A weighted finite element mass redistribution method for dynamic contact problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:345

Article

Dabaghi, F.¹  Krejci, P.²  Petrov, A.¹  Pousin, J.¹  Renard, Y.¹ 

[1] Univ Lyon, CNRS, INSA Lyon, Inst Camille Jordan UMR 5208, 20 Ave A Einstein, F-69621 Villeurbanne, France

[2] Czech Acad Sci, Inst Math, Zitna 25, CZ-11567 Prague 1, Czech Republic

关键词: Numerical solution;    Mass redistribution method;    Variational inequality;    Unilateral contact;    Energy conservation;   

DOI  :  10.1016/j.cam.2018.06.030

来源: Elsevier

【 摘 要 】

This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes. The convergence as well as an error estimate in time is proved. The analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution. However some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact. To overcome this difficulty, a new unconditionally stable and a very lightly dissipative scheme is proposed. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free