摘要
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.
作者
田利瑞
朱松
聂峰华
李冬明
孔令好
TIAN Lirui;ZHU Song;NIE Fenghua;LI Dongming;KONG Linghao(School of Civil Engineering and Architecture,Wuhan University of Technology,Wuhan 430070,Hubei,China)
出处
《武汉大学学报(理学版)》
CAS
CSCD
北大核心
2018年第5期431-440,共10页
Journal of Wuhan University:Natural Science Edition
基金
湖北省自然科学基金青年项目(2018CFB129)
中央高校基本科研业务费专项资金(2016IVA022)
关键词
准凸重构核近似
准凸重构核粒子法
重构核粒子法
弹性力学问题
弹性断裂问题
quasi-convex reproducing kernel approximation
quasi-convex reproducing kernel particle method
reproducing kernel particle method
elasticity problem
elastic fracture problem