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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

Kadapa, Chennakesava

Authors



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 one consisting only of displacements. The higher-order spatial discretization and the nonnegative 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.

Journal Article Type Article
Acceptance Date Sep 28, 2018
Online Publication Date Oct 31, 2018
Publication Date Feb 3, 2019
Deposit Date Aug 29, 2022
Journal International Journal for Numerical Methods in Engineering
Print ISSN 0029-5981
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 117
Issue 5
Pages 543-573
DOI https://doi.org/10.1002/nme.5967
Keywords B-bar formulation, Bernstein polynomials, Bézier elements, connecting rod, explicit elastodynamics
Public URL http://researchrepository.napier.ac.uk/Output/2893863