Never grow matrices inside loops (e.g., K(i,j) = value ). Preallocate space up front using zeros() . For large systems, use sparse preallocation via the sparse() syntax:
% Assemble global force vector for l = 1:size(loads,1) node = loads(l,1); dof = loads(l,2); val = loads(l,3); global_dof = 2*(node-1) + dof; F(global_dof) = F(global_dof) + val; end
Always initialize matrices before loops (e.g., K = zeros(n, n) ). Dynamic arrays that grow inside a loop degrade performance.
Mastering Finite Element Analysis in MATLAB: A Guide to Building M-Files matlab codes for finite element analysis m files
Writing Finite Element Analysis (FEA) code using MATLAB .m files allows engineers and researchers to customize algorithms, understand the underlying theory, and automate simulations. This article explores the structure of FEA M-files, provides examples, and discusses best practices for creating efficient FEA programs. 1. Core Components of a MATLAB FEA Program
) to find the unknown nodal degrees of freedom (displacements).
function stress = computeCSTStress(E, nu, coords, u_e) % Compute stress in a CST element % u_e: element nodal displacements [u1 v1 u2 v2 u3 v3] Never grow matrices inside loops (e
clear; close all; clc;
MATLAB provides an excellent platform for developing and testing finite element codes. The .m files can range from simple 1D bar problems to complex nonlinear 2D/3D simulations. Key advantages include rapid prototyping, built-in debugging, and powerful visualization. However, for large-scale production FEA (millions of DOFs), compiled languages like C++ or Fortran are preferred. The modular structure presented here—preprocessing, assembly, solver, postprocessing—serves as a robust template for any FEA implementation in MATLAB.
U = zeros(n_dof,1); U(free) = K(free,free) \ F(free); Dynamic arrays that grow inside a loop degrade performance
end
% Compute the stiffness matrix and load vector K = zeros(Nx*Ny, Nx*Ny); F = zeros(Nx*Ny, 1); for i = 1:Nx for j = 1:Ny idx = (i-1)*Ny + j; K(idx, idx) = 2*(1/(x(i+1, j)-x(i, j))^2 + 1/(y(i, j+1)-y(i, j))^2); F(idx) = (x(i+1, j)-x(i, j))*(y(i, j+1)-y(i, j))/4*g(x(i, j), y(i, j)) + ... (x(i+1, j)-x(i, j))*(y(i, j+1)-y(i, j))/4*g(x(i+1, j), y(i, j)) + ... (x(i+1, j)-x(i, j))*(y(i, j+1)-y(i, j))/4*g(x(i, j), y(i, j+1)) + ... (x(i+1, j)-x(i, j))*(y(i, j+1)-y(i, j))/4*g(x(i+1, j), y(i, j+1)); end end
for e = 1:nele sctr = element(e, :); el_coords = node(sctr, :); el_disp = d([2 sctr-1; 2 sctr]); % Extract element displacements
Typically involves numerical integration (Gauss quadrature). C. Assembly Function ( assemble_global.m )
). This requires numerical integration, typically handled via Gauss Quadrature for higher-order elements. Global Assembly