Reproducing kernel particle boundary element-free method for elasticity

Abstract

By combining the reproducing kernel particle method (RKPM) and boundary integral equation method for elasticity, the reproducing kernel particle boundary element-free (RKP-BEF) method is presented in this paper. Formulae for the RKP-BEF method are derived. The discrete boundary integral equations of the RKP-BEF method are established by considering the numerical integral schemes and the treatment of singular integrals, and the formulae of the displacement and stress of inner points for the RKP-BEF method are given. The RKP-BEF method has a higher precision as the smoothness of the shape function of RKP method is the same as that of the kernel function, and the values of polynomials at interpolating points can be exactly reconstructed. Numerical examples are given for verifying the effectiveness and correctness of the RKP-BEF method presented in this paper.