MATLAB: Problem using a double integral function: integral2

double integralintegral2

I can't calculate the integral using the function integral2, matlab gives the following error
>> Untitled
Undefined function 'mpower' for input arguments of type 'function_handle'.
Error in @(x,y)Dx*(dwidx2)^2+Dy*(dwidy2)^2+Dxy*dwidx2*dwidy2+4*G*dwidydx2
Error in integral2Calc>integral2t/tensor (line 229)
        Z = FUN(X,Y);  NFE = NFE + 1;
Error in integral2Calc>integral2t (line 56)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);
Error in integral2Calc (line 10)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);
Error in integral2 (line 107)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);
Error in Untitled (line 39)
    integral2(func,0,1.436,0,1.981)
my program is as follows:
clear all 
a=1.436;
b=1.981;
Nx=0.947;
Ny=0.639;
Nxy=0.799;
Dx=1;
Dy=1;
Dxy=1;
G=12*10^9;
M = eye(9,2);
A = eye(9,1);
%matriz que define os pontos
i=1;
for m=1:3
    for n=1:3
       M(i,:)= [m n];
       i=i+1;
    end 
end
for i=1:9
    m=M(i,1);
    n=M(i,2);
      ym=(4*m+1)*(pi/4);
      yn=(4*n+1)*(pi/4);
      Xm=@(x)(cosh(((ym/b)^2)*x)-cos((ym/b)^2*x))-((cosh((ym^2)/b)-cos((ym^2)/b))/((sinh((ym^2)/b)-sin((ym^2)/b))))*(sinh((ym/b)^2*x)-sin((ym/b)^2*x));
      Yn=@(y) cosh(((yn/a)^2)*y)+cos((yn/a)^2*y)-((cosh((yn^2)/a)+cos((yn^2)/a))/(sinh((yn^2)/a)+sin((yn^2)/a)))*(sinh((yn/a)^2*y)+sin((yn/a)^2*y));
      wi=@(x,y)Xm*Yn; 
      dwidx2=@(x,y)diff(wi,x,2);
      dwidy2=@(x,y)diff(wi,y,2);
      dwidydx2=@(x,y)diff(diff(wi,x),y);
      func=@(x,y)Dx*(dwidx2)^2+Dy*(dwidy2)^2+Dxy*dwidx2*dwidy2+4*G*dwidydx2;
      integral2(func,0,1.436,0,1.981)
  end

Best Answer

Look again at the lines such as
dwidydx2=@(x,y)diff(diff(wi,x),y);
func=@(x,y)Dx*(dwidx2)^2+Dy*(dwidy2)^2+Dxy*dwidx2*dwidy2+4*G*dwidydx2;
dwidx2 and dwidy2 and dwidx2 and dwidy2 and dwidydx2 are function handles, so you are trying to do arithmetic operations on function handles.
You want to instead invoke the function handles on actual arguments, such as
func=@(x,y)Dx*(dwidx2(x,y))^2+Dy*(dwidy2(x,y))^2+Dxy*dwidx2(x,y)*dwidy2(x,y)+4*G*dwidydx2(x,y);
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