弹性力学问题中的双重互易杂交边界点法  

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD IN ELASTICITY PROBLEMS

作　　者：苗雨[1,2] 晏飞[1,2] 

机构地区：[1]华中科技大学土木工程与力学学院,湖北武汉430074 [2]华中科技大学控制结构湖北重点实验室,湖北武汉430074

出　　处：《南阳理工学院学报》2009年第1期52-55,75,共5页Journal of Nanyang Institute of Technology

基　　金：国家自然科学基金赞助项目(No.50808090)

摘　　要：杂交边界点法是一种边界类型的纯无网格方法,它同时具有边界元法降维的优势和无网格法无需插值和积分网格的优良特性。但在求解非齐次问题时,不可避免的需要域内积分。本文将双重互易法引入到该方法中,将对非齐次项的域内积分转化成边界积分,形成双重互易杂交边界点法。该方法将问题的解分为通解和特解两部分,通解使用杂交边界点方法求解,特解利用局部径向基函数近似。为了达到特解插值的通用性,本文提出了特解基本形式。该方法是一种边界型纯无网格方法。数值算例表明,该方法是一种计算量小、精度较高的数值方法,适合于求解各种弹性力学问题。As a boundary-type truly meshless method, the hybrid boundary node method has the advantages of both dimensionality reduction of BEM and meshless for interpolation and integral of meshless method. Unfortunately, when it is applied to solve inhomoge- neous problems, the domain integral is inevitable. In this paper, the dual reciprocity method is introduced into the hybrid boundary node method, then the domain integral for inhomogeneous term is changed into the integral on the boundary and the dual reciprocity hybrid boundary node method is obtained. In this method, the solution is divided into two parts-particular and general solutions. The general solution is solved by means of HBNM, and the particular one is approximated by using the radial basis functions. This method is also a boundary-type truly meshless method. It does not need extra equations to compute internal parameters in the domain. The numerical examples show that this method has some advantages such as small computation and high precision and can be applied to various elasticity computations.

关 键 词：杂交边界点法 双重互易法 移动最小二乘法 非齐次弹性力学问题 

分 类 号：O241[理学—计算数学]