MATLAB: How to generate a figure/plot with a curve that connects the point data from the for loop

Question

I understand that it not best practice to try and plot data extracted from a for loop statement, but I cannot think of another way to perform the matrix computation, seeing as matrix "x" is a matrix containing other matrices (i.e. S11bar, S12bar, S22bar, S16bar, S26bar, S66bar), and linear algebraic conditions cannot be satisfied for the matrix multiplication operation.

E1 = 161.3; 
E2 = 8.4; 
v12 = 0.32;
G12 = 5.2; 
S11 = 1/E1;
S22 = 1/E2;
S12 = -v12/E1;
S66 = 1/G12;
A = [epsilon_xx; 0; gamma_xy];
B = [-1; sigma_yy; 0];
figure; hold on
for th = -90:15:90
m = cosd(th);
n = sind(th);
S11bar = S11*m.^4+(2*S12+S66)*n.^2.*m.^2+S22*n.^4;
S12bar = (S11+S22-S66)*n.^2.*m.^2+S12*(n.^4+m.^4);
S22bar = S11*n.^4+(2*S12+S66)*n.^2.*m.^2+S22*m.^4;
S16bar = (2*S11-2*S12-S66)*n.*m.^3+(2*S12-2*S22+S66)*n.^3.*m;
S26bar = (2*S11-2*S12-S66)*n.^3.*m+(2*S12-2*S22+S66)*n.*m.^3;
S66bar = 2*(2*S11+2*S22-4*S12-S66)*n.^2.*m.^2+S66*(n.^4+m.^4);
x = [S11bar S12bar S16bar; S12bar S22bar S26bar; S16bar S26bar S66bar];
matrixeqn = A == x*B;
sol = solve(matrixeqn);
v_sigma_yy = double(sol.sigma_yy);
plot(th,v_sigma_yy,'-*','LineWidth',3);
xlabel('\theta (degrees)');
xticks([-90:45:90]);
ylabel('${\sigma}_{yy}$','Interpreter','Latex');
yticks('auto');
set(gca,'FontSize',16);
end
hold off

Thanks for your help!

Answer 1

Use numerical solution for this kind of problems

A = [S11bar S12bar S16bar; S12bar S22bar S26bar; S16bar S26bar S66bar];
y = A\B;
sigma(i,:) = y';                % write result in array

See the attached script