On a solution strategy for energy-based mesh optimization in finite hyperelastostatics

Scherer, M., Denzer, R. and Steinmann, P. (2008) On a solution strategy for energy-based mesh optimization in finite hyperelastostatics. Computer Methods in Applied Mechanics and Engineering, 197(6-8), pp. 609-622. (doi: 10.1016/j.cma.2007.08.005)

Abstract

The objective of this work is the development of a numerical solution strategy for energy-based mesh optimization in finite hyperelastostatics. In finite element computations that rely on the principle of minimum potential energy, the variational principle itself provides the basis for r-adaptive methods. The numerical solution can be improved by further minimizing the discrete potential energy with respect to the material node point positions. In this paper, we regard the mesh optimization as a nonlinear minimization problem with equality and inequality constraints. The equality constraints correspond to the spatial equilibrium condition, whereas the inequality constraints are given by the natural restriction that material elements with a negative volume (Jacobian) are inadmissible. Based on this interpretation, we develop a stable numerical solution strategy in which two approaches of nonlinear programming are combined. Applying a barrier method, the minimization problem is transformed into a sequence of problems without inequality constraints. Each problem of the sequence is solved by means of a Newton scheme that operates on the constrained surface given by the spatial equilibrium condition.

• Item Type: Articles
• Additional Information: The authors would like to thank the “Deutsche Forschungsgemeinschaft” (DFG) for their support of this work under the Grant STE 544/24-1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Scherer, M., Denzer, R., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Publisher: Elsevier
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 01 September 2007

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