Adaptive Finite Element Methods for the Identification of Elastic Constants

Authors:
Tao Feng;Mårten Gulliksson;Wenbin Liu
Affiliations:
Department of Engineering, Physics and Mathematics, Mid Sweden University, Sundsvall, Sweden S-851 70;Department of Engineering, Physics and Mathematics, Mid Sweden University, Sundsvall, Sweden S-851 70;Institute of Mathematics and Statistics, University of Kent, Canterbury, UK CT2 7NF
Venue:
Journal of Scientific Computing
Year:
2006

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Abstract

In this paper, the elastic constants of a material are recovered from measured displacements where the model is the equilibrium equations for the orthotropic case. The finite element method is used for the discretization of the state equation and the Gauss---Newton method is used to solve the nonlinear least squares problem attained from the parameter estimation problem. A posteriori error estimators are derived and used to improve the accuracy by an appropriate mesh refinement. A numerical experiment is presented to show the applicability of the approach.