Identification of geometric shapes and material properties of inclusions in two-dimensional finite bodies by boundary parameterization

A system identification scheme based on the boundary element method (BEM) is proposed to determine geometric shape and elastic material properties of an inclusion in a finite body. The proposed algorithm is based on the minimization of least squared errors between measured displacement and calculated displacement by a boundary element model. A regularization function that consists of the geometric term and material property term is added to the error function to overcome ill-posedness of inverse problems. To deal with the shape variation of an inclusion during the optimization process, the boundary parameterization technique is applied to the BEM. The recursive quadratic programming (RQP) technique with line search is used for optimization.

[1]  Masataka Tanaka,et al.  A boundary element method for some inverse problems in elastodynamics , 1989 .

[2]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[3]  J. V. Beck,et al.  Combined function specification-regularization procedure for solution of inverse heat conduction problem , 1984 .

[4]  R. T. Fenner,et al.  OPTIMUM SHAPE DESIGN AND POSITIONING OF FEATURES USING THE BOUNDARY INTEGRAL EQUATION METHOD , 1996 .

[5]  Keith Hjelmstad,et al.  CRACK IDENTIFICATION IN A CANTILEVER BEAM FROM MODAL RESPONSE , 1996 .

[6]  Soobong Shin,et al.  A numerical study on detecting defects in a plane-stressed body by system identification , 1999 .

[7]  L. M. Bezerra,et al.  A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection , 1993 .

[8]  D. Schnur,et al.  An inverse method for determining elastic material properties and a material interface , 1992 .

[9]  Kim Stelson,et al.  Finite Element Analysis of Some Inverse Elasticity Problems , 1989 .

[10]  S. P. Neuman,et al.  A statistical approach to the inverse problem of aquifer hydrology: 1. Theory , 1979 .

[11]  D. Schnur,et al.  Finite element solution of two‐dimensional inverse elastic problems using spatial smoothing , 1990 .

[12]  D. Schnur,et al.  Spatially regularized solution of inverse elasticity problems using the BEM , 1989 .

[13]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .

[14]  Keith D. Hjelmstad,et al.  Damage detection and assessment of structures from static response , 1997 .

[15]  M. H. Aliabadi,et al.  Flaw identification using the boundary element method , 1995 .

[16]  C. W. Groetsch,et al.  The theory of Tikhonov regularization for Fredholm equations of the first kind , 1984 .

[17]  Huy Duong Bui,et al.  Inverse Problems in the Mechanics of Materials: An Introduction , 1994 .

[18]  Yusuke Honjo,et al.  Inverse analysis of an embankment on soft clay by extended Bayesian method , 1994 .

[19]  K. Hjelmstad,et al.  Parameter Estimation of Structures from Static Response. I. Computational Aspects , 1994 .