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Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics / Chennakesava Kadapa

International Journal for Numerical Methods in Engineering, Volume: 117, Issue: 5, Pages: 543 - 573

Swansea University Author: Chennakesava, Kadapa

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DOI (Published version): 10.1002/nme.5967

Abstract

In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa44783
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Abstract: In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes with quadratic Bézier triangular/tetrahedral elements from the corresponding quadratic Lagrange elements that can be easily generated using the existing mesh generators. Numerical issues arising in the case of nearly incompressible materials are addressed using the consistent B‐bar formulation, thus reducing the finite element formulation to the one consisting only of displacements. The higher‐order spatial discretisation and the non‐negative nature of Bernstein polynomials are shown to yield significant computational benefits. The optimal spatial convergence of the B‐bar formulation for the quadratic triangular and tetrahedral elements is demonstrated by computing error norms in displacement and stresses. The applicability and computational efficiency of the proposed elements for elastodynamic simulations are demonstrated by studying several numerical examples involving real‐world geometries with complex features. Numerical results obtained with the standard linear triangular and tetrahedral elements are also presented for comparison.
Keywords: Bézier elements; Bernstein polynomials; Explicit elastodynamics; B-bar formulation; Connecting rod
College: College of Science
Issue: 5
Start Page: 543
End Page: 573