MATLAB Program Code for Finite Element Mesh Generation

In Finite Element Analysis (FEA), mesh generation represents the core preprocessing step that directly impacts computational accuracy and efficiency. MATLAB's powerful matrix operations and flexible programming environment make it ideal for developing lightweight finite element preprocessing tools.

Programs like 3DMATLAB-FEM-PREP-MESH typically implement the following key functionalities:

Geometry Model Import and Processing Support for CAD software exports or manual geometry definition, often implemented through STL file parsing or node coordinate arrays for 3D geometry description. The code includes validation checks (e.g., enclosure validation, normal vector consistency) and geometry simplification routines using functions like stlread and custom boundary detection algorithms.

Automatic Mesh Generation Algorithms Implementation of Delaunay triangulation (2D cases using delaunayTriangulation) or advancing front method (3D cases) to discretize geometries into triangular/tetrahedral elements. Higher-order element handling may include midpoint generation logic and shape function mapping procedures.

Mesh Quality Optimization Application of Laplacian smoothing techniques and topological optimization methods to adjust nodal positions. The code monitors quality parameters like Jacobian determinant and aspect ratio through matrix calculations, preventing distorted elements that compromise solver stability using optimization loops and constraint functions.

Boundary Condition Labeling Node/element labeling for loads/constraints, typically implemented through geometric feature recognition (coordinate range checks) or interactive selection interfaces. This prepares input data for subsequent solvers using logical indexing and label assignment matrices.

The advantage of such MATLAB tools lies in their high customizability - users can adjust mesh density strategies (e.g., local refinement in stress concentration zones) through parameter modifications. However, compared to professional FEM software, they may have limitations in handling complex geometries and parallel computing capabilities due to MATLAB's inherent computational constraints.