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The singular dynamic method for constrained second order hyperbolic equations: Application to dynamic contact problems

Author:

Yves RenardAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 234, Issue 3

Pages 906 - 923

https://doi.org/10.1016/j.cam.2010.01.058

Published: 01 June 2010 Publication History

Abstract

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The main application is dynamic contact problems. The principle consists in the use of a singular mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. We prove that the semi-discretized problem is well-posed and energy conserving. Numerical experiments show that this is a crucial property to build stable numerical schemes.

References

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Carpenter, N.J., Lagrange constraints for transient finite element surface contact. Int. J. Num. Meth. Eng. v32. 103-128.

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Digital Library

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Digital Library

Cited By

Monjaraz Tec CGross JKrack M(2022)A massless boundary component mode synthesis method for elastodynamic contact problemsComputers and Structures10.1016/j.compstruc.2021.106698260:COnline publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1016/j.compstruc.2021.106698
Kolman RKopačka JGonzález JCho SPark K(2021)Bi-penalty stabilized technique with predictor–corrector time scheme for contact-impact problems of elastic barsMathematics and Computers in Simulation10.1016/j.matcom.2021.03.023189:C(305-324)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.matcom.2021.03.023
Di Stasio JDureisseix DGeorges GGravouil AHomolle T(2021)An explicit time-integrator with singular mass for non-smooth dynamicsComputational Mechanics10.1007/s00466-021-02021-568:1(97-112)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00466-021-02021-5
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The singular dynamic method for constrained second order hyperbolic equations: Application to dynamic contact problems

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Published In

cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 234, Issue 3

June, 2010

324 pages

ISSN:0377-0427

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Copyright © Elsevier B.V. © 2010.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 June 2010

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Cited By

Monjaraz Tec CGross JKrack M(2022)A massless boundary component mode synthesis method for elastodynamic contact problemsComputers and Structures10.1016/j.compstruc.2021.106698260:COnline publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1016/j.compstruc.2021.106698
Kolman RKopačka JGonzález JCho SPark K(2021)Bi-penalty stabilized technique with predictor–corrector time scheme for contact-impact problems of elastic barsMathematics and Computers in Simulation10.1016/j.matcom.2021.03.023189:C(305-324)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.matcom.2021.03.023
Di Stasio JDureisseix DGeorges GGravouil AHomolle T(2021)An explicit time-integrator with singular mass for non-smooth dynamicsComputational Mechanics10.1007/s00466-021-02021-568:1(97-112)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00466-021-02021-5
(2016)A robust finite element redistribution approach for elastodynamic contact problemsApplied Numerical Mathematics10.1016/j.apnum.2015.12.004103:C(48-71)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1016/j.apnum.2015.12.004

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