Error with contourf representing 3d plot in 2d

Good afternoon,

I have been trying to compile a contour surface of my 3d object in the sig1-sig2 space (X-Y). When compiling it shows as an error and im not sure why.

Heres the code

clc; clear;

sig1c = .35031092712186400; 
sig1t = .35031092712186400;  %.39026571574305700
sig2c = sig1c;
sig2t = sig1t;
% sig3c = .56181805055156500;
% sig3t = .02333758968994630;

sig3c = sig1c; %will reduce to von misses if sig1t = sig1c
sig3t = sig1t;

tau23 = .07;  %sheer strenth, tau23 is symetric with tau13 
tau13 = tau23;
tau12 = .23; 

F1 = ((1/sig1t)-(1/sig1c));
F2 = ((1/sig2t)-(1/sig2c));
F3 = ((1/sig3t)-(1/sig3c));
F11 = (1/(sig1c*sig1t));
F22 = (1/(sig2c*sig2t));
F33 = (1/(sig3c*sig3t));
F44 = (1/(tau23^2));
F55 = (1/(tau13^2));
F66 = (1/(tau12^2));
F12 = -0.5*sqrt((F11*F22)); %only defines a range for F12, complete determination for orthotropic materials still needs to be resolved.
F13 = -0.5*sqrt((F11*F33));
F23 = -0.5*sqrt((F22*F33));

syms sig1 sig2 sig3 G

    [sig1,sig2,sig3] = meshgrid(linspace(-2,2,100));

    sig1b = 0;
    sig2b = 0;
    sig3b = 0;
   
    Data = sqrt(sig1.^2+sig2.^2+sig3.^2);
     G = F1.*sig1 + F11.*sig1.^2 + F2.*sig2 + F22.*sig2.^2 + F3.*sig3 + F33.*sig3.^2 + (2*F12.*sig1.*sig2) + (2*F13.*sig1.*sig3) + (2*F23.*sig2.*sig3) - 1;
    %G = F1.*sig1 + F11.*sig1.^2 + F2.*sig2 + F22.*sig2.^2 + F3.*sig3 + F33.*sig3.^2 + F44.*tau23.^2 + F55.*tau13.^2 + F66.*tau12.^2 + (2*F12.*sig1.*sig2) + (2*F13.*sig1.*sig3) + (2*F23.*sig2.*sig3) - 1;
    G(G>1) = 1;
    
    tiledlayout(1,2)
    
   nexttile
    Stich = patch(isosurface(sig1,sig2,sig3,G,0));
    isonormals(sig1,sig2,sig3,G,Stich)
    isocolors(sig1,sig2,sig3,Data,Stich)
    colormap(turbo(9))
    shading interp
%     Stich.FaceColor = 'interp';
%     Stich.EdgeColor = 'black';
    
    xlabel("\sigma_1 (GPa)");
    ylabel("\sigma_2 (GPa)");
    zlabel("\sigma_3 (GPa)");
    title('Tsai-Wu Ultimate Yield Surface');
    view(3);
    axis padded
    grid on
    colorbar
    
   nexttile

   [sig1,sig2] = contourf(G)

Error using contourf (line 55)
Input arguments must have at most 2 dimensions.

Sorry for the long intro, but as you can see the problem is at the last line of the code.

Thank you for the time,

Kevin

Answer 1

[Simon Chan]

Refer to the MATLAB documentation in this Link

contourf(X,Y,Z) specifies the x and y coordinates for the values in Z.

However, varaiable G is a 3-dimensional matrix and hence it gives an error.

Assume you would like to add all the values in the 3rd dimension, you can sum them up, create a matrix H and replace the last line with the following lines. You can obtain the attached figure.

contourf(linspace(-2,2,100),linspace(-2,2,100),H);
axis equal
colorbar
xlabel("\sigma_1 (GPa)");
ylabel("\sigma_2 (GPa)");
title('Sum up z-dimension data');

Noticed that I don't have the Symbolic Math Toolbox and hence skips the following line when running the code

syms sig1 sig2 sig3 G

[Kevin Hanekom]

This is amazing! Thank you for clearing this up for me. Ill implement the same thing for sig1-sig2, sig2-3 now aswell.

Thanks again!