写一段matlab代码，用位移法计算三维空间刚架结构的应力

以下是一个简单的 MATLAB 代码，用于使用位移法计算三维空间刚架结构的应力：

% 定义结构体
node(1).x = 0; node(1).y = 0; node(1).z = 0;
node(2).x = 3; node(2).y = 0; node(2).z = 0;
node(3).x = 3; node(3).y = 3; node(3).z = 0;
node(4).x = 0; node(4).y = 3; node(4).z = 0;
node(5).x = 0; node(5).y = 0; node(5).z = 4;
node(6).x = 3; node(6).y = 0; node(6).z = 4;
node(7).x = 3; node(7).y = 3; node(7).z = 4;
node(8).x = 0; node(8).y = 3; node(8).z = 4;

element(1).nodes = [1, 2]; element(1).area = 1; element(1).E = 200e9;
element(2).nodes = [2, 3]; element(2).area = 1; element(2).E = 200e9;
element(3).nodes = [3, 4]; element(3).area = 1; element(3).E = 200e9;
element(4).nodes = [4, 1]; element(4).area = 1; element(4).E = 200e9;
element(5).nodes = [5, 6]; element(5).area = 1; element(5).E = 200e9;
element(6).nodes = [6, 7]; element(6).area = 1; element(6).E = 200e9;
element(7).nodes = [7, 8]; element(7).area = 1; element(7).E = 200e9;
element(8).nodes = [8, 5]; element(8).area = 1; element(8).E = 200e9;
element(9).nodes = [1, 5]; element(9).area = 1; element(9).E = 200e9;
element(10).nodes = [2, 6]; element(10).area = 1; element(10).E = 200e9;
element(11).nodes = [3, 7]; element(11).area = 1; element(11).E = 200e9;
element(12).nodes = [4, 8]; element(12).area = 1; element(12).E = 200e9;
element(13).nodes = [2, 4]; element(13).area = 1; element(13).E = 200e9;
element(14).nodes = [6, 8]; element(14).area = 1; element(14).E = 200e9;
element(15).nodes = [1, 3]; element(15).area = 1; element(15).E = 200e9;
element(16).nodes = [5, 7]; element(16).area = 1; element(16).E = 200e9;

% 计算单元刚度矩阵
for i = 1:length(element)
    node1 = element(i).nodes(1);
    node2 = element(i).nodes(2);
    x1 = node(node1).x; y1 = node(node1).y; z1 = node(node1).z;
    x2 = node(node2).x; y2 = node(node2).y; z2 = node(node2).z;
    L = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2);
    cosx = (x2-x1)/L; cosy = (y2-y1)/L; cosz = (z2-z1)/L;
    k = element(i).E*element(i).area/L*[cosx^2, cosx*cosy, cosx*cosz, -cosx^2, -cosx*cosy, -cosx*cosz;
                                          cosx*cosy, cosy^2, cosy*cosz, -cosx*cosy, -cosy^2, -cosy*cosz;
                                          cosx*cosz, cosy*cosz, cosz^2, -cosx*cosz, -cosy*cosz, -cosz^2;
                                          -cosx^2, -cosx*cosy, -cosx*cosz, cosx^2, cosx*cosy, cosx*cosz;
                                          -cosx*cosy, -cosy^2, -cosy*cosz, cosx*cosy, cosy^2, cosy*cosz;
                                          -cosx*cosz, -cosy*cosz, -cosz^2, cosx*cosz, cosy*cosz, cosz^2];
    element(i).k = k;
end

% 组装全局刚度矩阵
K = zeros(24, 24);
for i = 1:length(element)
    node1 = element(i).nodes(1);
    node2 = element(i).nodes(2);
    idx = [3*node1-2, 3*node1-1, 3*node1, 3*node2-2, 3*node2-1, 3*node2];
    K(idx, idx) = K(idx, idx) + element(i).k;
end

% 边界条件
BC = [1, 0; 2, 0; 3, 0; 22, 0; 23, 0; 24, 0];

% 计算位移
K_reduced = K;
for i = 1:size(BC, 1)
    idx = 3*BC(i, 1) - BC(i, 2);
    K_reduced(idx, :) = 0;
    K_reduced(:, idx) = 0;
    K_reduced(idx, idx) = 1;
end
F = zeros(24, 1);
F(14) = -10000;
F_reduced = F;
for i = 1:size(BC, 1)
    idx = 3*BC(i, 1) - BC(i, 2);
    F_reduced(idx) = [];
    K_reduced(idx, :) = [];
    K_reduced(:, idx) = [];
end
U_reduced = K_reduced\F_reduced;
U = zeros(24, 1);
for i = 1:size(BC, 1)
    idx = 3*BC(i, 1) - BC(i, 2);
    U(idx) = BC(i, 2);
end
U(~(U==0)) = U_reduced;

% 计算应力
stress = zeros(length(element), 1);
for i = 1:length(element)
    node1 = element(i).nodes(1);
    node2 = element(i).nodes(2);
    idx = [3*node1-2, 3*node1-1, 3*node1, 3*node2-2, 3*node2-1, 3*node2];
    u = U(idx);
    k = element(i).k;
    stress(i) = element(i).E*element(i).area/element(i).L*[-1, 1]*k*[u(1); u(2); u(3); u(4); u(5); u(6)];
end

disp(stress);

这个代码定义了一个简单的八节点体系，每个节点都有三个自由度（x，y，z）。它首先计算每个单元的刚度矩阵，然后组装全局刚度矩阵，并施加边界条件和外力。接下来，它计算位移并使用它来计算每个元素的应力。