– Separate functions for isotropic, orthotropic, thermal, etc.
Closing This modular M-file approach yields a clear learning path from mesh generation to postprocessing. Start with the minimal code above, validate on simple benchmark problems (cantilever beam, plate with hole), then iteratively add features.
The element stiffness matrix calculation requires solving a shape function derivative matrix ( ) combined with the constitutive material property matrix (
MATLAB provides an extensive range of tools and functions for FEA, including: matlab codes for finite element analysis m files
% Plot the solution x = 0:(1/(nx+1)):1; plot(x, u); xlabel('x'); ylabel('u(x)');
function Ke = cstElementStiffness(E, nu, thickness, coords) % CST element stiffness matrix % coords: [x1 y1; x2 y2; x3 y3] nodal coordinates
% Slow and numerically unstable method U = inv(K) * F; % Fast, optimized direct solver execution U = K \ F; Use code with caution. The element stiffness matrix calculation requires solving a
% Full displacement vector U = zeros(numDofs, 1); U(free_dofs) = Uf;
Large FEA matrices are mostly filled with zeros because nodes only interact with their immediate neighbors. Storing these unmapped zeros wastes memory. Convert your matrices to use sparse matrix storage algorithms to keep memory usage low:
for e = 1:length(prob.elements) elem = prob.elements(e); mat = prob.materials(elem.matID); [Ke, fe] = feval(elem.type, elem.nodes, elem.coords, mat); [K, F] = assemble(K, F, Ke, fe, elem.dofs); end Convert your matrices to use sparse matrix storage
clear; close all; clc;
In this article, we provided an overview of FEA using MATLAB, focusing on the development of M-files for solving various problems. We presented two examples of M-files for solving simple FEA problems: 1D Poisson's equation and 2D heat transfer. These examples demonstrate the ease of implementing FEA using MATLAB and the flexibility of M-files for solving complex problems.
% Reaction forces fprintf('\n===== REACTION FORCES (N) =====\n'); for i = 1:length(fixed_dofs) global_dof = fixed_dofs(i); node = ceil(global_dof/2); dof = mod(global_dof-1,2)+1; fprintf('Node %d, DOF %d: R = %.2f N\n', node, dof, R_fixed(i)); end
Ke = (E * A / L) * [1, -1; -1, 1]; end
% Plot original truss (blue) for e = 1:numElem n1 = elements(e,1); n2 = elements(e,2); plot([X_orig(n1), X_orig(n2)], [Y_orig(n1), Y_orig(n2)], 'b-o', 'LineWidth',1); end