Shape Functions for FEA

Version 1.0.3 (291 KB) by Eric Trudel
Shape or basis functions interpolate along or within a polygon. This script will derive shape functions for many shapes.
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Updated 26 May 2023

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This Script will derive Shape/Basis functions for many shapes
The gaussian weights for numerical integration (gaussian quadrature) of some shapes are also presented.
Additionally the "B" matrix for finite element is also provided for some shapes. This would be the "strain displacement matrix".
Shapes for basis functions within the script include:
  • Lines
  • Triangle (2D)
  • Quadrilateral (2D)
  • Cube
  • Tetrahedron
  • Prism/Wedge
  • Pyramid
  • Pentagon (2D)
  • Rectangular-Pentagon (3D)

Cite As

Eric Trudel (2024). Shape Functions for FEA (https://www.mathworks.com/matlabcentral/fileexchange/129889-shape-functions-for-fea), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2020b
Compatible with R2020b and later releases
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.3

Added Rectangular Pentagon with 3D wachpress coordinates.
Refined descriptions.
1.0.2

Added a description for an additional method for constructing shape functions.
The 2nd Order Prism shape function has an additional derivation method that produces better results.
1.0.1

Fixed grammar mistakes in the summary.
1.0.0