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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...
| Published in: | International Journal for Numerical Methods in Engineering |
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| ISSN: | 00295981 |
| Published: |
2019
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| Online Access: |
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| 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. |
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| Keywords: |
Bézier elements; Bernstein polynomials; Explicit elastodynamics; B-bar formulation; Connecting rod |
| College: |
Faculty of Science and Engineering |
| Issue: |
5 |
| Start Page: |
543 |
| End Page: |
573 |