弹性动力学的双互易杂交边界点法  

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR ELASTODYNAMICS

作　　者：苗雨[1] 王元汉[1] 

机构地区：[1]华中科技大学,土木工程与力学学院,武汉430074

出　　处：《力学学报》2009年第1期122-128,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(50808090)~~

摘　　要：将双互易法同杂交边界点法相结合,提出了求解弹性动力问题的新型数值方法——双互易杂交边界点方法.该算法在求解弹性动力问题时,将控制方程非齐次项的域内积分转化为边界积分.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法求得,特解则使用局部径向基函数插值得到,从而实现了使用静力问题的基本解来求解动力问题。计算时仅仅需要边界上离散点的信息,无论积分还是插值都不需要网格,域内节点仅用来插值非齐次项,因此该算法仍是一种边界类型的无网格方法.数值算例表明,该方法后处理简单,计算精度高,适合于求解弹性动力问题.Combined the hybrid boundary node method boundary-type meshless method, dual reciprocity hybrid （HBNM） and the dual reciprocity principle, a truly boundary node method （DR-HBNM）, is presented for elastodynamics. HBNM is a truly boundary-type meshless method, which has the advantages of meshless method and the BEM. The HBNM is used to solve the homogeneous equations, and the DRM is employed to solve the inhomogeneous terms using radial basis functions （RBF）. The domain integrals for the inhomogeneous terms in the govern equations of elastodynamics can be taken into boundary integrals using the reciprocity principle. The solution is divided into the particular part and the general part. No meshes axe needed either for the interpolation purposes or for integration process. Only discrete nodes are constructed on the boundary of a domain and several nodes in the domain are needed just for the RBF interpolation. The serious ＂boundary layer effect＂ in the HBNM is circumvented by the adaptive integration scheme. The present method has many advantages, such as simple postprocess and higher accuracy. The numerical examples have demonstrated the accuracy and convergence of the present scheme.

关 键 词：双互易杂交边界点法 最小移动二乘法 弹性动力学 径向基函数 

分 类 号：O242.2[理学—计算数学]