帮我设计一个matlab程序，用于首先对桁架结构进行有限元单元划分，求解桁架结构在单点激励力作用下的位移、速度、加速度响应，要求用newmark-β法

好的，以下是一个简单的 MATLAB 程序示例，用于对桁架结构进行有限元单元划分，并使用 Newmark-β 方法求解桁架结构在单点激励力作用下的位移、速度和加速度响应。请注意，这只是一个示例程序，可能需要根据您的具体问题进行修改和优化。

% 定义桁架结构的节点、单元和材料参数
nodes = [0 0; 0 5; 5 5; 5 0; 2.5 2.5; 2.5 0; 5 2.5];
elements = [1 6; 1 5; 2 5; 2 6; 3 6; 3 5; 4 5; 4 6];
E = 210e9; % 弹性模量
A = 0.01; % 桁架截面积
rho = 7800; % 材料密度

% 计算单元的长度、方向余弦和刚度矩阵
num_elements = size(elements, 1);
L = zeros(num_elements, 1);
cos_theta = zeros(num_elements, 2);
k = zeros(num_elements, 4, 4);
for i = 1:num_elements
    n1 = elements(i, 1);
    n2 = elements(i, 2);
    x1 = nodes(n1, 1);
    y1 = nodes(n1, 2);
    x2 = nodes(n2, 1);
    y2 = nodes(n2, 2);
    L(i) = sqrt((x2-x1)^2 + (y2-y1)^2);
    cos_theta(i, :) = (nodes(n2, :) - nodes(n1, :)) / L(i);
    k(i, :, :) = (E*A/L(i)) * [cos_theta(i,1)^2, cos_theta(i,1)*cos_theta(i,2), -cos_theta(i,1)^2, -cos_theta(i,1)*cos_theta(i,2);
                               cos_theta(i,1)*cos_theta(i,2), cos_theta(i,2)^2, -cos_theta(i,1)*cos_theta(i,2), -cos_theta(i,2)^2;
                               -cos_theta(i,1)^2, -cos_theta(i,1)*cos_theta(i,2), cos_theta(i,1)^2, cos_theta(i,1)*cos_theta(i,2);
                               -cos_theta(i,1)*cos_theta(i,2), -cos_theta(i,2)^2, cos_theta(i,1)*cos_theta(i,2), cos_theta(i,2)^2];

% 定义时间步长、时间向量、初始位移和速度
dt = 0.01;
t = 0:dt:10;
num_steps = length(t);
u = zeros(2*size(nodes, 1), 1);
v = zeros(2*size(nodes, 1), 1);

% 定义单点激励力作用下的外力向量
f = zeros(2*size(nodes, 1), 1);
f(11) = 1000;

% 初始化加速度、位移和速度向量
a = zeros(2*size(nodes, 1), 1);
u_history = zeros(num_steps, 2*size(nodes, 1));
v_history = zeros(num_steps, 2*size(nodes, 1));
a_history = zeros(num_steps, 2*size(nodes, 1));

% 定义 Newmark-β 方法中的参数
beta = 0.25;
gamma = 0.5;

% 开始时间步迭代
for i = 1:num_steps
    % 计算加速度、位移和速度
    if i == 1
        a(:, i) = inv(mass_matrix(nodes, elements, rho)) * (f - damping_matrix(nodes, elements, u(:, i), v(:, i)) - stiffness_matrix(elements, k, cos_theta, u(:, i)));
        v(:, i) = v(:, i) + dt*a(:, i);
        u(:, i) = u(:, i) + dt*v(:, i) + 0.5*dt^2*a(:, i);
    else
        a(:, i) = inv(mass_matrix(nodes, elements, rho)) * (f - damping_matrix(nodes, elements, u(:, i), v(:, i)) - stiffness_matrix(elements, k, cos_theta, u(:, i)));
        v(:, i) = v(:, i-1) + dt*((1-gamma)*a(:, i-1) + gamma*a(:, i));
        u(:, i) = u(:, i-1) + dt*v(:, i-1) + dt^2*((0.5-beta)*a(:, i-1) + beta*a(:, i));
    end
    
    % 存储加速度、位移和速度
    u_history(i, :) = u(:, i);
    v_history(i, :) = v(:, i);
    a_history(i, :) = a(:, i);
end

% 绘制节点的位移、速度和加速度响应
figure;
subplot(3, 1, 1);
plot(t, u_history(:, 1:2:end), '-');
ylabel('Displacement');
subplot(3, 1, 2);
plot(t, v_history(:, 1:2:end), '-');
ylabel('Velocity');
subplot(3, 1, 3);
plot(t, a_history(:, 1:2:end), '-');
ylabel('Acceleration');
xlabel('Time');

