problem with double integral, dblquad and quad2d

Question

Ozan 2012-3-25

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/33399-problem-with-double-integral-dblquad-and-quad2d

Hi, I have been struggling to solve an double integral problem for the last couple of weeks. I have read wide variety of questions and answers, I have tried everything I know (int, dblqad, quad2d); however no result I got. The simplfied version of my code is below. After I find the way for below problem I believe I can handle the rest.

syms epsilon eta zeta;

ne=1; me=1; K1=76*10^9; K2=150*10^9; G1=26*10^9; G2=78*10^9;

Vs=(((zeta/2)+(1/2))^ne)*((eta/2)^me);

f1=(G1.*(9.*K1+8.*G1))/(6.*(K1+2*G1));

Gasil=G1+(Vs.*(G2-G1))./(1+(1-Vs).*((G2-G1)./(G1+f1)));

Kasil=K1+(Vs.*(K2-K1))./(1+(1-Vs).*((3.*(K2-K1))./(3.*K1+4.*G1)));

Easil=(9.*Kasil.*Gasil)./(3.*Kasil+Gasil);

K11(dongu1)=(int(int(Easil,eta,-1,1),zeta,-1,1))

It is worth to note that "ne" and "me" are not constant values. I will change them between 0 and 100 to see the effect of "ne" and "me" to K11.

I would really appreciate some help, idea, thought...

Ozan

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Answer 1

Mike Hosea 2012-3-26

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https://ww2.mathworks.cn/matlabcentral/answers/33399-problem-with-double-integral-dblquad-and-quad2d#answer_42126

在 MATLAB Online 中打开

syms ne me epsilon eta zeta;
K1=76*10^9; K2=150*10^9; G1=26*10^9; G2=78*10^9;
Vs=(((zeta/2)+(1/2))^ne)*((eta/2)^me);
f1=(G1.*(9.*K1+8.*G1))/(6.*(K1+2*G1));
Gasil=G1+(Vs.*(G2-G1))./(1+(1-Vs).*((G2-G1)./(G1+f1)));
Kasil=K1+(Vs.*(K2-K1))./(1+(1-Vs).*((3.*(K2-K1))./(3.*K1+4.*G1)));
Easil=(9.*Kasil.*Gasil)./(3.*Kasil+Gasil);
f = matlabFunction(Easil)
ne = 3;
me = 4;
integrand = @(zeta,eta)f(eta,me,ne,zeta);
% Splitting the integral may not be necessary if ne and me are always
% integers, but it does tend to be necessary otherwise, when the output is
% complex.
Q = quad2d(integrand,-1,0,-1,0) + ...
    quad2d(integrand,-1,0,0,1) + ...
    quad2d(integrand,0,1,-1,0) + ...
    quad2d(integrand,0,1,0,1)

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Answer 2

bym 2012-3-25

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https://ww2.mathworks.cn/matlabcentral/answers/33399-problem-with-double-integral-dblquad-and-quad2d#answer_41997

在 MATLAB Online 中打开

Use the matlabFunction() to change the symbolic equation to something dblquad can evaluate:

f = matlabFunction(Easil)
f = 
      @(eta,zeta)-(((26000000000.*eta.*(zeta./2+1./2))./((192.*eta.*(zeta./2+1./2))./415-799./415)-26000000000).*((333000000000.*eta.*(zeta./2+1./2))./((111.*eta.*(zeta./2+1./2))./332-277./166)-684000000000))./((111000000000.*eta.*(zeta./2+1./2))./((111.*eta.*(zeta./2+1./2))./332-277./166)+(26000000000.*eta.*(zeta./2+1./2))./((192.*eta.*(zeta./2+1./2))./415-799./415)-254000000000)
>> dblquad(f,-1,1,-1,1)
ans =
    2.8366e+011