FEM is not limited to solid mechanics. Incompressible fluid flow can be modeled using the Navier‑Stokes equations, and compact MATLAB codes exist for this purpose.
%% Boundary conditions (fixed at both ends) fixed_dofs = [1, 3]; fixed_values = [0, 0];
function K_global = assembleGlobalStiffness(K_global, Ke, element_dofs) % Assemble element stiffness into global matrix % element_dofs: list of global DOF indices for this element
Maps local nodal degrees of freedom (DOFs) to the global system. D. Post-Processing Function ( visualize.m ) matlab codes for finite element analysis m files
figure; hold on; for e = 1:size(elements,1) x = [nodes(elements(e,:),1); nodes(elements(e,1),1)]; y = [nodes(elements(e,:),2); nodes(elements(e,1),2)]; plot(x, y, 'k-'); end axis equal; title('Finite Element Mesh'); end
Demo runner (demo_run.m)
: It covers advanced topics such as free vibrations, buckling of Timoshenko beams, and Mindlin plates, as well as laminated and functionally graded materials. FEM is not limited to solid mechanics
The function bmatrix computes the strain‑displacement matrix, and D is the material constitutive matrix (plane stress or plane strain). When you assemble these element matrices into the global system and solve for nodal displacements, you obtain the full displacement and stress fields. Such M‑files are not only educational but also practical for small‑scale engineering analyses.
What you want to capture (static structural, thermal, modal vibrations)?
Building a Finite Element Analysis tool in MATLAB using M-files provides deep insight into FEA theory. By structuring the code with specialized functions for assembly and using sparse solvers, you can create a powerful 1D, 2D, or 3D FEM software. When you assemble these element matrices into the
% Area of triangle A_e = 0.5 * abs(det([1 x(1) y(1); 1 x(2) y(2); 1 x(3) y(3)]));
: The text is well-organized, moving logically from the simplest 1D cases to complex 3D structural models.
% Apply boundary conditions: T = 0 at left, f = 10 at right K(1,:) = 0; K(1,1) = 1; f(1) = 0; % Dirichlet f(end) = 10; % Neumann