RKPM形状函数的矩式显式表述及快速计算

Explicit form and efficient computation of RKPM shape functions in terms of moments

给出了计算再生核质点法(RKPM)形状函数及其导数的矩式显式处理方法。其特点是在计算形状函数及其导数时不涉及矩阵的求逆或者线性方程组的求解,从而减少计算误差的产生并提高了计算速度。二维及三维形状函数计算算例表明该方法是提高RKPM计算效率的一种有效途径。

Reproducing Kernel Particle Method (RKPM) shape functions and their derivatives are expressed explicitly in terms of moments. This eliminates totally the errors arisen from numerical computation of matrix inversion and solution of linear equations. Furthermore, this method can improve computation efficiencies as well as save computer memory. Numerical examples associated with computation of 2-D and 3-D shape functions are presented, and comparisons between the classical numerical method and the analytical method are included. The analytical method constitutes prominent advantages especially when a large number of unknowns are involved.