Matlab Codes For Finite Element Analysis M Files 【2024-2026】

% --- Apply Boundary Conditions --- % Penalty method (or elimination method) penalty = 1e12; K_global(fixed_dof, fixed_dof) = K_global(fixed_dof, fixed_dof) + penalty; F_global(fixed_dof) = penalty * 0; % zero displacement

% 1D Truss Finite Element Analysis clear; clc; close all; % --- Pre-processing --- % Material properties E = 210e9; % Young's modulus (Pa) A = 0.01; % Cross-sectional area (m^2)

% Plane stress constitutive matrix D = (E/(1-nu^2)) * [1, nu, 0; nu, 1, 0; 0, 0, (1-nu)/2]; matlab codes for finite element analysis m files

% Element stiffness matrix (2x2) ke = (E * A / L) * [1, -1; -1, 1];

% --- Solve --- U = K_global \ F_global; % --- Apply Boundary Conditions --- % Penalty

% --- Post-processing --- % Reshape displacements: each row = [ux, uy] for node U_nodes = reshape(U, 2, [])';

% Geometry: nodes and elements nodes = [0; 0.5; 1.0]; % Nodal coordinates (m) elements = [1 2; 2 3]; % Element connectivity fixed_dof) = K_global(fixed_dof

% Boundary conditions: fix left edge (nodes 1 and 4) fixed_dofs = [1, 2; % Node 1: DOF 1 (ux), DOF 2 (uy) 4, 2]; % Node 4: DOF 2? Actually Node 4 DOF 7 and 8 % Convert to global DOF numbering (2 DOF per node) % Global DOF: (node-1)*2 + 1 for ux, +2 for uy fixed_global = []; for i = 1:size(fixed_dofs,1) node = fixed_dofs(i,1); dof_type = fixed_dofs(i,2); % 1=ux, 2=uy fixed_global = [fixed_global, (node-1)*2 + dof_type]; end

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

% --- Solve --- U = K \ F;