Matlab Codes For Finite Element Analysis M Files -

% Nodes (x, y) nodes = [0, 0; % Node 1 0.1, 0; % Node 2 0.1, 0.1; % Node 3 0, 0.1]; % Node 4

% 1. Pre-processing % - Define geometry, material properties, boundary conditions % - Generate mesh (nodes and elements) % 2. Assembly % - Initialize global stiffness matrix K and force vector F % - Loop over elements, compute element stiffness matrix, assemble

% --- Solve --- U = K_global \ F_global;

% Plot deformed shape plot(nodes, U, 'ro-', 'LineWidth', 2); xlabel('X (m)'); ylabel('Displacement (m)'); title('1D Truss Deformation'); grid on; Problem: Thin plate with a hole under tension (simplified mesh). M-file: cst_plate.m matlab codes for finite element analysis m files

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

% Plane stress constitutive matrix D = (E/(1-nu^2)) * [1, nu, 0; nu, 1, 0; 0, 0, (1-nu)/2];

for e = 1:size(elements, 1) n1 = elements(e, 1); n2 = elements(e, 2); % Nodes (x, y) nodes = [0, 0; % Node 1 0

% Area area = 0.5 * abs((x(2)-x(1))*(y(3)-y(1)) - (x(3)-x(1))*(y(2)-y(1)));

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

% --- 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 M-file: cst_plate

% 2D CST Finite Element Analysis - Plane Stress clear; clc; close all; % --- Pre-processing --- % Material properties E = 70e9; % Pa (Aluminum) nu = 0.33; thickness = 0.005; % m

function [ke, fe] = bar2e(E, A, L, options) % BAR2E 2-node bar element stiffness matrix and equivalent nodal forces % KE = BAR2E(E, A, L) returns element stiffness matrix % [KE, FE] = BAR2E(E, A, L, 'distload', q) adds distributed load q (N/m) ke = (E * A / L) * [1, -1; -1, 1]; fe = zeros(2,1); if nargin > 3 && strcmp(options, 'distload') q = varargin1; fe = (q * L / 2) * [1; 1]; end end