B-spline based boundary conditions in the material point method
B-spline based boundary conditions in the material point method
复制标题
DOI：
10.1016/j.compstruc.2018.11.003
复制
发表时间：
2019-02
影响因子：
4.7
通讯作者：
Y. Bing;M. Cortis;T. J. Charlton;W. Coombs;C. Augarde
中科院分区：
文献类型：
--
作者：
Y. Bing;M. Cortis;T. J. Charlton;W. Coombs;C. Augarde
材料点法是解决大变形固体力学问题的一种日益流行的方法。然而，在该方法中应用边界条件存在一些问题，到目前为止，还没有提出同时施加诺伊曼和狄利克雷边界条件的一般方法。本文提出了一种新的基于b样条的边界方法，作为标准物质点法中边界表示、边界跟踪和边界条件施加的完整方法。采用b样条插值技术形成独立于背景网格的连续边界。将b样条边界与隐式边界相结合，实现了Dirichlet边界条件。沿b样条边界的表面牵引力的直接积分包含了诺伊曼边界条件。当使用隐式求解器实现时，这种通用边界方法不仅扩大了物质点法所有变体可以分析的问题，而且也适用于其他嵌入和非匹配网格方法。虽然Dirichlet边界条件仅限于隐式方法，但边界表示、跟踪和Neumann边界条件的实施可以应用于显式和隐式方法。
The material point method is an increasingly popular method for tackling solid mechanics problems involving large deformations. However, there are issues associated with applying boundary conditions in the method and, to date, no general approach for imposing both Neumann and Dirichlet boundary conditions has been proposed. In this paper, a new B-spline based boundary method is developed as a complete methodology for boundary representation, boundary tracking and boundary condition imposition in the standard material point method. The B-spline interpolation technique is employed to form continuous boundaries which are independent of the background mesh. Dirichlet boundary conditions are enforced by combining the B-spline boundaries with an implicit boundary method. Neumann boundary conditions are included by direct integration of surface tractions along the B-spline boundary. This general boundary method not only widens the problems that can be analysed by all variants of the material point method, when implemented using an implicit solver, but is also applicable to other embedded and non-matching mesh approaches. Although the Dirichlet boundary conditions are restricted to implicit methods, boundary representation, tracking and Neumann boundary condition enforcement can be applied to explicit and implicit methods.