请帮我写一个matlab的位移法计算三维空间刚架的应力的代码

好的，以下是一个简单的 Matlab 代码实现位移法计算三维空间刚架的应力：

% 定义刚架结构
nodes = [0 0 0; 0 1 0; 1 1 0; 1 0 0; 0 0 1; 0 1 1; 1 1 1; 1 0 1];
elements = [1 2; 2 3; 3 4; 4 1; 5 6; 6 7; 7 8; 8 5; 1 5; 2 6; 3 7; 4 8];
E = 200e9; % 弹性模量
nu = 0.3; % 泊松比
thickness = 0.01; % 板厚度
P = 1000; % 外加荷载

% 计算单元刚度矩阵
for e = 1:size(elements, 1)
    node1 = elements(e, 1);
    node2 = elements(e, 2);
    x1 = nodes(node1, 1);
    y1 = nodes(node1, 2);
    z1 = nodes(node1, 3);
    x2 = nodes(node2, 1);
    y2 = nodes(node2, 2);
    z2 = nodes(node2, 3);
    L = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2);
    cos_alpha = (x2 - x1) / L;
    cos_beta = (y2 - y1) / L;
    cos_gamma = (z2 - z1) / L;
    T = [cos_alpha, cos_beta, cos_gamma, 0, 0, 0;
        0, 0, 0, cos_alpha, cos_beta, cos_gamma];
    k_local = E * thickness / L * [1 -nu 0; -nu 1 0; 0 0 (1-nu)/2];
    k_global = T' * k_local * T;
    elements(e, 3:11) = reshape(k_global, 1, 9);
end

% 组装全局刚度矩阵
n = size(nodes, 1) * 3;
K = zeros(n, n);
for e = 1:size(elements, 1)
    node1 = elements(e, 1);
    node2 = elements(e, 2);
    k = reshape(elements(e, 3:11), 3, 3);
    index1 = (node1-1)*3 + 1;
    index2 = (node2-1)*3 + 1;
    K(index1:index1+2, index1:index1+2) = K(index1:index1+2, index1:index1+2) + k(1:3, 1:3);
    K(index1:index1+2, index2:index2+2) = K(index1:index1+2, index2:index2+2) + k(1:3, 4:6);
    K(index2:index2+2, index1:index1+2) = K(index2:index2+2, index1:index1+2) + k(4:6, 1:3);
    K(index2:index2+2, index2:index2+2) = K(index2:index2+2, index2:index2+2) + k(4:6, 4:6);
end

% 处理边界条件
fixed_nodes = [1 2 3 4];
fixed_dofs = [fixed_nodes*3-2, fixed_nodes*3-1, fixed_nodes*3];
free_dofs = setdiff(1:n, fixed_dofs);
K_ff = K(free_dofs, free_dofs);
F_f = zeros(length(free_dofs), 1);
F_f(1) = -P;
U_f = K_ff \ F_f;

% 计算节点位移和应力
U = zeros(n, 1);
U(free_dofs) = U_f;
stress = zeros(size(elements, 1), 3);
for e = 1:size(elements, 1)
    node1 = elements(e, 1);
    node2 = elements(e, 2);
    x1 = nodes(node1, 1);
    y1 = nodes(node1, 2);
    z1 = nodes(node1, 3);
    x2 = nodes(node2, 1);
    y2 = nodes(node2, 2);
    z2 = nodes(node2, 3);
    L = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2);
    cos_alpha = (x2 - x1) / L;
    cos_beta = (y2 - y1) / L;
    cos_gamma = (z2 - z1) / L;
    T = [cos_alpha, cos_beta, cos_gamma, 0, 0, 0;
        0, 0, 0, cos_alpha, cos_beta, cos_gamma];
    u1 = U((node1-1)*3+1:(node1-1)*3+3);
    u2 = U((node2-1)*3+1:(node2-1)*3+3);
    u_local = T * [u1; u2];
    strain = 1/E * [-nu 0 0; 0 -nu 0; 0 0 (1-nu)/2] * [u_local(1); u_local(2); 0];
    stress(e, :) = E * thickness * strain';
end

% 输出结果
fprintf('节点位移：\n');
fprintf('%f %f %f\n', reshape(U, 3, [])');
fprintf('单元应力：\n');
fprintf('%f %f %f\n', stress');

这段代码实现了一个简单的八节点立方体刚架的应力计算，其中 `nodes` 和 `elements` 分别定义了刚架的节点坐标和单元连接信息。首先计算了每个单元的局部刚度矩阵，然后组装成全局刚度矩阵，并处理了边界条件，最后求解节点位移和应力。注意，这里的应力是按照线弹性理论计算的，不考虑材料非线性和接触等效应。