% 定义质量矩阵、阻尼矩阵和刚度矩阵的函数
function M = mass_matrix(nodes, elements, rho)
    num_nodes = size(nodes, 1);
    M = zeros(2*num_nodes, 2*num_nodes);
    for i = 1:size(elements, 1)
        n1 = elements(i, 1);
        n2 = elements(i, 2);
        m = rho * norm(nodes(n2, :) - nodes(n1, :)) / 6;
        index1 = [2*n1-1, 2*n1, 2*n2-1, 2*n2];
        index2 = [2*i-1, 2*i, 2*i+1, 2*i+2];
        M(index1, index1) = M(index1, index1) + m * eye(4);
        M(index1, index2) = M(index1, index2) + m * [-1 0 1 0; 0 -1 0 1; -1 0 1 0; 0 -1 0 1];
        M(index2, index1) = M(index2, index1) + m * [-1 0 -1 0; 0 -1 0 -1; 1 0 1 0; 0 1 0 1];
        M(index2, index2) = M(index2, index2) + m * [1 0 -1 0; 0 1 0 -1; -1 0 1 0; 0 -1 0 1];
    end
end

function C = damping_matrix(nodes, elements, u, v)
    num_nodes = size(nodes, 1);
    C = zeros(2*num_nodes, 2*num_nodes);
    alpha = 0.01;
    beta = 0.05;
    for i = 1:size(elements, 1)
        n1 = elements(i, 1);
        n2 = elements(i, 2);
        x1 = nodes(n1, 1) + u(2*n1-1);
        y1 = nodes(n1, 2) + u(2*n1);
        x2 = nodes(n2, 1) + u(2*n2-1);
        y2 = nodes(n2, 2) + u(2*n2);
        L = sqrt((x2-x1)^2 + (y2-y1)^2);
        cos_theta = [(x2-x1)/L, (y2-y1)/L];
        v1 = [v(2*n1-1); v(2*n1)];
        v2 = [v(2*n2-1); v(2*n2)];
        v_local = [cos_theta, cos_theta; -cos_theta, -cos_theta] * [v1; v2];
        v_avg = 0.5 * (v_local(1) + v_local(2));
        c = alpha * L + beta * abs(v_avg);
        m = rho * norm(nodes(n2, :) - nodes(n1, :)) / 6;
        index1 = [2*n1-1, 2*n1, 2*n2-1, 2*n2];
        index2 = [2*i-1, 2*i, 2*i+1, 2*i+2];
        C(index1, index1) = C(index1, index1) + c * m * eye(4);
        C(index1, index2) = C(index1, index2) + c * m * [-1 0 1 0; 0 -1 0 1; -1 0 1 0; 0 -1 0 1];
        C(index2, index1) = C(index2, index1) + c * m * [-1 0 -1 0; 0 -1 0 -1; 1 0 1 0; 0 1 0 1];
        C(index2, index2) = C(index2, index2) + c * m * [1 0 -1 0; 0 1 0 -1; -1 0 1 0; 0 -1 0 1];
    end
end

function K = stiffness_matrix(elements, k, cos_theta, u)
    num_nodes = max(elements(:));
    K = zeros(2*num_nodes, 2*num_nodes);
    for i = 1:size(elements, 1)
        n1 = elements(i, 1);
        n2 = elements(i, 2);
        index1 = [2*n1-1, 2*n1, 2*n2-1, 2*n2];
        index2 = [2*i-1, 2*i, 2*i+1, 2*i+2];
        u_local = [u(index1(1:2)); u(index1(3:4))];
        u_global = [cos_theta, -cos_theta; cos_theta, -cos_theta] * u_local;
        K(index1, index1) = K(index1, index1) + squeeze(k(i, :, :)) + [zeros(2, 2), zeros(2, 2); zeros(2, 2), zeros(2, 2)] + [zeros(2, 2), zeros(2, 2); zeros(2, 2), zeros(2, 2)];
        K(index1, index2) = K(index1, index2) + [-cos_theta, -sin_theta, cos_theta, sin_theta; -sin_theta, -cos_theta, sin_theta, cos_theta; cos_theta, sin_theta, -cos_theta, -sin_theta; sin_theta, cos_theta, -sin_theta, -cos_theta] * squeeze(k(i, :, :)) * [1, 0, 0, 0; 0, 0, 1, 0];
        K(index2, index1) = K(index2, index1) + [1, 0, 0, 0; 0, 0, 1, 0] * squeeze(k(i, :, :)) * [-cos_theta; -sin_theta; cos_theta; sin_theta;];
        K(index2, index2) = K(index2, index2) + [0, 0, 0, 0; 0, 0, 0, 0; 0, 0, 0, 0; 0, 0, 0, 0];
    end
end