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A variational r-adaption and shape-optimization method for finite-deformation elasticity

Thoutireddy, P. and Ortiz, M. (2004) A variational r-adaption and shape-optimization method for finite-deformation elasticity. International Journal for Numerical Methods in Engineering, 61 (1). pp. 1-21. ISSN 0029-5981. doi:10.1002/nme.1052.

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This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions.

Item Type:Article
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URLURL TypeDescription ItemTechnical Report
Ortiz, M.0000-0001-5877-4824
Additional Information:© 2004 John Wiley & Sons. Received 1 May 2003. Revised 16 September 2003. Accepted 24 December 2003. Published online 30 June 2004. Support from the DoE through Caltech’s ASCI/ASAP Center for the Simulation of the DynamicResponse of Solids, and from the ONR grant number N00014-96-1-0068, is gratefully acknowledged.
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Office of Naval Research (ONR)N00014-96-1-0068
Subject Keywords:r-adaption; variational methods; configurational forces; finite elements; mesh optimization; shape optimization
Issue or Number:1
Record Number:CaltechAUTHORS:20171128-114428592
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Official Citation:Thoutireddy, P. and Ortiz, M. (2004), A variational r-adaption and shape-optimization method for finite-deformation elasticity. Int. J. Numer. Meth. Engng., 61: 1–21. doi:10.1002/nme.1052
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83526
Deposited By: Lydia Suarez
Deposited On:28 Nov 2017 21:47
Last Modified:15 Nov 2021 20:11

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