弹性静力学问题的边界积分形式的数值流形法  

The numerical manifold method for boundary integrals in elastostatics

作　　者：聂治豹 郑宏 万涛 林姗 NIE Zhi-bao;ZHENG Hong;WAN Tao;LIN Shan(Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124

出　　处：《岩土力学》2020年第4期1429-1436,共8页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.51538001,No.11572009)。

摘　　要：传统的数值流形法(NMM)一般均采用区域积分形式。结合边界单元法(BEM),提出了一种边界积分形式的数值流形法。该方法既能发挥NMM的可以灵活选取局部基的优势,又具有BEM降低问题求解维数的特点。针对二维的弹性静力学问题,对3个具有解析解的不同基准算例进行了数值应用,验证了所提方法的有效性和效率。计算结果表明,提高局部基的阶次可有效提高方法的计算精度。The traditional numerical manifold method(NMM)adopts the form of regional integration.This paper proposed a new NMM in the form of boundary integral by integrating the advantages of both the boundary element method(BEM)and the NMM,namely the dimension reduction of BEM and the flexibility of local base selection of NMM.For two-dimensional elastostatics problems,three different benchmark examples with analytical solutions are applied to verify the validity and efficiency of the newly proposed NMM.The results show that the accuracy of the proposed procedure can be effectively improved by increasing the order of the local basis.

关 键 词：数值流形法 边界单元法 弹性静力问题 应力集中因子 

分 类 号：TU452[建筑科学—岩土工程]