%
%subroutine objective funtion
%file name = cable_obj.m
%cable nonlinear problem
%objective function
%Total Potential Energy
%Prof. Reyolando Brasil - May 2021
%Design variables:  x(1) = u   x(2) = v
function p=cable_obj(x,Prob_data)
%problem data
V=Prob_data(1);%vertical load V, KN
H=Prob_data(2);%horizontal load H, KN
A=Prob_data(3);%cable cross section, mē
E=Prob_data(4);%Young's Modulus,KN/mē
La=Prob_data(5);%La length, m
Lb=Prob_data(6);%Lb length, m
N0=Prob_data(7);%N0 KN
ka=E*A/La;kb=E*A/Lb;
%stretched length
LLa=sqrt(x(2)^2+(La+x(1))^2);
LLb=sqrt(x(2)^2+(Lb-x(1))^2);
%length change
da=LLa-La;db=LLb-Lb;
%axial forces
Na=ka*da;Nb=kb*db;
%strain energy
U=(N0+Na/2)*da+(N0+Nb/2)*db;
%work of external conservative forces
W=H*x(1)+V*x(2);
%Total Potential Energy
p=U-W;