truss analysis in matlab

main.m
% Define truss geometry
coord = [0 0; 10 0; 20 0; 30 0; 10 10; 20 10];
connect = [1 5; 2 5; 2 6; 3 6; 4 6; 5 6];

% Set material properties and loads
E = 1e7; % Modulus of elasticity (Pa)
A = 0.0001; % Area (m^2)
f = [0; 0; 0; 0; -1000; 0]; % External loads (N)

% Assemble stiffness matrix and load vector
num_nodes = size(coord, 1);
num_dofs = num_nodes * 2;
K = zeros(num_dofs);
F = zeros(num_dofs, 1);
for i = 1:size(connect, 1)
    node1 = connect(i, 1);
    node2 = connect(i, 2);
    x1 = coord(node1, 1);
    y1 = coord(node1, 2);
    x2 = coord(node2, 1);
    y2 = coord(node2, 2);
    L = norm([x2-x1 y2-y1]);
    cos_theta = (x2-x1) / L;
    sin_theta = (y2-y1) / L;
    k = [cos_theta^2 cos_theta*sin_theta -cos_theta^2 -cos_theta*sin_theta;
        cos_theta*sin_theta sin_theta^2 -cos_theta*sin_theta -sin_theta^2;
        -cos_theta^2 -cos_theta*sin_theta cos_theta^2 cos_theta*sin_theta;
        -cos_theta*sin_theta -sin_theta^2 cos_theta*sin_theta sin_theta^2];
    k = E * A / L * k;
    dofs = [node1*2-1 node1*2 node2*2-1 node2*2];
    K(dofs, dofs) = K(dofs, dofs) + k;
end
F(5:6) = f;

% Apply boundary conditions
fixed_nodes = [1 2 3 4];
free_nodes = setdiff(1:num_nodes, fixed_nodes);
fixed_dofs = [fixed_nodes*2-1 fixed_nodes*2];
free_dofs = reshape(setdiff(1:num_dofs, fixed_dofs), [], 1);
Kf = K(free_dofs, free_dofs);
Ff = F(free_dofs);
df = Kf \ Ff;
d = zeros(num_dofs, 1);
d(free_dofs) = df;

% Calculate reaction forces and element forces
R = K * d - F;
for i = 1:size(connect, 1)
    node1 = connect(i, 1);
    node2 = connect(i, 2);
    x1 = coord(node1, 1);
    y1 = coord(node1, 2);
    x2 = coord(node2, 1);
    y2 = coord(node2, 2);
    L = norm([x2-x1 y2-y1]);
    cos_theta = (x2-x1) / L;
    sin_theta = (y2-y1) / L;
    dofs = [node1*2-1 node1*2 node2*2-1 node2*2];
    u = d(dofs);
    f = E * A / L * [-cos_theta -sin_theta cos_theta sin_theta] * u';
    fprintf('Element %d: Force = %f N\n', i, f)
end
fprintf('Reaction forces: Ry = %f N, Rx = %f N\n', R(5), R(6))
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