奇异边界法模拟二维弹性力学问题  

SINGULAR BOUNDARY METHOD FOR TWO DIMENSIONAL ELASTICITY PROBLEMS

作　　者：谷岩[1] 陈文[1] 

机构地区：[1]河海大学力学与材料学院工程力学系,南京210098

出　　处：《固体力学学报》2014年第3期217-225,共9页Chinese Journal of Solid Mechanics

基　　金：国家重点基础研究发展规划(973)项目(2010CB832702);国家杰出青年科学基金(11125208)项目资助

摘　　要：奇异边界法是一种新的边界型无网格数值离散方法.该方法使用基本解作为插值基函数,在继承传统边界型方法优点的同时,不需要费时费力的网格划分和奇异积分,数学简单,编程容易,是一个真正的无网格方法.为避免配置点与插值源点重合时带来的基本解源点奇异性,该方法提出了源点强度因子的概念,从而将边界型强格式方法的核心归结为求解源点强度因子.论文首次将该方法应用于求解平面弹性力学问题.数值算例表明,本文算法稳定,效率高,并可达到很高的计算精度.The singular boundary method （SBM） belongs to the family of meshless boundary collocation methods and can be viewed as one kind of modified method of fundamental solutions （MFS）. This method was originally proposed in 2009, based on the notion of boundary element method （BEM） and MFS,fully inherited the merits of both and in the meantime possessing its unique advantages. The key idea is to introduce the concept of the origin intensity factor to isolate the singularity of the fundamental solutions, so that the source points can be directly placed on the real boundary. This overcomes a perplexing fictitious boundary outside physical domain in the MFS. This paper makes the first attempt to apply the method to two dimensional elasticity problems. The accuracy and stability of the proposed method are tested to three benchmark elasticity examples in which the SBM solutions are compared with the results obtained by using the MFS,traditional SBM,and the finite element method （FEM）.

关 键 词：边界型无网格方法 奇异边界法 基本解 源点强度因子 弹性力学问题 

分 类 号：O343.1[理学—固体力学]