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Variational r-adaption in elastodynamics

Zielonka, M. G. and Ortiz, M. and Marsden, J. E. (2008) Variational r-adaption in elastodynamics. International Journal for Numerical Methods in Engineering, 74 (7). pp. 1162-1197. ISSN 0029-5981. http://resolver.caltech.edu/CaltechAUTHORS:20100917-153815166

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Abstract

We develop a variational r-adaptive finite element framework for solid dynamic applications and explore its conceptual links with the theory of dynamic configurational forces. The central idea underlying the proposed approach is to allow Hamilton’s principle of stationary action to determine jointly the evolution of the displacement field and the discretization of the reference configuration of the body. This is accomplished by rendering the action stationary with respect to the material and spatial nodal coordinates simultaneously. However, we find that a naive consistent Galerkin discretization of the action leads to intrinsically unstable solutions. Remarkably, we also find that this unstable behavior is eliminated when a mixed, multifield version of Hamilton’s principle is adopted. Additional features of the proposed numerical implementation include the use of uncoupled space and time discretizations; the use of independent space interpolations for velocities and deformations; the application of these interpolations over a continuously varying adaptive mesh; and the application of mixed variational integrators with independent time interpolations for velocities and nodal parameters. The accuracy, robustness and versatility of the approach are assessed and demonstrated by way of convergence tests and selected examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/nme.2205DOIUNSPECIFIED
http://onlinelibrary.wiley.com/doi/10.1002/nme.2205/abstract;jsessionid=5A980613FA6762AA76FCBA85FF071182.d03t01PublisherUNSPECIFIED
Additional Information:© 2007 John Wiley & Sons, Ltd. Contract/grant sponsor: Department of Energy Contract/grant sponsor: NSF-ITR; contract/grant number: ACI-0204932.
Funders:
Funding AgencyGrant Number
Department of EnergyUNSPECIFIED
NSF-ITRACI-0204932
Subject Keywords:variational methods; mesh adaption; elastodynamics
Record Number:CaltechAUTHORS:20100917-153815166
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100917-153815166
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20026
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:20 Sep 2010 18:01
Last Modified:26 Dec 2012 12:26

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