径向基点插值法计算效率的改进方法  

Improvement of Radial Point Interpolation Method in Computational Efficiency

作　　者：胡海浪[1] 曹子龙[1] 关玉璞[1] 陈伟[1,2] HU Hailang CAO Zilong GUAN Yupu CHEN Wei(Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics ＆ Astronautics, Nanjing, 210016, China Collaborative Innovation Center of Advanced Aero Engine, Nanjing, 210016, China)

机构地区：[1]南京航空航天大学江苏省航空动力系统重点实验室,南京210016 [2]先进航空发动机协同创新中心,南京210016

出　　处：《南京航空航天大学学报》2017年第1期117-124,共8页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：伽辽金弱形式和径向基点插值法(Radial basis point interpolation method,RPIM)的无网格法在解决偏微分方程问题中表现出良好的性能,但是在同时提高计算效率和精度方面存在困难。为了提高此类无网格法的计算效率,本文定义了一种基于背景网格的定义域,在计算定义域内的积分点插值时采用同一批节点,在插值计算过程中减少了部分矩阵计算次数,降低了RPIM无网格法的计算时间。在提高计算精度方面,本文提出一种杂交应力的无网格方法,用Hellinger-Reissner(H-R)变分原理推导求解方程,采用无网格方法求解。数值算例表明,本文方法计算二维固体力学时,在具备良好的计算精度的同时提高了计算速度,具有较高的实际应用价值。The meshless method with Galerkin weak form and radial basis point interpolation method （RPIM） shows good performance in solving partial differential equation （PDE）, but it is difficult to improve the computational efficiency and accuracy at the same time. In order to improve the efficiency of the meshless method, this paper sets up a domain based on the background grid, and uses the same node during the process of integral interpolation within the domain, which can reduce some matrix computa- tions and computing time of the RPIM method. In terms of accuracy, this paper proposes a meshless method of hybrid stress, i. e. , using Hellinger-Reissner （H-R） variational principle to derive the solving equations and using meshless method to solve the problem. Numerical example demonstrates that the new method has the higher computational accuracy and the faster computational speed when calculating two-dimensional solid mechanics, thus it has a high practical application value.

关 键 词：计算力学 无网格法 径向基点插值法 杂交应力 

分 类 号：O343.1[理学—固体力学]