An Inverse Analysis for Determining Geometric Shape and Material

    Properties of an Inclusion

    in a Finite body using Domain Parameterization

    Yong Han Kim


This paper presents a system identification scheme to determine geometric shape and elastic material properties of an inclusion in a finite body. Material properties and the coordinates of control nodes that represent discretized boundary of an inclusion are selected as the system parameters. The parameters are identified by minimizing the least squared errors between the measured displacement field and the calculated displacement field by finite element model.

   The domain parameterization technique is adopted to deal with the shape variation of an inclusion. Variational statement in the referential configuration is discretized by utilizing isoparametric mapping and Laplace mapping. Regularization technique is employed to stabilize the minimization process by imposing regularization function defined by discretized surface length of an inclusion. The scheme of updating regularization factor is proposed for maximizing regularization effect.

   To prevent unreasonable mesh distortion leading to non-unique isoparametric mapping and negative element area, nonlinear constraint is imposed on each element. To maintain feasibility of the solution calculated by linearized constraint in each iteration, return mapping algorithm based on the gradient projection method is adopted. The modified Levenberg-Marquardt method with Fletcher's active set algorithm is adopted for the minimization process. The sensitivity of displacement with respect to design variables is obtained by the direct differentiation of the variational statement of the equilibrium equation. The validity of the proposed method is demonstrated through three examples.


Key Word

Domain parameterization technique, Regularization, Return mapping, Modified Levenberg-Marquardt method, Direct differentiation, Sensitivity

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