Development of contact algorithm for three‐dimensional numerical manifold method
Development of contact algorithm for three‐dimensional numerical manifold method
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DOI：
10.1002/nme.4591
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发表时间：
2013-10
影响因子：
2.9
通讯作者：
Lei He;X. An;Z. Zhao
中科院分区：
文献类型：
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作者：
Lei He;X. An;Z. Zhao
针对三维数值流形方法（NMM），定制了一种接触检测和加强方案。建立了一个层次化的接触检测系统。数学网格，在NMM中的一个独特的组件，用于可能的接触块和元素的全局搜索，然后通过局部搜索，以确定原始层次。所有潜在的接触对，然后转化为两个基本的入口模式之一：点到面和交叉线模式，其中真实的接触对通过一个统一的公式检测。采用罚函数法来加强接触约束，建立了三维数值MM中接触问题的一般求解方法。由于隐式框架，在每个时间步内执行开闭迭代，以确定多体之间的接触对的正确数量，并实现相应位置处的施加接触力的完全收敛。所提出的接触算法广泛地利用了NMM的大部分原始组件，即数学网格/单元和流形元素，以及与接触相关联的外部组件，例如接触体、接触面和接触顶点。特别地，利用两个相互接近的数学单元在检测接触区域方面是有效的，这使得该方法对于凸体和非凸体都特别有效。通过三个基准问题验证了所提出的接触算法的有效性和准确性。版权所有© 2013约翰威利父子有限公司.
This paper customizes a contact detection and enforcing scheme to fit the three‐dimensional (3‐D) numerical manifold method (NMM). A hierarchical contact system is established for efficient contact detection. The mathematical mesh, a unique component in the NMM, is utilized for global searching of possible contact blocks and elements, followed by the local searching to identify primitive hierarchies. All the potential contact pairs are then transformed into one of the two essential entrance modes: point‐to‐plane and crossing‐lines modes, among which real contact pairs are detected through a unified formula. The penalty method is selected to enforce the contact constraints, and a general contact solution procedure in the 3‐D NMM is established. Because of the implicit framework, an open‐close iteration is performed within each time step to determine the correct number of contact pairs among multi‐bodies and to achieve complete convergence of imposed contact force at corresponding position. The proposed contact algorithm extensively utilizes most of the original components of the NMM, namely, the mathematical mesh/cells and the manifold elements, as well as the external components associated with contacts, such as the contact body, the contact facet and the contact vertex. In particular, the utilization of two mutually approaching mathematical cells is efficient in detecting contacting territory, which makes this method particularly effective for both convex and non‐convex bodies. The validity and accuracy of the proposed contact algorithm are verified and demonstrated through three benchmark problems. Copyright © 2013 John Wiley & Sons, Ltd.