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

The application of the singular boundary method(SBM),a relatively new meshless boundary collocation method,to the inverse Cauchy problem in threedimensional(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.