The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity

The meshless method based on the local boundary integral equation (LBIE) is a promising method for solving boundary value problems, using an local uns ymmetric weak form and shape functions from the moving least squares approx imation. In the present paper, the meshless method based on the LBIE for so lving problems in linear elasticity is developed and numerically implemente d. The present method is a truly meshless method, as it does not need a "fi nite element mesh", either for purposes of interpolation of the solution va riables, or for the integration of the energy. All integrals in the formula tion can be easily evaluated over regularly shaped domains (in general, sph eres in three-dimensional problems) and their boundaries. The essential bou ndary conditions in the present formulation can be easily imposed even when the non-interpolative moving least squares approximation is used. Several numerical examples are presented to illustrate the implementation and perfo rmance of the present method. The numerical examples show that high rates o f convergence with mesh refinement for the displacement and energy norms ar e achievable. No postprocessing procedure is required to compute the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.