含体力的边界元法研究及在大坝力学分析中的应用  

The Boundary Element Method with Body Force and its Application in Mechanical Analysis of Dam

作　　者：李响[1] 张浩东[1] 王桥[1] 周伟[1] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,武汉430072

出　　处：《中国农村水利水电》2017年第5期58-62,共5页China Rural Water and Hydropower

基　　金：国家自然科学基金金资助项目(51609181)

摘　　要：边界元法具有对求解问题降维的优势,只需要对边界进行单元离散。然而,边界元法在求解非齐次方程时,得到的积分方程往往含有域积分,限制了边界元法的应用范围。拟提出一种处理域积分的新方法——自适应背景网格积分法,该方法在背景网格中积分,背景网格通过边界单元和四叉树结构构造,在构造过程中只需要边界单元的信息。因此,该方法只需要对边界进行离散,非常适合应用于边界元法中。该方法非常方便与快速多极算法结合起来求解大规模问题,可将该方法应用于大坝仿真分析中。Boundary element method （BEM） have the advantage that the dimension of the problem can bereduced by one. However, BEMis not suitable for nonlinear problems since it will have domain integrals whilesolving nonhomogeneous equations, which limits the application of BEM.A new technology for treatment of domain integrals will be proposedin this paper, called as the adaptive cell-based domain integration method （CDIM）. The integrals are performed in cells, and the cells are created from the boundary elements and aquad-treestructure. The method is a boundary-only diseretization method since only the information of the boundary elements is needed. Thus, it can be applied in BEM very easily and is very suitable for large scale problems by coupling with fast muhipole method. The method has been applied in the me- chanical analysis of dam.

关 键 词：边界元法 域积分 自适应背景网格积分法 

分 类 号：TV731.1[水利工程—水利水电工程] TV312