含体力的边界元法研究及在大坝力学分析中的应用

发布时间：2018-04-01 18:45

本文选题：边界元法　切入点：域积分　出处：《中国农村水利水电》2017年05期

【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。
[Abstract]:The boundary element method has the advantage of reducing the dimension of the problem and only needs to discretize the boundary. However, the integral equation obtained by the boundary element method often contains domain integral when solving the inhomogeneous equation. In this paper, an adaptive background mesh integration method, which is a new method to deal with domain integration, is proposed. The method is integrated in the background grid, and the background mesh is constructed by boundary element and quadtree structure. In the process of construction, only the information of the boundary element is required. Therefore, the method only needs to discretize the boundary and is very suitable for application in the boundary element method. This method is very convenient to combine with the fast multipole algorithm to solve large-scale problems. The method can be applied to dam simulation analysis.
【作者单位】：武汉大学水资源与水电工程科学国家重点实验室;
【基金】：国家自然科学基金金资助项目(51609181)
【分类号】：TV64

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