Trouble integrating function & trouble plotting it to see if there are singularities

Hi all,

I have a rather complex function that i am trying to integrate - it is the result of trying to re-orient the compliance matrix of a fibre reinforced epoxy.

the compliance matrix (S) is a 6X6 matrix and is an input The transformation matrices are 2 6x6 matrices (T1, T2)

function[S_prime] = orientation_random_3(S)

% 3D Orientational average of compliance matrix as defined by RUC subject

% to periodic BC's

% T1 = Stress Transformation Matrix

% T2 = Strain Transformation Matrix

% S = Compliance Matrix of RUC

% theta = angle from X1 axis

% phi = angle from X3 axis

% Input 6x6 compliance matrix

% Output 6x6 orientational averaged compliance matrix

syms('x','y');

pi = 3.14159265359;

S_prime_variable = zeros(6); S_Prime = zeros(6);

T1 = [cos(y).^2.*cos(x).^2,sin(y).^2.*cos(x).^2,sin(x).^2,-2.*sin(y).*cos(x).*sin(x),-2.*cos(y).*cos(x).*sin(x),2.*cos(y).*sin(y).*cos(x).^2;sin(y).^2,cos(y).^2,0,0,0,2.*cos(y).*sin(y);cos(y).^2.*sin(x).^2,sin(y).^2.*sin(x).^2,cos(x).^2,-2.*sin(y).*cos(x).*sin(x),2.*cos(y).*cos(x).*sin(x),-2.*cos(y).*sin(y).*sin(x).^2;sin(y).*cos(y).*sin(x),-sin(y).*cos(y).*sin(x),0,cos(y).*cos(x),sin(y).*cos(x),(cos(y).^2-sin(y).^2).*sin(x);cos(y).^2.*cos(x).*sin(x),-sin(y).^2.*cos(x).*sin(x),-sin(x).*cos(x),sin(y).*(cos(x).^2+sin(x).^2),cos(y).*(cos(x).^2-sin(x).^2),0;cos(y).*sin(y).*cos(x),cos(y).*sin(y).*cos(x),0,-cos(y).*sin(x),-sin(y).*sin(x),(cos(y).^2+sin(y).^2).*cos(x)];

T2 = [cos(y).^2.*cos(x).^2,sin(y).^2.*cos(x).^2,sin(x).^2,-sin(y).*cos(x).*sin(x),-cos(y).*cos(x).*sin(x),cos(y).*sin(y).*cos(x).^2;sin(y).^2,cos(y).^2,0,0,0,cos(y).*sin(y);cos(y).^2.*sin(x).^2,sin(y).^2.*sin(x).^2,cos(x).^2,-sin(y).*cos(x).*sin(x),cos(y).*cos(x).*sin(x),-cos(y).*sin(y).*sin(x).^2;2.*sin(y).*cos(y).*sin(x),-2.*sin(y).*cos(y).*sin(x),0,cos(y).*cos(x),sin(y).*cos(x),(cos(y).^2-sin(y).^2).*sin(x);2.*cos(y).^2.*cos(x).*sin(x),-2.*sin(y).^2.*cos(x).*sin(x),-2.*sin(x).*cos(x),sin(y).*(cos(x).^2+sin(x).^2),cos(y).*(cos(x).^2-sin(x).^2),0;2.*cos(y).*sin(y).*cos(x),2.*cos(y).*sin(y).*cos(x),0,-cos(y).*sin(x),-sin(y).*sin(x),(cos(y).^2+sin(y).^2).*cos(x)];

S_prime_variable = T2\S*T1;

%My goal is to integrate each of the 36 terms of S_prime_variable from 0->pi over x, and 0->2pi over y.

for j=1:6

    for i=1:6

        fun = matlabFunction(S_prime_variable(i,j)*sin(x));

        k = int(fun,x);

        l = subs(k,x,pi);
        m = subs(k,x,0);

        n = l-m;

        n2 = matlabFunction(n);

        o = int(n2,y);

        p = subs(o,y,2*pi);
        q = subs(o,y,0);

        S_Prime(i,j) = (p-q);

    end
end

with the above code i get an error @ o:

Error using mupadmex

Error in MuPAD command: Unexpected 'identifier' [line 1, col 253]

Error in sym/int (line 110)

       r = mupadmex('symobj::intindef',f.s,x.s,options);

Error in orientation_random_2 (line 46)

        o = int(n2,y);

I am only integrating this way because i have had incredible amount of trouble trying 2D integration techniques.

Further, while trying to evaluate the functions by creating a meshgrid and meshing the surfaces, i get the following error:

Error using mesh (line 76)

X, Y, Z, and C cannot be complex.

Here is an example input compliance matrix:

X = [0.2174,-0.0630,-0.0630,0,0,0;-0.0630,0.5832,-0.2748,0,0,0;-0.0630,-0.2748,0.5832,0,0,0;0,0,0,0.858,0,0;0,0,0,0,0.858,0;0,0,0,0,0,0.858]

Does anyone have an idea how to evaluate at least what is going on? Im totally lost here and have been struggling for over a week.

Any help would be greatly appreciated!!