A multisymplectic integrator for elastodynamic frictionless impact problems

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• 作者：Franç ; ois Demoures^a ; ^b ; ^{demoures@lmd.ens.fr} ; Franç ; ois Gay-Balmaz^b ; ^{francois.gay-balmaz@lmd.ens.fr} ; Mathieu Desbrun^c ; ^{mathieu@cms.caltech.edu} ; Tudor S. Ratiu^d ; ^e ; ^{ratiu@sjtu.edu.cn} ; ^{tudor.ratiu@epfl.ch} ; Alejandro M. Aragó ; n^f ; ^{A.M.Aragon@tudelft.nl}
• 关键词：Structure preserving discretization ; Collisions ; Elastic bodies ; Multisymplectic integrator
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：315
• 期：Complete
• 页码：1025-1052
• 全文大小：4189 K
• 卷排序：315

文摘

We present a structure preserving numerical algorithm for the collision of elastic bodies. Our integrator is derived from a discrete version of the field-theoretic (multisymplectic) variational description of nonsmooth Lagrangian continuum mechanics, combined with generalized Lagrange multipliers to handle inequality constraints. We test the resulting explicit integrator for the longitudinal impact of two elastic linear bar models, and for the collision of a nonlinear geometrically exact beam model with a rigid plane. Numerical simulations for various physical parameters are presented to illustrate the behavior and performance of our approach.