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3D Virtual Elements for Elastodynamic Problems
Author(s) -
Cihan Mertcan,
Aldakheel Fadi,
Hudobivnik Blaž,
Wriggers Peter
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000175
Subject(s) - discretization , finite element method , stiffness matrix , virtual work , mass matrix , ansatz , mathematics , computer science , nonlinear system , mixed finite element method , mathematical analysis , structural engineering , engineering , physics , quantum mechanics , neutrino , nuclear physics , mathematical physics
A virtual element framework for nonlinear elastodynamics is outlined within this work. The virtual element method (VEM) can be considered as an extension of the classical finite element method. While the finite element method (FEM) is restricted to the usage of regular shaped elements, VEM allows to use non‐convex shaped elements for the spatial discretization [1]. It has been applied to various engineering problems in elasticity and other areas, such as plasticity or fracture mechanics as outlined in [3, 4]. This work deals with the extension of VEM to dynamic problems. Low‐order ansatz functions in two and three dimensions, with elements being arbitrary shaped, are used in this contribution. The formulations considered in this framework are based on minimization of energy, where a pseudo potential is used for the dynamic behavior. While the stiffness‐matrix needs a suitable stabilization, the mass‐matrix can be calculated fully through the projection part. For the implicit time integration, Newmark‐Method is used. To show the performance of the method, various numerical examples in 2D and 3D are presented.