% --- Assembly --- K_global = zeros(n_dof); F_global = zeros(n_dof, 1);

% --- Apply Boundary Conditions (Penalty Method) --- penalty = 1e12 * max(max(K)); for i = 1:length(fixed_global) dof = fixed_global(i); K(dof, dof) = K(dof, dof) + penalty; F(dof) = penalty * 0; end

% Coordinates x = nodes([n1,n2,n3], 1); y = nodes([n1,n2,n3], 2);

% Deformed plot scale = 10; % deformation scale factor deformed = nodes + scale * U_nodes; figure; patch('Faces', elements, 'Vertices', deformed, 'FaceColor', 'cyan', 'EdgeColor', 'red'); hold on; patch('Faces', elements, 'Vertices', nodes, 'FaceColor', 'none', 'EdgeColor', 'black', 'LineStyle', '--'); axis equal; grid on; xlabel('X (m)'); ylabel('Y (m)'); title('Deformed (cyan) vs Undeformed (dashed) Shape'); legend('Deformed', 'Undeformed'); | Tip | Description | |------|-------------| | Vectorization | Avoid loops when possible; use reshape , repmat , and index vectors | | Sparse Matrices | For large problems, use sparse() to store global K matrix | | Modular Programming | Write functions for elem_stiffness , elem_mass , post_process | | Input Files | Store mesh, BCs, and loads in separate .mat or .txt files | | Visualization | Use patch , trisurf , quiver for 2D/3D results | | Verification | Compare with analytical solutions for simple cases | 6. Example Function Library (Modular Approach) File: bar2e.m (2-node bar element)

% Element stiffness matrix ke = thickness * area * (B' * D * B);

disp('Nodal displacements (m):'); for i = 1:size(nodes,1) fprintf('Node %d: ux = %.4e, uy = %.4e\n', i, U_nodes(i,1), U_nodes(i,2)); end

% 4. Solve % - Solve K * U = F for nodal displacements U

% Element stresses for e = 1:size(elements,1) n1 = elements(e,1); n2 = elements(e,2); L = nodes(n2) - nodes(n1); u1 = U(n1); u2 = U(n2); strain = (u2 - u1)/L; stress = E * strain; fprintf('Element %d: Strain = %.4e, Stress = %.2f MPa\n', e, strain, stress/1e6); end