动力分析的二阶一致无网格法  

Quadratically consistent meshfree method for dynamics

作　　者：王冰冰[1] 陈嵩涛 段庆林[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《应用力学学报》2014年第3期353-358,487,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11102036;11072046;11232003;11372066);973计划(2010CB731502);中央高校基本科研业务费专项资金(DUT12LK08);教育部留学回国人员科研启动基金

摘　　要：为改善无网格法动力分析的效率和精度,将具有二阶一致性的三点积分方法(Quadratically Consistent 3-point integration method,QC3)从静力问题的无网格法分析拓展到弹性动力问题;形函数采用二次的移动最小二乘近似;采用修正的节点导数计算积分点上的刚度阵;并应用Newmark法进行时域积分。数值计算结果表明:QC3对于动力分析十分有效,相比于仅满足线性一致性的一点积分方法(Linear Consistent 1-point integration method,LC1),精度提高了一个数量级,且可以得到光滑无振荡的应力场;与标准的三角形(Standard Triangle,ST)16点积分方案相比,计算精度相当,但仅消耗了约为其1/6的CPU时间。In order to improve the accuracy and computational efficiency of meshfree method for dynamic analysis, this paper extends the quadratically consistent 3-point integration method(QC3) originally developed for static problem to the meshfree analysis of elastodynamics. Quadratic base is used in the Moving Least-Square(MLS) approximation. The stiffness matrix at quadrature points are computed by the corrected nodal derivatives. Newmark method is adopted for time integration. Numerical results show that QC3 is very effective for dynamic analysis: In comparison with the linear consistent 1-point integration method(LC1), QC3 improves the accuracy one order higher and results in smooth stress fields; In comparison with the standard triangle 16-point(ST16) integration method, they have comparable accuracy, however, QC3 consumes only 1/6 the CPU time consumed by ST16.

关 键 词：无网格 数值积分 导数修正 弹性动力学 一致性 

分 类 号：O326[理学—一般力学与力学基础]