%file name = plate_con.m
%optimization of simply supported rectangular steel plate
%uniformly loaded and own weight
%design variable thickness x, m
%constraints
%Prof. Reyolando Brasil - May 2021
function [g,h]=plate_con(x,Prob_data)
%problem data
a=Prob_data(1);%lenght in x direction, m
b=Prob_data(2);%lenght in y direction, m
q=Prob_data(3);%uniform loading, N/m²
rho=Prob_data(4);%steel density, kg/m³
Ta=Prob_data(5);%steel alowble stress, N/m²
E=Prob_data(6);%steel Young's Modulus, N/m²
nu=Prob_data(7);%Poisson's ratio
%
D=E*x^3/12/(1-nu^2);
w=x^2/6;
%
r=round(b/a,1);%b/a ratio, between 1 and 2, 11 possible values, round to first decimal
k=10*(r-1)+1;%table position
qmp=q+10*rho*x;%gravity acceleration 10 m/s²
%
%Table 8 "Theory of Plates an Shells", Timoshenko
%
alfa=[0.00406; 0.00485; 0.00564;  0.00638; 0.00705; 0.00772; 0.00830; 0.00883; 0.00931; 0.00974; 0.01013];
%
beta=[0.0479; 0.0554; 0.0627;  0.0694; 0.0755; 0.0812; 0.0862; 0.0908; 0.0948; 0.0985; 0.1017];
%
vmax=alfa(k)*qmp*a^4/D;%maximum vertical displacement, m
%
Mx_max=beta(k)*qmp*a^2;%maximun bending moment Mx, Nm/m
%constraints
g(1)=(Mx_max/w)/Ta-1;
g(2)=400*vmax/a-1;
%
h=[];