A NITSCHE FINITE ELEMENT METHOD FOR DYNAMIC CONTACT: 1. SPACE SEMI-DISCRETIZATION AND TIME-MARCHING SCHEMES

被引：18

作者：

Chouly, Franz ^{[1
]}

Hild, Patrick ^{[2
]}

Renard, Yves ^{[3
]}

机构：

[1] Univ Franche Comte, UMR CNRS 6623, Lab Math Besancon, F-25030 Besancon, France

[2] Univ Toulouse 3, UMR CNRS 5219, Inst Math Toulouse, F-31062 Toulouse 9, France

[3] Univ Lyon, CNRS, INSA Lyon, ICJ UMR5208,LaMCoS UMR5259, F-69621 Villeurbanne, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2015年 / 49卷 / 02期

关键词：

Unilateral contact; elastodynamics; finite elements; Nitsche's method; time-marching schemes; stability; MASS REDISTRIBUTION METHOD; CONSERVING ALGORITHMS; UNILATERAL CONSTRAINT; CONVERGENCE; ENERGY; APPROXIMATION; FORMULATION; EXISTENCE; IMPACT;

D O I：

10.1051/m2an/2014041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new approximation of elastodynamic frictionless contact problems based both on the finite element method and on an adaptation of Nitsche's method which was initially designed for Dirichlet's condition. A main interesting characteristic is that this approximation produces well-posed space semi-discretizations contrary to standard finite element discretizations. This paper is then mainly devoted to present an analysis of the space semi-discretization in terms of consistency, well-posedness and energy conservation, and also to study the well-posedness of some time-marching schemes (theta-scheme, Newmark and a new hybrid scheme). The stability properties of the schemes and the corresponding numerical experiments can be found in a second paper [F. Chouly, P. Hild and Y. Renard, A Nitsche finite element method for dynamic contact. 2. Stability analysis and numerical experiments. ESAIM: M2AN 49 (2015) 503-528.].

引用

页码：481 / 502

页数：22

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