奇异杂交边界点法求解扭转问题  

Singular Hybrid Boundary Node Method in Solving Torsion Problems

作　　者：苗雨[1] 晏飞[1] 郑伟峰 

机构地区：[1]华中科技大学土木工程与力学学院 [2]河南省禹州市公路管理局,河南禹州461670

出　　处：《华中科技大学学报（城市科学版）》2007年第3期45-48,共4页Journal of Huazhong University of Science and Technology

基　　金：中国科学院武汉岩土力学研究所岩土力学重点实验室开放课题基金资助项目(Z110507);华中科技大学校科研基金资助项目

摘　　要：提出了一种新的边界类型的无网格方法——奇异杂交边界点法用于求解扭转问题,该方法是以修正变分原理和移动最小二乘近似为基础,同时利用无网格法局部边界积分方程中的局部化思想,计算时仅仅需要边界上离散点的信息,因此它同时具有边界元法和无网格法的优良特性。本文将该方法同双重互易法结合用来求解扭转问题,将该问题的解分为通解和特解两部分,其中通解使用奇异杂交边界点方法求解,特解则利用局部径向基函数近似,彻底避免了域内积分。使用刚体位移法处理方法中的强奇异积分,同时提出了一种自适应的积分方案,解决了边界类型方法中存在的"边界层效应"。数值计算表明,本文方法具有较高的精度和收敛性。A new boundary type meshless method, which is called singular hybrid boundary node method （SHBNM）, is presented for solving torsion problems. It is based on a modified variational principle and moving least squares （MLS） approximation, and exploiting the localization idea from MLBIE, Only randomly distributed nodal points on the bounding surface of the domain are required in computation, so it has the advantages of both BEM and meshless methods. The dual reciprocity method （DRM） is combined with SHBNM to solve torsion problems. The solution of the problem is devided into particular solution and homogeneous solution. The homogeneous solution is solved by means of SHBNM, and the particular solution is approximated by using radial basis functions. And the interior integrals can be avoided. The rigid movement method is employed to solve the hypersingular integrations. The boundary layer effect, which is the main drawback of the boundary type mothods, has been overcome by an adaptive integration scheme. Numerical examples show high accuracy and high convergence rates of the presented scheme.

关 键 词：奇异杂交边界点法 双重互易法 扭转问题 

分 类 号：O343.1[理学—固体力学]