Numerical 2D Integration in MATLAB - Error

Question

Tyler 2013-3-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/68353-numerical-2d-integration-in-matlab-error

Hi All,

I am having issues with using 2d numerical integration in Matlab 2011b.

I am trying to create a function that takes an input compliance matrix (6x6) and outputs an orientational averaged compliance matrix (6x6).

This is done through the use of transformation equations (which are quite complicated).

Ultimately, I take 2 6x6 transformation matrices (full of cos(x), cos(y), sin(x), sin(y)) and multiply them together with the input stiffness matrix, and then attempt to loop through each cell and numerically integrate to get the orientational average.

I have attached my code:

function[S_prime] = orientation_random_2(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');
m = cos(y);
n = sin(y);
p = cos(x);
q = sin(x);
pi = 3.14159265359;
S_prime_variable = zeros(6);
S_Prime_Temp = zeros(6);
S_Prime = zeros(6);
T1 = [m^2*p^2,n^2*p^2,q^2,-2*n*p*q,-2*m*p*q,2*m*n*p^2;n^2,m^2,0,0,0,2*m*n;m^2*q^2,-n^2*q^2,p^2,-2*n*p*q,(m+n)*p*q,-2*m*n*q^2;n*m*q,-n*m*q,0,m*p,n*p,(m^2-n^2)*q;m^2*p*q,-n^2*p*q,-q*p,n*(p^2-q^2),m*(p^2-q^2),0;m*n*p,m*n*p,0,-m*q,-n*q,(m^2+n^2)*p];
T2 = [m^2*p^2,n^2*p^2,q^2,-n*p*q,-m*p*q,m*n*p^2;n^2,m^2,0,0,0,m*n;m^2*q^2,-n^2*q^2,p^2,-n*p*q,0.5*(m+n)*p*q,-m*n*q^2;2*n*m*q,-2*n*m*q,0,m*p,n*p,(m^2-n^2)*q;2*m^2*p*q,-2*n^2*p*q,-2*q*p,n*(p^2-q^2),m*(p^2-q^2),0;2*m*n*p,2*m*n*p,0,-m*q,-n*q,(m^2+n^2)*p];
S_prime_variable =  T2\S*T1;
for j=1:6
       for i=1:6
          fun = @(x,y)S_prime_variable(i,j)*sin(x);
          S_Prime(i,j)=quad2d(fun,0,pi,0,2*pi);
      end
  end

and my error:

>> Y = orientation_random_2(X)
Undefined function 'max' for input arguments of type 'sym'.
Error in quad2d/tensor (line 353)
              if any(any(abs(Z1-Z0) > max(ATOL,RTOL*max(abs(Z1),abs(Z0)))))
Error in quad2d (line 164)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);
Error in orientation_random_2 (line 40)
          S_Prime(i,j)=quad2d(fun,0,pi,0,2*pi);