Matlab Codes For Finite Element Analysis M Files -

% Element length L = nodes(n2) - nodes(n1);

% Elements (triangle connectivity: node1, node2, node3) elements = [1, 2, 3; 1, 3, 4];

% 3. Apply Boundary Conditions % - Modify K and F to enforce Dirichlet (displacement) BCs

% Boundary conditions fixed_dof = 1; % Node 1 fixed force_dof = 3; % Node 3 loaded applied_force = 10000; % N matlab codes for finite element analysis m files

% --- Post-processing --- disp('Nodal displacements (m):'); disp(U);

for e = 1:size(elements,1) % Element nodes n1 = elements(e,1); n2 = elements(e,2); n3 = elements(e,3);

% Element stiffness matrix (2x2) ke = (E * A / L) * [1, -1; -1, 1]; % Element length L = nodes(n2) - nodes(n1);

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

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

% Number of nodes and DOFs (1 DOF per node for axial) n_nodes = length(nodes); n_dof = n_nodes; dof_list) = K(dof_list

for e = 1:size(elements, 1) n1 = elements(e, 1); n2 = elements(e, 2);

% --- 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

% Assembly dof_list = [(n1-1)*2+1, (n1-1)*2+2, ... (n2-1)*2+1, (n2-1)*2+2, ... (n3-1)*2+1, (n3-1)*2+2]; K(dof_list, dof_list) = K(dof_list, dof_list) + ke; end