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Adaptive Timestep Control for the Contact-Stabilized Newmark Method

Please always quote using this URN:urn:nbn:de:0296-matheon-7112
  • The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.

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Metadaten
Author:Corinna Klapproth, Anton Schiela, Peter Deuflhard
URN:urn:nbn:de:0296-matheon-7112
Referee:Ralf Kornhuber
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/12/09
Release Date:2010/03/09
Tag:
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K15 Numerical methods for variational inequalities and related problems
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L06 Multistep, Runge-Kutta and extrapolation methods
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Mxx Special kinds of problems / 74M15 Contact
Preprint Number:721
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