A new bipenalty formulation for ensuring time step stability in time domain computational dynamics

SUMMARY It is well known that use of standard penalty methods can decrease the critical time step of time domain dynamic finite element analyses. The bipenalty method utilises both stiffness and mass penalties to impose constraints that have a minimal effect on the eigenfrequencies of the finite ele...

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Bibliographic Details
Published in:	International journal for numerical methods in engineering Vol. 90; no. 3; pp. 269 - 286
Main Authors:	Hetherington, Jack, Rodríguez-Ferran, Antonio, Askes, Harm
Format:	Journal Article Publication
Language:	English
Published:	Chichester, UK John Wiley & Sons, Ltd 20.04.2012 Wiley John Wiley & Sons
Subjects:	74 Mechanics of deformable solids 74S Numerical methods Algebra Anàlisi numèrica Bipenalty method Classificació AMS Constraints Critical time step Exact sciences and technology Explicit time integration Finite element methods Fundamental areas of phenomenology (including applications) Linear and multilinear algebra, matrix theory Matemàtiques i estadística Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Mètodes numèrics Numerical analysis Numerical analysis. Scientific computation Numerical methods and algorithms Partial differential equations, initial value problems and time-dependant initial-boundary value problems Penalty method Physics Resistència de materials Sciences and techniques of general use Solid mechanics Structural and continuum mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Àrees temàtiques de la UPC Constraint explicit time integration Modeling constraints Penalty method Natural frequency Finite element method Time domain method finite element methods Eigenvalue problem bipenalty method Time integration critical time step
ISSN:	0029-5981, 1097-0207
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Summary:	SUMMARY It is well known that use of standard penalty methods can decrease the critical time step of time domain dynamic finite element analyses. The bipenalty method utilises both stiffness and mass penalties to impose constraints that have a minimal effect on the eigenfrequencies of the finite element system. One way of achieving this goal is to find a ratio of stiffness and mass penalty parameters—the critical penalty ratio (CPR)—that does not affect the maximum eigenfrequency (and therefore, for conditionally stable solution schemes, the critical time step) of a system. In this contribution, we develop a new method of calculating the CPR associated with a finite element formulation by examining the eigenvalue problem in detail. Advantages of the method compared with previous solutions include increased simplicity and generality and the ability to consider multiple constraints. The method is demonstrated by deriving CPRs for a few finite element formulations, which are then verified using simple numerical examples. The superiority of the bipenalty method over standard mass penalty methods is also demonstrated. Copyright © 2011 John Wiley & Sons, Ltd.
Bibliography:	istex:FA85B66B7BFE6902F0053BE0695C6A6674AFE96A ArticleID:NME3314 ark:/67375/WNG-J8ZR59BN-V
ISSN:	0029-5981 1097-0207
DOI:	10.1002/nme.3314