基于快速多极杂交边界点法的三维弹性力学问题求解  

Solving 3D Elasticity Problems Based on Fast Multipole Hybrid Boundary Node Method

作　　者：李祥[1] 刘彪 张宗亮 臧耀辉 LI Xiang;LIU Baio;ZHANG Zongliang;ZANG Yaohui(China Renewable Energy Engineering Institute,Beijing 100120 China;College of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210024 Jiangsu China)

机构地区：[1]水电水利规划设计总院,北京100120 [2]河海大学水利水电学院,江苏南京210024

出　　处：《水力发电》2024年第7期38-42,共5页Water Power

基　　金：国家自然科学基金资助项目(52309153);中国电建科技项目(DJ-ZDXM-2022-01)。

摘　　要：杂交边界点法是近年来快速发展的一种无网格方法,国内外学者已成功将快速多极算法与边界元方法相结合,使得边界元的应用范围进一步扩大。为此,开展了将快速多极算法与杂交边界点法相结合计算三维弹性力学问题的研究。三维弹性力学的基本解利用球谐函数展开为级数,并通过自适应八叉树结构将求解域分解为分级不相邻的区域。数值算例表明,快速多极杂交边界点法具有很好的计算精度和计算效率,该算法在普通个人电脑上,可以在令人接受的时间内完成40万以上自由度的计算。因此,该算法在大规模问题的计算中具有显著优势,对于复合材料、加筋混凝土等更为复杂材料的力学问题具有实用性。The hybrid boundary node method is a meshless method developed rapidly in recent years.Scholars at home and abroad have successfully combine fast multipole method with boundary element method,which further expands the application range of boundary element.Therefore,the combination of hybrid boundary node method and fast multipole method for solving 3D elasticity problems is studied in this paper.The fundamental solution of 3D elasticity problems is expanded in terms of series,and for subdividing the computational domain into well-separated cells hierarchically and invoking the multipole expansion approximation,an oct-tree data structure is adopted.Numerical examples show that the fast multipole hybrid boundary node method has higher computational accuracy and efficiency,and it can compute more than 400,000 degree of freedoms in an acceptable time on a common personal computer.The results show that the method has significant advantages in the calculation of large-scale problems,and is practical for the mechanical problems of more complex materials such as composite materials and reinforced concrete.

关 键 词：快速多极算法 杂交边界点法 三维弹性力学 大规模问题 

分 类 号：TV31[水利工程—水工结构工程] TU31[建筑科学—结构工程]