Question

matlab解方程组，答案是sym没有具体数值

clear all
clc

E=2*10^5;
v=0.3;
G=E/(2*(1+v));
lambda=(v*E)/((1+v)*(1-2*v));
epsilon11=1.7833*10^-3;
epsilon22=1.6*10^-3;
syms sigma11 sigma22 epsilon33;

eq1=sym('sigma11=2*G*epsilon11+lambda*(epsilon11+epsilon22+epsilon33)');
eq2=sym('sigma22=2*G*epsilon22+lambda*(epsilon11+epsilon22+epsilon33)');
eq3=sym('epsilon33=-v*(sigma11+sigma22)/E');

[sigma11,sigma22,epsilon33]=solve(eq1,eq2,eq3);
sigma11=vpa(sigma11,8);
sigma22=vpa(sigma22,8);
epsilon33=vpa(epsilon33,8);

程序如上，需要的答案sigma11, sigma22, epsilon33都是1x1 sys类型，没有具体数字，请问怎么解决？

Answer 1

修改如下：
clear all; clc

E=2*10^5;
v=0.3;
G=E/(2*(1+v));
lambda=(v*E)/((1+v)*(1-2*v));
epsilon11=1.7833*10^-3;
epsilon22=1.6*10^-3;
syms sigma11 sigma22 epsilon33;

eq1= sigma11==2*G*epsilon11+lambda*(epsilon11+epsilon22+epsilon33);
eq2= sigma22==2*G*epsilon22+lambda*(epsilon11+epsilon22+epsilon33);
eq3= epsilon33==-v*(sigma11+sigma22)/E;

[sigma11,sigma22,epsilon33]=solve(eq1,eq2,eq3);
sigma11=vpa(sigma11,8);
sigma22=vpa(sigma22,8);
epsilon33=vpa(epsilon33,8);

val_sigma11 = double(sigma11)
val_sigma22 = double(sigma22)
val_epsilon33 = double(epsilon33)

matlab2013b下运行通过，版本太低了别怪别人。
val_sigma11 =

-0.0014

val_sigma22 =

497.4286

val_epsilon33 =

469.2286

追问

正确答案应该是epsilon33=-0.0014， sigma11=497.4286，sigma22=469.2286。

答案位置错了，请问是怎么回事？

追答

[epsilon33, sigma11, sigma22]=solve(eq1,eq2,eq3, epsilon33, sigma11, sigma22);

solve那句这么改试试。

Answer 2

解方程组失效，可将程序改为：
clear
E=2*10^5;
v=0.3;
G=E/(2*(1+v));
lambda=(v*E)/((1+v)*(1-2*v));
epsilon11=1.7833*10^-3;
epsilon22=1.6*10^-3;
epsilon33=-2*v*(G+lambda)*(sigma11+sigma22)/(2*v+E)
sigma11=2*G*epsilon11+lambda*(epsilon11+epsilon22+epsilon33)
sigma22=2*G*epsilon22+lambda*(epsilon11+epsilon22+epsilon33)

最后运行结果是：
>> epsilon33=-2*v*(G+lambda)*(epsilon11+epsilon22)/(2*v+E)
epsilon33 =
-0.0020
>> sigma11=2*G*epsilon11+lambda*(epsilon11+epsilon22+epsilon33)
sigma11 =
439.5156
>> sigma22=2*G*epsilon22+lambda*(epsilon11+epsilon22+epsilon33)
sigma22 =
411.3156