problem with double integral, dblquad and quad2d
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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
采纳的回答
Mike Hosea
2012-3-26
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)
更多回答（2 个）
bym
2012-3-25
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
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