How can I simplify my my program so as not to give the following warning: Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test. ? ?

Question

Maria 2012-12-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/56019-how-can-i-simplify-my-my-program-so-as-not-to-give-the-following-warning-warning-reached-the-maxim

the full warning is the following:

 Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test. 
> In funfun\private\integral2Calc>integral2t at 130
  In funfun\private\integral2Calc at 10
  In integral2 at 107
  In pjodc at 165 
 Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test. 
> In funfun\private\integral2Calc>integral2t at 130
  In funfun\private\integral2Calc at 10
  In integral2 at 107
  In pjodc at 166 
 Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test. 
> In funfun\private\integral2Calc>integral2t at 130
  In funfun\private\integral2Calc at 10
  In integral2 at 107
  In pjodc at 168 
 Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test. 
> In funfun\private\integral2Calc>integral2t at 130
  In funfun\private\integral2Calc at 10
  In integral2 at 107
  In pjodc at 169 
 Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test. 
> In funfun\private\integral2Calc>integral2t at 130
  In funfun\private\integral2Calc at 10
  In integral2 at 107
  In pjodc at 170

And my program is the following:

clear all 
a=1.436;
b=1.981;
Nx=0.947;
Ny=0.639;
Nxy=0.799;
t=0.0088;
v12=0.23;
E1=60*10^9;
E2=24.8*10^9;
v21=v12*(E2/E1);
p=2620;
Dx=(t^3*E1)/(12*(1-v12*v21));
Dy=(t^3*E2)/(12*(1-v12*v21));
Dxy=(t^3*E1*v21)/(12*(1-v12*v21));
K=56.915;
G=12*10^9;
x = sym('x','real');
y = sym('y','real');
     mi=1
     ni=1
     mj=3
     nj=1
     ymi=(4*mi+1)*(pi/4);
     yni=(4*ni+1)*(pi/4);
     ymj=(4*mj+1)*(pi/4);
     ynj=(4*nj+1)*(pi/4);
     %PARA i
      Hxi=cosh(((ymi/a).^2)*x)-cos((ymi/a).^2*x);
      Fxi=cosh((ymi.^2)/a)-cos((ymi.^2)/a);
      Jxi=sinh((ymi.^2)/a)-sin((ymi.^2)/a);
      Kxi=sinh((ymi/a).^2*x)-sin((ymi/a).^2*x);
      Hyi=cosh(((yni/b).^2)*y)+cos((yni/b).^2*y);
      Fyi=cosh((yni.^2)/b)+cos((yni.^2)/b);
      Jyi=sinh((yni.^2)/b)+sin((yni.^2)/b);
      Kyi=sinh((yni/b).^2*y)+sin((yni/b).^2*y);
      %para j
      Hxj=cosh(((ymj/a).^2)*x)-cos((ymj/a).^2*x);
      Fxj=cosh((ymj.^2)/a)-cos((ymj.^2)/a);
      Jxj=sinh((ymj.^2)/a)-sin((ymj.^2)/a);
      Kxj=sinh((ymj/a).^2*x)-sin((ymj/a).^2*x);
      Hyj=cosh(((ynj/b).^2)*y)+cos((ynj/b).^2*y);
      Fyj=cosh((ynj.^2)/b)+cos((ynj.^2)/b);
      Jyj=sinh((ynj.^2)/b)+sin((ynj.^2)/b);
      Kyj=sinh((ynj/b).^2*y)+sin((ynj/b).^2*y);
      Xmi=Hxi-((Fxi)/(Jxi))*(Kxi);
      Yni=Hyi-((Fyi)/(Jyi))*Kyi;
      Xmj=Hxj-((Fxj)/(Jxj))*(Kxj);
      Ynj=Hyj-((Fyj)/(Jyj))*(Kyj);
      wi=Xmi*Yni; 
      wj=Xmj*Ynj;
      vpa(wi,6);
      vpa(wj,6);
      dwidx2=diff(wi,x,2);
      dwidy2=diff(wi,y,2);
      dwidydx2=diff(diff(wi,x),y);
     dwjdx2=diff(wj,x,2);
     dwjdy2=diff(wj,y,2);
     dwjdydx2=diff(diff(wj,x),y);
     vpa(dwidx2,6);
     vpa(dwidy2,2);
     vpa(dwidydx2,2);
     vpa(dwjdx2,2);
     vpa(dwjdy2,2);
     vpa(dwjdydx2,2);
      dwidx2=matlabFunction(dwidx2);
      dwidy2=matlabFunction(dwidy2);   
      dwidydx2=matlabFunction(dwidydx2);
      dwjdx2=matlabFunction(dwjdx2);
      dwjdy2=matlabFunction(dwjdy2);
      dwjdydx2=matlabFunction(dwjdydx2);
      wj=matlabFunction(wj); 
      wi=matlabFunction(wi);
      func1=@(x,y)Dx.*(dwidx2(x,y).*(dwjdx2(x,y)));
      func2=@(x,y)Dy.*(dwidy2(x,y).*(dwjdy2(x,y)));    
      func3=@(x,y)Dxy.*(dwidx2(x,y).*dwidy2(x,y));
      func4=@(x,y)Dxy.*dwjdx2(x,y).*dwjdy2(x,y);
      func5=@(x,y)4.*G.*dwidydx2(x,y).*dwjdydx2(x,y);
      func6=@(x,y)K.*wi(x,y).*wj(x,y);
      vpa(func1,6);
      vpa(func2,6);
      vpa(func3,6);
      vpa(func4,6);
      vpa(func5,6);
      vpa(func6,6);
      a1=integral2(func1,0,1.436,0,1.981);
      b1=integral2(func2,0,1.436,0,1.981);
      c1=integral2(func3,0,1.436,0,1.981);
      d1=integral2(func4,0,1.436,0,1.981);
      e1=integral2(func5,0,1.436,0,1.981);
      f1=integral2(func6,0,1.436,0,1.981);
      A12=a1+b1+c1+d1+e1+f1;
      A12

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Answer 1

Walter Roberson 2012-12-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/56019-how-can-i-simplify-my-my-program-so-as-not-to-give-the-following-warning-warning-reached-the-maxim#answer_67873

It isn't a matter of simplifying your function that is being integrated: the problem is that at least one of the functions is not sufficiently smooth to be integrated in 10000 calls with the default error tolerance.

You can increase the error tolerance or you can increase the allowed number of function calls. You would use an options structure either way.

4 个评论
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Walter Roberson 2012-12-16

Sorry, it appears that integral2() is not one of the routines that allows maximum number of function calls to be changed. Try reducing the area to be integrated over and see if you can at least get an integral over part of it; if you can then you can start thinking about doing piecewise integration.

Side Note: those vpa() calls are not doing anything useful as you are not displaying the output and not assigning the output to anything.

Mike Hosea 2012-12-17

Right. INTEGRAL2 does not allow for increasing the maximum number of function evaluations, though QUAD2D does. Try using QUAD2D with FailurePlot,'true' to see where the problems are. The formulation seems to have some numerical issues in certain areas. I recommend examining those areas, maybe refactoring the integrand to avoid whatever numerical issues are causing the problem.

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