How to calculate integral of these complicated functions?

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Jamal 2016-11-7

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https://ww2.mathworks.cn/matlabcentral/answers/311030-how-to-calculate-integral-of-these-complicated-functions

评论： Jamal 2016-11-10

Integral.m

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);

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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.

Jamal 2016-11-10