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A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach
Author(s) -
Scovazzi Guglielmo,
Carnes Brian,
Zeng Xianyi,
Rossi Simone
Publication year - 2015
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.5138
Subject(s) - finite element method , piecewise linear function , spurious relationship , nonlinear system , computation , compressibility , tetrahedron , mathematics , linear elasticity , elasticity (physics) , transient (computer programming) , mathematical analysis , physics , computer science , mechanics , algorithm , geometry , statistics , quantum mechanics , thermodynamics , operating system
Summary We propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate. Copyright © 2015 John Wiley & Sons, Ltd.