TY - JOUR
T1 - A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics
AU - Zhang , Aixia
AU - Gu , Yan
AU - Hua , Qingsong
AU - Chen , Wen
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1459
EP - 1477
PY - 2018
DA - 2018/09
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2018-0103
UR - https://global-sci.org/intro/article_detail/aamm/12722.html
KW - Meshless method, singular boundary method, method of fundamental solutions, elastostatics, inverse problem.
AB - <p style="text-align: justify;">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.</p>