Energy conservation and dissipation properties of time-integration methods for nonsmooth elastodynamics with contact

被引：30
作者：
Acary, Vincent [1 ,2 ]
机构：
[1] Inria Rhone Alpes, 655 Ave Europe, F-38330 Montbonnot St Martin, France
[2] Inria Chile, Ave Apoquindo 2827, Las Condes, Santiago De Chi, Chile
来源：
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2016年 / 96卷 / 05期
关键词：
Contact dynamics; impact; computational contact mechanics; numerical time integration; energy conservation; dissipation properties; IMPROVED NUMERICAL DISSIPATION; GENERALIZED-ALPHA SCHEME; MECHANICAL SYSTEMS; CONSERVING ALGORITHMS; DYNAMICS; EQUATIONS; NEWMARK; CONSTRAINTS; STABILITY;
D O I：
10.1002/zamm.201400231
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article is devoted to the study of the conservation and the dissipation properties of the mechanical energy of several time-integration methods dedicated to the elasto-dynamics with unilateral contact. Given that the direct application of the standard schemes as the Newmark schemes or the generalized-alpha schemes leads to energy blow-up, we study two schemes dedicated to the time-integration of nonsmooth systems with contact: the Moreau-Jean scheme and the nonsmooth generalized-alpha scheme. The energy conservation and dissipation properties of the Moreau-Jean is firstly shown. In a second step, the nonsmooth generalized-alpha scheme is studied by adapting the previous works of Krenk and Hogsberg in the context of unilateral contact. Finally, the known properties of the Newmark and the Hilber-Hughes-Taylor (HHT) scheme in the unconstrained case are extended without any further assumptions to the case with contact. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
收藏
页码：585 / 603
页数：19
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