A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics (Advances in Applied Mathematics and Mechanics, 2021)
The application of the singular boundary method (SBM), a relatively newmeshless boundary collocation method, to the inverse Cauchy problem in three-dimensional(3D) linear elasticity is investigated. The SBM involves a coupling betweenthe non-singular boundary element method (BEM) and the method of fundamentalsolutions (MFS). The main idea is to fully inherit the dimensionality advantagesof the BEM and the meshless and integration-free attributes of the MFS. Dueto the boundary-only discretizations and its semi-analytical nature, the method canbe viewed as an ideal candidate for the solution of inverse problems. The resultingill-conditioned algebraic equations is regularized here by employing the first-orderTikhonov regularization technique, while the optimal regularization parameter is determinedby the $L$-curve criterion. Numerical results with both smooth and piecewisesmooth geometries show that accurate and stable solution can be obtained with a comparativelylarge level of noise added into the input data.