x=1.73;qq=2.0;L=14;v=0.3;
syms g r;
i=1;
izp=1/(8*pi*(1-v))*((1-2*v)*((i*qq)-L)/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq-L)^2))^3-(1-2*v)*((i*qq)-L)/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^3+3*((i*qq)-L)^3/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq-L)^2))^5+(3*(3-4*v)*(i*qq)*((i*qq)+L)^2-3*L*((i*qq)+L)*(5*(i*qq)-L))/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^5+30*L*(i*qq)*((i*qq)+L)^3/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^7);
求izp对r在0到0.5，g在0到2*pi的双重积分。

梯形积分


>> x=1.73;qq=2.0;L=14;v=0.3;
  syms g r;
  i=1;
izp=1/(8*pi*(1-v))*((1-2*v)*((i*qq)-L)/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq-L)^2))^3-(1-2*v)*((i*qq)-L)/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^3+3*((i*qq)-L)^3/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq-L)^2))^5+(3*(3-4*v)*(i*qq)*((i*qq)+L)^2-3*L*((i*qq)+L)*(5*(i*qq)-L))/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^5+30*L*(i*qq)*((i*qq)+L)^3/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^7);
>> q=int(1/(8*pi*(1-v))*((1-2*v)*((i*qq)-L)/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq-L)^2))^3-(1-2*v)*((i*qq)-L)/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^3+3*((i*qq)-L)^3/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq-L)^2))^5+(3*(3-4*v)*(i*qq)*((i*qq)+L)^2-3*L*((i*qq)+L)*(5*(i*qq)-L))/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^5+30*L*(i*qq)*((i*qq)+L)^3/(sqrt(x^2+r^2-2*r*x*cos(g)+(i*qq+L)^2))^7),0,2*pi);
>> w=int('q',0,.5)
 
w =
 
1/8
 
>>