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A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics

A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics
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Year:    2018

Author:    Aixia Zhang, Yan Gu, Qingsong Hua, Wen Chen

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1459–1477

Abstract

The application of the singular boundary method (SBM), a relatively new meshless boundary collocation method, to the inverse Cauchy problem in three-dimensional (3D) linear elasticity is investigated. The SBM involves a coupling between the non-singular boundary element method (BEM) and the method of fundamental solutions (MFS). The main idea is to fully inherit the dimensionality advantages of the BEM and the meshless and integration-free attributes of the MFS. Due to the boundary-only discretizations and its semi-analytical nature, the method can be viewed as an ideal candidate for the solution of inverse problems. The resulting ill-conditioned algebraic equations is regularized here by employing the first-order Tikhonov regularization technique, while the optimal regularization parameter is determined by the $L$-curve criterion. Numerical results with both smooth and piecewise smooth geometries show that accurate and stable solution can be obtained with a comparatively large level of noise added into the input data.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0103

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1459–1477

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Meshless method singular boundary method method of fundamental solutions elastostatics inverse problem.

Author Details

Aixia Zhang

Yan Gu

Qingsong Hua

Wen Chen

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