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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
Author(s) -
Kadapa Chennakesava
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5967
Subject(s) - tetrahedron , quadratic equation , finite element method , discretization , mathematics , polygon mesh , compressibility , convergence (economics) , hexahedron , mesh generation , geometry , mathematical analysis , structural engineering , physics , mechanics , engineering , economics , economic growth
Summary 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.