Matlab圆筒特征值屈曲分析详解

Matlab圆筒特征值屈曲分析

% 圆筒特征值屈曲分析
clear;
clc;
% 圆筒的物理参数
diameter = 0.1;    % 圆筒直径(m)
thickness = 0.01;  % 圆筒壁厚(m)
E = 200e9;         % 弹性模量(Pa)
nu = 0.3;          % 泊松比
% 圆筒的几何参数
L = 1.0;           % 圆筒长度(m)
r = diameter / 2;  % 圆筒半径(m)
% 组装圆筒的刚度矩阵
K = cylinder_stiffness(L, r, thickness, E, nu);
% 求解圆筒的特征值和特征向量
[eig_vec, eig_val] = eig(K);
% 选取最小特征值对应的特征向量，并对其进行范数化
min_eig_val = min(diag(eig_val));
min_eig_vec = eig_vec(:, diag(eig_val) == min_eig_val);
min_eig_vec = min_eig_vec / norm(min_eig_vec);
% 按照自然坐标系、仿射坐标系、柱坐标系、螺旋坐标系，以及原始坐标系分别绘制圆筒的形态
figure(1); clf;
plot_cylinder(L, r, thickness, min_eig_vec, 'x');

以下是 `cylinder_stiffness` 和 `plot_cylinder` 函数的代码示例，供参考：

```
function K = cylinder_stiffness(L, r, thickness, E, nu)
% 组装圆筒的刚度矩阵
% L：圆筒长度(m)，r：圆筒半径(m)，thickness：圆筒壁厚(m)，E：弹性模量(Pa)，nu：泊松比

% 矩阵各个块的系数
k11 = E * r / (2 * (1 - nu^2) * thickness);
k12 = E * r^3 / (12 * (1 - nu^2) * thickness^3);
k22 = E * thickness / (2 * (1 - nu^2) * r);

% 矩阵的各个块
K11 = k11 * [L / r + 4 * r / thickness, -6 * r / thickness; -6 * r / thickness, 4 * r^3 / (thickness^3)];
K12 = k12 * [-2 * L / r + 2 * r / thickness, L / r - 4 * r / thickness; L / r - 4 * r / thickness, -L / r + 2 * r / thickness];
K21 = K12;
K22 = k22 * [4 * L * thickness / r + 12 * thickness^2 / r^2, -6 * L * thickness / r - 12 * thickness^2 / r^2; -6 * L * thickness / r - 12 * thickness^2 / r^2, 4 * L * thickness^3 / (r^3) + 12 * thickness^2 / r^2];

% 组装刚度矩阵
K = [K11, K12; K21, K22];

end
```

```
function plot_cylinder(L, r, thickness, coords, marker)
% 根据给定的坐标系(coords)，绘制圆筒的形态
% L：圆筒长度(m)，r：圆筒半径(m)，thickness：圆筒壁厚(m)，coords：坐标系，marker：绘制圆筒时使用的标记

% 将圆筒分成的段数
nsegments = 20;

% 坐标系变换矩阵
if strcmp(coords, 'affine')
    M = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1];
elseif strcmp(coords, 'cylindrical')
    M = [cos(pi/4), sin(pi/4), 0, 0; -sin(pi/4), cos(pi/4), 0, 0; 0, 0, 1, 0; 0, 0, 0, 1];
elseif strcmp(coords, 'helical')
    M = [cos(pi/4), sin(pi/4), 0, 0; -sin(pi/4), cos(pi/4), 0, 0; 0, 0, 1, 0; 0, 0, 2*pi/L, 1];
elseif strcmp(coords, 'original')
    M = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1];
else
    error('Invalid coordinate system!');
end

% 圆的角度向量
theta = linspace(0, 2*pi, nsegments);

% 绘制圆筒的底面和顶面
x = [r*cos(theta); r*cos(theta)] + L/2;
y = [r*sin(theta); r*sin(theta)];
z = [-ones(1, nsegments) * L/2; ones(1, nsegments) * L/2];
X = [x; markers(nsegments + 1:end)];
Y = [y; markers(nsegments + 1:end)];
Z = [z; markers(nsegments + 1:end)];
P = [X; Y; Z; ones(1, 2*nsegments+2)];
P = M * P;
plot3(P(1,:), P(2,:), P(3,:), marker, 'LineWidth', 2); hold on;

% 绘制圆筒的侧面
for i = 1:nsegments
    x = [r*cos(theta(i)), r*cos(theta(i+1)); r*cos(theta(i)), r*cos(theta(i+1))] + L/2;
    y = [r*sin(theta(i)), r*sin(theta(i+1)); r*sin(theta(i)), r*sin(theta(i+1))];
    z = [-L/2, -L/2; L/2, L/2];
    X = [x; markers(3:4)];
    Y = [y; markers(3:4)];
    Z = [z; markers(3:4)];
    P = [X; Y; Z; ones(1, 4)];
    P = M * P;
    plot3(P(1,:), P(2,:), P(3,:), marker, 'LineWidth', 2);
end

% 设置图像属性
axis equal; axis off; view(40, 30); hold off;

end
```

这里 `plot_cylinder` 函数可以根据需要自行更改以绘制更加符合实际的圆筒形态

免责声明：本文系网络转载或改编，未找到原创作者，版权归原作者所有。如涉及版权，请联系删