How to calculate integral of these complicated functions?

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Jamal
Jamal 2016-11-7
评论： Jamal 2016-11-10
I have two difficult functions with symbolic parameters (x(1),x(2),x(3),t). I tried to use 'integral'. I tried 'int', but the integral is too complicated and even after 30 mins I get no result- 'busy'. Is there any other method for integral solving? I attach my code here. Would you recommend me how to claculate Integral I and II.
2- then, after calculating integrals, I am trying to fit these integrals to experimental data and acquire those parameteres ( x(1), x(2) ,x(3)). I want to help me to curve fit with experiment data.
Thanks.
clc;
clear all;
%%Analytical solution
beta=0.002;
alfa=0.004;
nu=0.49;
del=0.010;
t0=1.35;
syms eta G1 G2 A s t taw
x=sym('x',[1 3]);
p1=(eta)/(G1+G2);
q1=(2*G1*eta)/(G1+G2);
q0=(2*G1*G2)/(G1+G2);
B1=(2*G1*(1+nu))/(3*(1-2*nu));
B2=(2*G2*(1+nu))/(3*(1-2*nu));
B3=(2*eta*(1+nu))/(3*(1-2*nu));
q2=3*B1*B2/(B1+B2);
q3=B3/(B1+B2);
q4=3*B1*B3/(B1+B2);
Pc1=1+p1*A;
Qc1=q0+q1*A;
Pc2=1+q3*A;
Qc2=q2+q4*A;
f1=Pc1*Qc2*Pc1+2*Pc1*Pc2*Qc1;
c1 = coeffs(f1, A);
c1=simplify(c1);
f2=2*Pc1*Qc1*Qc2+Qc1*Pc2*Qc1;
c2=coeffs(f2,A);
c2=simplify(c2);
GG1= ilaplace((4*beta/(3*t0*sqrt(alfa)))*del*(c2(1,3)*s^2+c2(1,2)*s+c2(1,1))/((c1(1,3)*s^4+c1(1,2)*s^3+c1(1,1)*s^2)), t);
GG2=ilaplace((4*beta/(3*t0*sqrt(alfa)))*del*(c2(1,3)*s^2+c2(1,2)*s+c2(1,1))/((c1(1,3)*s^3+c1(1,2)*s^2+c1(1,1)*s)), t);
GGs1=subs(GG1, t, t-taw);
GGs2=subs(GG2, t, t-taw);
GGss1=subs(GGs1, {G1,G2,eta}, {x(1),x(2),x(3)});
GGss2=subs(GGs2, {G1,G2,eta}, {x(1),x(2),x(3)});
assume(x(1) > 0)
assume(x(2)> 0)
assume(x(3) > 0)
assume(x(1),'real')
assume(x(2),'real')
assume(x(3),'real')
% I want to caluculte Integral I
force1=int(GGss1*diff(taw^1.5,taw),taw,0,t,'IgnoreSpecialCases',true);
% I want to calculate integral II
force2=int(GGss2*diff(taw^1.5,taw),taw,0,t0,'IgnoreAnalyticConstraints',true);
  2 个评论
Jan
Jan 2016-11-7
Please, Jamaleddin , post your code in a readable format, when you want others to read it. Use the "{} Code" button to apply the formatting automatically.

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