%
%subroutine constraint functions
%file name = tre_redun_con.m
%redundant truss optimization
%constraint equations
%Prof. Reyolando Brasil - 2021
function [g,h]=tre_redun_con(x,Prob_data)
%design variables
x1=x(1);%vertical bar transverse section area, mē
x2=x(2);%diagonal bar transverse section area, mē
%problem data
PP=Prob_data(1);%gravity load P, KN
Ta=Prob_data(3);%alowble stress, KN/mē
E=Prob_data(4);%Young's Modulus, KN/mē
%solution
K=E*[x1+x2*sqrt(2)/4 -x1;-x1 x1+x2*sqrt(2)/4];%stiffness matrix
P=[0;-PP];%loading vector
p=K\P;%displacements vector
%bars normal forces
N1=E*x1*(p(1)-p(2));
N4=-E*x2*p(2)/2;
N5=-E*x2*p(1)/2;
%inequality constraints
g(1)=(N1/x1)/Ta-1;
g(2)=(N4/x2)/Ta-1;
g(3)=(N5/x2)/Ta-1;
%equality constraints (none)
h=[];