Additional overlapping finite elements - The pyramid and prism elements

doi:10.1016/j.compstruc.2022.106813

Additional overlapping finite elements - The pyramid and prism elements

2022-08-01

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Klaus‐Jürgen Bathe

DOI：10.1016/j.compstruc.2022.106813

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Abstract

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Our objective in this paper is to present two new overlapping finite elements: a pyramid element and a prism element. These elements are useful when meshing general three-dimensional geometries in pro-viding the possibility to transition between other overlapping and traditional elements. Both new over-lapping elements are compatible with overlapping brick and tetrahedral elements, and when used as coupling elements also with the traditional finite elements. We theoretically formulate the two new overlapping finite elements, show that only the rigid body modes correspond to zero eigenvalues (hence the elements contain no spurious zero energy mode), show that the patch test is passed, and test the ele-ments for their convergence behavior and condition numbers. We also show that the elements are quite insensitive to element distortions and revisit the imposition of displacement boundary conditions. Finally, we give some illustrative applications using the AMORE scheme in which also the new overlap-ping elements are employed.(c) 2022 Elsevier Ltd. All rights reserved.

Keywords:

Finite elements

Overlapping elements

Pyramid

Prism

Stability and accuracy

AMORE scheme

Additional overlapping finite elements - The pyramid and prism elements

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