弹性力学和弹性断裂问题的准凸重构核粒子法

Quasi-Convex Reproducing Kernel Particle Method for Elasticity and Elastic Fracture Problems

通过放宽重构条件,准凸重构核近似可以构造任意高阶正性更好的形函数.本文结合控制方程的Galerkin弱式,将准凸重构核近似应用于弹性力学和弹性断裂问题的计算,推导了相关计算公式,建立了弹性力学和弹性断裂问题的准凸重构核粒子法（quasi-convex reproducing kernel particle method,QCRKPM）.通过编写QCRKPM的MATLAB程序,对中心圆孔方板和边缘裂纹方板这两个算例进行了模拟计算.将QCRKPM的数值精度和计算效率与无单元Galerkin（element-free Galerkin,EFG）方法和重构核粒子法（reproducing kernel particle method,RKPM）进行对比,验证了QCRKPM的高效性和高精度.

By applying the relaxed reproducing conditions,the so-called quasi-convex reproducing kernel approximation gains the ability to construct arbitrary order shape functions with enhanced positivity.In this paper,combined with the Galerkin weak form of the control equations,the quasi-convex reproducing kernel approximation was applied to analyze elasticity and elastic fracture problems.The theoretical formulas were derived,and the quasi-convex reproducing kernel particle method（QCRKPM）for elasticity and elastic fracture problems were proposed.Two examples including a square plate with a central circular hole and a square plate with an edge crack were simulated by MATLAB.By comparing the numerical accuracy and computational efficiency of the proposed QCRKPM with that of the element-free Galerkin（EFG）method and reproducing kernel particle method（RKPM）,the high efficiency and precision of the QCRKPM were verified.