How to fix symbolic errors

I have the following function defined that will be used in a main script:

function ke = Ke2Diso(E, nu, Xe, Ye)

E_matrix = E/(1-nu^2)*[1 nu 0;nu 1 0;0 0 (1-nu)/2];

syms zeta eta ;

N1 = ((1-zeta)*(1+eta))/4;
N2 = ((1+zeta)*(1+eta))/4; 
N3 = ((1-zeta)*(1-eta))/4; 
N4 = ((1+zeta)*(1-eta))/4;
N = [N1 N2 N3 N4];

dxdzeta = 0;
dxdeta = 0 ;
dydzeta = 0;
dydeta = 0;

for i = 1:4
    dxdzeta =dxdzeta+ Xe(i)*diff(N(i),zeta);
    dxdeta =dxdeta+ Xe(i)*diff(N(i),eta);
    dydzeta =dydzeta+ Ye(i)*diff(N(i),zeta);
    dydeta =dydeta+ Ye(i)*diff(N(i),eta);

end


J = [dxdzeta dydzeta;dxdeta dydeta];

B_xy = zeros(2,4)
for i =1:4
    B_xy(1,i) = diff(N(i),zeta);
    B_xy(2,i) = diff(N(i),eta);
     
end

dNdx_dNdy = inv(J)* B_xy
%2 by 4 matrix

B_e =  [dNdx_dNdy(1,1) 0 dNdx_dNdy(1,2) 0 dNdx_dNdy(1,3) 0 dNdx_dNdy(1,4) 0;...
        0 dNdx_dNdy(2,1) 0 dNdx_dNdy(2,2) 0 dNdx_dNdy(2,3) 0 dNdx_dNdy(2,4) ;...
        dNdx_dNdy(2,1) dNdx_dNdy(1,1) dNdx_dNdy(2,2) dNdx_dNdy(1,2) dNdx_dNdy(2,3) dNdx_dNdy(1,3) dNdx_dNdy(2,4) dNdx_dNdy(1,4)];
%Gauss quadrature
B_e_new = subs(B_e)
%B_e_new = subs(B_e,[zeta,eta],[1/sqrt(3),1/sqrt(3)]) + subs(B_e,[zeta,eta],[1/sqrt(3),-1/sqrt(3)])+...
%            subs(B_e,[zeta,eta],[-1/sqrt(3),1/sqrt(3)])+subs(B_e,[zeta,eta],[-1/sqrt(3),-1/sqrt(3)])
B = B_e_new(1/sqrt(3),1/sqrt(3))+B_e_new(1/sqrt(3),-1/sqrt(3))+B_e_new(-1/sqrt(3),-1/sqrt(3))+B_e_new(-1/sqrt(3),1/sqrt(3))

E_matrix_new = subs(E_matrix)
J_new = subs(J,[zeta,eta],[1/sqrt(3),1/sqrt(3)])+subs(J,[zeta,eta],[-1/sqrt(3),1/sqrt(3)])+subs(J,[zeta,eta],[-1/sqrt(3),-1/sqrt(3)])+subs(J,[zeta,eta],[1/sqrt(3),-1/sqrt(3)])
ke = det(J_new)*(transpose(B)*E_matrix_new*B)

This script has the following error:

Unable to perform assignment because value of type 'sym' is not convertible to 'double'.

Error in Ke2Diso (line 31)
    B_xy(1,i) = diff(N(i),zeta);
    
 Error in K_assembly (line 15)
    ke = Ke2Diso(E, nu, Xe, Ye); % obtain element stiffness matrix

Error in Main2DElastic (line 24)
K = K_assembly(ne, nnodes, X, Y, E, nu, nodemap);

Caused by:
    Error using symengine
    Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.
    

I'm pretty confused about how to use subs properly. Can someone help me troubleshoot it?

Answer 1

[Star Strider]

The problem is in ‘line 31’ and I suspect the reason is that ‘B_xy’ is initialised as a double array.

I have no idea what the arguments should be, so see if —

B_xy = sym(zeros(2,4))

B_xy = 

whos B_xy

  Name      Size            Bytes  Class    Attributes

  B_xy      2x4                 8  sym                

will produce the desired result. It appears to work in this isolated example.

.