基于交叉节点对无网格Galerkin法的改进算法研究  

STUDY ON AN IMPROVED ALGORITHM OF ELEMENT-FREE GALERKIN METHOD BASED ON INTERACTING NODAL PAIRS

作　　者：龚曙光[1] 卢海山 张建平[1] 唐芳[1] 

机构地区：[1]湘潭大学机械工程学院,湖南湘潭411105

出　　处：《工程力学》2015年第8期16-21,28,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(51375417);湖南省高校科技创新团队项目(湘教通[2012]318号)

摘　　要：针对无网格Galerkin法刚度矩阵的稀疏存储实现难、节点与积分点的全局搜索效率低等问题,该文基于交叉节点对及其循环组装整体刚度矩阵的思想,利用CSR格式存储刚度矩阵,通过局部搜索方法来搜寻节点与积分点,提出了一种采用三角形网格进行积分计算的无网格Galerkin法。通过数值算例对比了不同节点规模的刚度矩阵存储消耗,以及节点与积分点的搜索效率。结果表明所提出算法在满足计算精度的前提下,能有效地节省存储空间和提高节点与积分点的搜索效率,并对复杂形状的几何模型具有良好的适应性。In order to save memory in the stiffness matrix and improve the global search efficiency for nodes and integral points, in this paper we propose an improved algorithm for the element free Galerkin method by using the idea of crossing interacting node pairs to assemble a stiffness matrix, and using the triangular integral mesh to carry out integral calculation. Meanwhile, the CSR format is employed to store stiffness matricies, and a local search method is presented for searching nodes and integral points. The memory requirements of the stiffness matrix and the search efficiency of nodes and integral points for different sized meshes are compared by numerical examples. The results obtained show that the improved algorithm can save memory effectively and improve the search efficiency of nodes and integral points, and is well adapted to complex geometry models.

关 键 词：无网格GALERKIN法 交叉节点对 CSR存储格式 局部搜索 三角形积分网格 

分 类 号：TH123[机械工程—机械设计及理论] O241.82[理学—计算数学]