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Unified Isoparametric 3D LagrangeFinite Elements

Marcin Maździarz1
1 Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, Poland

Computer Modeling in Engineering & Sciences 2010, 66(1), 1-24. https://doi.org/10.3970/cmes.2010.066.001

Abstract

The paper presents unified approach to 3D isoparametric Lagrange brick, tetra, and prism finite elements. All shape functions, linear, quadratic and cubic, are depicted in one Cartesian orthogonal coordinate system x,y,z regardless of the type of element. This allows one to use a single transformation rule to calculate global derivatives and a second for integration. Proper numerical Gauss quadratures for these isoparametric elements in a unified approach are presented additionally.

Keywords

Finite element method, Isoparametric elements, Numerical integration

Cite This Article

Maździarz, M. (2010). Unified Isoparametric 3D LagrangeFinite Elements. CMES-Computer Modeling in Engineering & Sciences, 66(1), 1–24.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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