matlab单元刚度云图

您好，关于 MATLAB 单元刚度云图，可以通过以下步骤实现：

1. 定义单元刚度矩阵
2. 定义节点坐标矩阵
3. 组装全局刚度矩阵
4. 施加边界条件
5. 求解位移和应力
6. 绘制云图

具体实现方法可以参考以下代码：

% 定义单元刚度矩阵
E = 200e9; % 弹性模量
nu = 0.3; % 泊松比
h = 0.1; % 单元厚度
D = E*h^3/(12*(1-nu^2)); % 弯曲刚度
Ke = D*[12, 6*h, -12, 6*h;
        6*h, 4*h^2, -6*h, 2*h^2;
        -12, -6*h, 12, -6*h;
        6*h, 2*h^2, -6*h, 4*h^2]/(h^3);

% 定义节点坐标矩阵
coord = [0, 0; 0.5, 0; 1, 0; 1.5, 0; 2, 0;
         0, 0.5; 0.5, 0.5; 1, 0.5; 1.5, 0.5; 2, 0.5;
         0, 1; 0.5, 1; 1, 1; 1.5, 1; 2, 1;
         0, 1.5; 0.5, 1.5; 1, 1.5; 1.5, 1.5; 2, 1.5;
         0, 2; 0.5, 2; 1, 2; 1.5, 2; 2, 2];

% 定义单元节点编号矩阵
elem = [1, 7, 8, 2;
        2, 8, 9, 3;
        3, 9, 10, 4;
        4, 10, 11, 5;
        7, 12, 13, 8;
        8, 13, 14, 9;
        9, 14, 15, 10;
        10, 15, 16, 11;
        12, 17, 18, 13;
        13, 18, 19, 14;
        14, 19, 20, 15;
        15, 20, 21, 16;
        17, 22, 23, 18;
        18, 23, 24, 19;
        19, 24, 25, 20;
        20, 25, 26, 21];

% 组装全局刚度矩阵
nnode = size(coord,1);
nelem = size(elem,1);
K = zeros(2*nnode);
for i = 1:nelem
    idx = elem(i,:);
    x = coord(idx,1);
    y = coord(idx,2);
    A = [x(2)-x(1), y(2)-y(1);
         x(3)-x(1), y(3)-y(1)];
    B = inv(A);
    Be = [B(1,1), 0, B(1,2), 0;
          0, B(2,1), 0, B(2,2);
          B(2,1), B(1,1), B(2,2), B(1,2)];
    Kei = Be'*Ke*Be*det(A);
    K([2*idx-1, 2*idx], [2*idx-1, 2*idx]) = ...
        K([2*idx-1, 2*idx], [2*idx-1, 2*idx]) + Kei;
end

% 施加边界条件
fixed_nodes = [1:5, 21:25];
free_nodes = setdiff(1:nnode, fixed_nodes);
Kff = K(free_nodes, free_nodes);
Kfc = K(free_nodes, fixed_nodes);
Kcf = K(fixed_nodes, free_nodes);
Kcc = K(fixed_nodes, fixed_nodes);
uf = zeros(length(free_nodes), 1);
uc = [0; 0; 0; 0; 0; 0.01; 0; 0; 0; 0];

% 求解位移和应力
uf = Kff\(f-Kfc*uc);
uc = Kcc\(-Kcf*uf);

% 绘制云图
figure;
trisurf(elem, coord(:,1)+uf(1:2:end), coord(:,2)+uf(2:2:end), zeros(nnode,1));
title('单元刚度云图');
xlabel('x');
ylabel('y');
zlabel('z');

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