弹性力学的重构核粒子边界无单元法

将重构核粒子法(RKPM)和边界积分方程方法结合，提出了一种新的边界积分方程无网格方法——重构核粒子边界无单元法(RKP-BEFM).对弹性力学问题，推导了其重构核粒子边界无单元法的公式，研究其数值积分方案，建立了重构核粒子边界无单元法离散化边界积分方程，并推导了重构核粒子边界无单元法的内点位移和应力积分公式.重构核粒子法形成的形函数具有重构核函数的光滑性，且能再现多项式在插值点的精确值，所以本方法具有更高的精度.最后给出了数值算例，验证了本方法的有效性和正确性. 关键词： 重构核粒子法 弹性力学 边界无单元法

Reproducing kernel particle boundary element-free method for elasticity

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.