Virtual Element Formulation for Finite Strain Elastodynamics Dedicated to Professor Karl Stark Pister for his 95th birthday  

作　　者：Mertcan Cihan Blaz Hudobivnik Fadi Aldakheel Peter Wriggers 

机构地区：[1]Institute for Continuum Mechanics,Leibniz Universitat Hannover,Hannover,30419,Germany

出　　处：《Computer Modeling in Engineering & Sciences》2021年第12期1151-1180,共30页工程与科学中的计算机建模（英文）

基　　金：The authors gratefully acknowledges support for this research by the“German Research Foundation”(DFG)in(i)the Collaborative Research Center CRC 1153 and(ii)the Priority Program SPP 2020.

摘　　要：The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far the virtual element method has been applied to various engineering problems such as elasto-plasticity,multiphysics,damage and fracture mechanics.This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations.Within this framework,we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape.The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior.Generally the construction of a virtual element is based on a projection part and a stabilization part.While the stiffness matrix needs a suitable stabilization,the mass matrix can be calculated using only the projection part.For the implicit time integration scheme,Newmark-Method is used.To show the performance of the method,various two-and three-dimensional numerical examples in are presented.

关 键 词：Virtual element method three-dimensional dynamics finite strains 

分 类 号：O17[理学—数学]