MATLAB,在主应力空间内,绘制mises屈服面在π平面轨迹
时间: 2023-10-22 13:04:53 浏览: 74
在MATLAB中,可以使用以下步骤绘制Mises屈服面在π平面的轨迹:
1. 首先,定义Mises应力函数:
```matlab
function [sigma_m] = mises(sigma)
% Calculate Mises stress from stress tensor
sigma_dev = sigma - trace(sigma)/3*eye(3);
sigma_m = sqrt(1.5*sum(diag(sigma_dev).^2));
end
```
2. 然后,生成一个π平面的网格点:
```matlab
theta = linspace(0,2*pi,100);
pi_plane = [cos(theta); sin(theta); zeros(size(theta))];
```
3. 接下来,将网格点投影到主应力空间,计算每个点的Mises应力值:
```matlab
% Define stress tensor invariants
I1 = trace(sigma);
I2 = 0.5*(trace(sigma)^2 - trace(sigma^2));
I3 = det(sigma);
% Calculate principal stresses
p = [1 -I1 I2 -I3];
eigvals = roots(p);
[sigma1, ind1] = max(eigvals);
[sigma3, ind3] = min(eigvals);
sigma2 = I1 - sigma1 - sigma3;
% Calculate Mises stress
sigma = [sigma1 0 0; 0 sigma2 0; 0 0 sigma3];
sigma_m = mises(sigma);
% Project onto pi plane
pi_proj = pi_plane - (pi_plane'*sigma/pi_plane'*pi_plane)*sigma/pi_plane'*sigma;
pi_proj_m = zeros(1,length(theta));
for i = 1:length(theta)
sigma_proj = pi_proj(:,i)'*sigma*pi_proj(:,i)/(pi_proj(:,i)'*pi_proj(:,i));
pi_proj_m(i) = mises(sigma_proj);
end
```
4. 最后,绘制Mises屈服面在π平面的轨迹:
```matlab
figure;
plot(pi_proj_m/pi_plane(1,:),pi_plane(2,:));
xlabel('\pi_1/\sigma_1');
ylabel('\pi_2/\sigma_1');
title('Mises Yield Surface in \pi Plane');
```
这样就可以得到Mises屈服面在π平面的轨迹图。