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

共 11 条

[1] A NITSCHE FINITE ELEMENT METHOD FOR DYNAMIC CONTACT: 2. STABILITY OF THE SCHEMES AND NUMERICAL EXPERIMENTS
Chouly, Franz
Hild, Patrick
Renard, Yves
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2015, 49 (02) : 503 - 528
[2] Nitsche method for contact with Coulomb friction: Existence results for the static and dynamic finite element formulations
Chouly, Franz
Hild, Patrick
Lleras, Vanessa
Renard, Yves
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 416
[3] A time-marching finite element method for an electromagnetic scattering problem
Van, T
Wood, A
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2003, 26 (12) : 1025 - 1045
[4] Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems
Cockburn, Bernardo
Du, Shukai
Sanchez, Manuel A.
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS, 2023, 9
[5] Convolution finite element method: an alternative approach for time integration and time-marching algorithms
Amiri-Hezaveh, A.
Masud, A.
Ostoja-Starzewski, M.
COMPUTATIONAL MECHANICS, 2021, 68 (03) : 667 - 696
[6] Convolution finite element method: an alternative approach for time integration and time-marching algorithms
A. Amiri-Hezaveh
A. Masud
M. Ostoja-Starzewski
Computational Mechanics, 2021, 68 : 667 - 696
[7] θ schemes for finite element discretization of the space-time fractional diffusion equations
Guan, Qingguang
Gunzburger, Max
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 288 : 264 - 273
[8] A Semi-Discretization Method Based on Finite Difference and Differential Transform Methods to Solve the Time-Fractional Telegraph Equation
Sahraee, Zahra
Arabameri, Maryam
SYMMETRY-BASEL, 2023, 15 (09):
[9] A multiscale finite element space-time discretization method for transient transport phenomena using bubble functions
Nassehi, V.
Parvazinia, M.
FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2009, 45 (05) : 315 - 323
[10] Space-time finite element method with domain reduction techniques for dynamic soil-structure interaction problems
Sharma, Vikas
Shimizu, Shion
Fujisawa, Kazunori
INTERNATIONAL JOURNAL OF MECHANICAL SYSTEM DYNAMICS, 2024, 4 (02): : 117 - 130

← 1 2 →