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A Variational r-Adaption and Shape-Optimization Method for Finite-Deformation Elasticity

Thoutireddy, P. and Ortiz, M. (2003) A Variational r-Adaption and Shape-Optimization Method for Finite-Deformation Elasticity. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechCACR:CACR-2003-206

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Abstract

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 configuration forces for isoparametric elements and nonlinear, 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 nonlinear elastic bodies; and the optimization of the shape of elastic inclusions.


Item Type:Report or Paper (Technical Report)
Group:Center for Advanced Computing Research
Record Number:CaltechCACR:CACR-2003-206
Persistent URL:http://resolver.caltech.edu/CaltechCACR:CACR-2003-206
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28150
Collection:CaltechCACR
Deposited By: Imported from CaltechCACR
Deposited On:03 Mar 2004
Last Modified:26 Dec 2012 14:31

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