.016 0.009 0.005 0.016 0.013 0.008 0.003 0.014 0.0030.006 0.004 0.016 0.015 0.019 0.008 0.005 0.008 0.012 0.014 0.0160.019 0.015 0.016 0.003 0.005 0.016 0.013 0.008 0.003 0.014 0.0160.019 0.015 0.016 0.007 0.019 0.014 0.019 0.008 0.019 0.014 0.0030.019 0.002 0.016 0.015 0.005 0.016 0.013 0.008 0.003 0.014 0.0030.019 0.004 0.016 0.015 0.019 0.014 0.005 0.008 0.019 0.014 0.0030.019 0.015 0.016 0.003 0.005 0.015 0.005 0.008 0.003 0.016 0.0030.019 0.015 0.006 0.003 0.009 0.016 0.013 0.008 0.003 0.014 0.0030.019 0.015 0.009 0.017 0.009 0.002 0.009 0.009 0.01 0.015 0.0160.019 0.015 0.016 0.014 0.005 0.016 0.013 0.008 0.003 0.014 0.0030.019 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 0.003times 20 14 20 9 6 14 10 16 12 17 15

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 0.0020.008 0.014 0.012 0.007 0.002 0.011 0.016 0.008 0.017 0.006 0.0020.004 0.014 0.012 0.016 0.002 0.013 0.017 0.003 0.016 0.012 0.0060.008 0.014 0.012 0.008 0.002 0.018 0.016 0.014 0.01 0.006 0.0080.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.014 0.012 0.007 0.002 0.012 0.016 0.014 0.02 0.006 0.0020.008 0.014 0.019 0.007 0.002 0.018 0.016 0.014 0.01 0.019 0.0020.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.014 0.016 0.007 0.002 0.018 0.016 0.014 0.017 0.006 0.0020.004 0.014 0.012 0.016 0.002 0.012 0.017 0.003 0.016 0.012 0.0060.008 0.014 0.002 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.02 0.016 0.001 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.019 0.017 0.007 0.002 0.018 0.019 0.014 0.01 0.006 0.0020.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.001 0.012 0.007 0.002 0.018 0.011 0.014 0.01 0.006 0.0020.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.014 0.012 0.007 0.004 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.014 0.012 0.007 0.002 0.018 0.016 0.008 0.013 0.006 0.0020.008 0.014 0.012 0.007 0.002 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.015 0.012 0.016 0.002 0.002 0.017 0.017 0.007 0.012 0.0020.008 0.014 0.012 0.007 0.014 0.018 0.016 0.014 0.01 0.006 0.0020.008 0.014 0.012 0.006 0.002 0.004 0.016 0.014 0.01 0.006 0.0020.008 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