Research Article

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

  1. P. Thoutireddy,
  2. M. Ortiz*

Article first published online: 30 JUN 2004

DOI: 10.1002/nme.1052

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 61, Issue 1, pages 1–21, 7 September 2004

Additional Information

How to Cite

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: 1–21. doi: 10.1002/nme.1052

Author Information

  1. Division of Engineering and Applied Science, California Institute of Technology, 1200 East California Boulevard, MS 105-50, Pasadena, CA 91125, U.S.A.

*Division of Engineering and Applied Science, California Institute of Technology, 1200 East California Boulevard, MS 105-50, Pasadena, CA 91125, U.S.A.

Publication History

  1. Issue published online: 13 AUG 2004
  2. Article first published online: 30 JUN 2004
  3. Manuscript Accepted: 24 DEC 2003
  4. Manuscript Revised: 16 SEP 2003
  5. Manuscript Received: 1 MAY 2003

Funded by

  • Calltech/ASCI/ASAP
  • ONR. Grant Number: N00014-96-1-0068

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Keywords:

  • r-adaption;
  • variational methods;
  • configurational forces;
  • finite elements;
  • mesh optimization;
  • shape optimization

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 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. Copyright © 2004 John Wiley & Sons, Ltd.

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