A Monte Carlo solution method for linear elasticity

A probabilistic method is proposed and implemented to solve linear elastici ty problems. The method, called walk on the boundary method (WBM), uses the same governing equations as the boundary element method, Unlike in finite element and boundary element methods, WBM does not require any meshing, Als o, error estimates for WBM are easier to obtain than in finite element and boundary element methods. Furthermore, WBM obtains a point solution at a sp ecific point of interest instead of a full field solution as in finite elem ent and boundary element methods. WBM is developed for general traction bou ndary value problems in antiplane shear, plane strain, and 3D elasticity. N umerical implementations are performed for three example problems: (1) anti plane shear problem with a centrally located circular hole being loaded by uniformly applied traction, (2) plane strain problem with centrally located circular hole being loaded by uniform tension, and (3) 3D elasticity probl em with a centrally located spherical cavity being loaded by uniform tensio n. Results from the three example problems compared favorably with results from the analytical and finite element solution. Three critical issues asso ciated with the WBM for linear elasticity are pointed out for its further i mprovement. (C) 2000 Elsevier Science Ltd. All rights reserved.