弹性扭转问题的多互易杂交边界点解法  

Multiple reciprocity hybrid boundary node method for elastic torsion problems

作　　者：谭飞[1] 王元汉[1] 胡浩军[1] 

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

出　　处：《华中科技大学学报（自然科学版）》2010年第10期128-132,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50808090);华中科技大学博士学位论文创新基金资助项目(0109240013)

摘　　要：将弹性扭转问题视为泊松方程的边值问题,结合正则杂交边界点法与多互易法,提出一种新的边界类型的无网格方法——多互易杂交边界点法.该方法将问题的解分为通解和特解两部分,其中通解采用正则杂交边界点方法求解,特解则利用多互易法的高阶基本解近似.因而此解法既具有边界元法和无网格法的优良特性,也避免了域内积分和布点.引入坐标变换,各向异性杆的扭转问题也得到了求解.数值算例表明,该方法精度高、效率高、收敛性好.Elastic torsion may be considered as a boundary value problem of Poisson＇s equation. Combining the regular hybrid boundary node method （RHBNM） and multiple reciprocity method （MRM）, a new boundary meshless method, which is called multiple reciprocity hybrid boundary node method （MRHBNM）, is proposed for solving the elastic torsion problem. The solution of the problem was di- vided into two parts, i. e. , the complementary and particular solutions. The complementary solution is solved by RHBNM, and the particular solution was approximated by the high-order fundamental so- lutions. Therefore, it has the advantages of the both BEM and meshless methods, the interior integrals and inner points can also be avoided. The torsion problem of anisotropic bar was also solved, in which the coordinate conversion is employed. Numerical examples show that the present method is accurate, effective and convergent.

关 键 词：弹性扭转 泊松方程 正则杂交边界点法 多互易法 高阶基本解 

分 类 号：O343.1[理学—固体力学]