matlab画莫尔圆与包络线

为了绘制莫尔圆和破坏包络线，可以使用MATLAB中的polarplot函数。下面是一个简单的例子，展示如何使用MATLAB绘制莫尔圆和破坏包络线。

% 定义应力和应变
sigma1 = 100;
sigma2 = 50;
tau12 = 30;
epsilon1 = 0.1;
epsilon2 = -0.05;

% 计算莫尔圆半径和圆心
R = sqrt(((sigma1-sigma2)/2)^2 + tau12^2);
Xc = (sigma1+sigma2)/2;
Yc = 0;

% 绘制莫尔圆
theta = 0:0.01:2*pi;
rho = ones(size(theta))*R;
polarplot(theta, rho, 'k');
hold on;

% 绘制破坏包络线
theta = 0:0.01:2*pi;
rho = zeros(size(theta));
for i = 1:length(theta)
    sigma = Xc + R*cos(theta(i));
    tau = R*sin(theta(i));
    epsilon1p = (sigma-epsilon1)/E;
    epsilon2p = (tau-epsilon2)/G;
    rho(i) = sqrt(epsilon1p^2 + epsilon2p^2);
end
polarplot(theta, rho, 'r');
hold off;

% 添加图例和标题
legend('莫尔圆', '破坏包络线');
title('莫尔圆和破坏包络线');