Angle-Based Contact Detection in Discontinuous Deformation Analysis
Angle-Based Contact Detection in Discontinuous Deformation Analysis
复制标题
不连续变形分析中基于角度的接触检测
DOI：
10.1007/s00603-020-02206-z
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发表时间：
2020-08
影响因子：
6.2
通讯作者：
Chen Jian-gang
中科院分区：
文献类型：
--
作者：
Zhang Hong;Zhang Jing-wen;Wu Wei;Wang Xi;Zhu Hehua;Lin Jeen-shang;Chen Jian-gang
本文提出了一种新的基于角度的接触检测方法，用于解决任意多面体的凹接触问题，包括凸多面体和凹多面体，具有空腔和/或孔的多面体，以及可能的并集。首先，本文引入了最重要的数学概念“角”来表示一般的多面体。使用角度，多面体的拓扑结构可以比以前研究的更复杂和更普遍，允许面的共面性和边的共线性，并且不将多面体限制为简单的同胚到封闭的三维（3-D）球体。其次，利用入口公式确定了两个一般角的所有局部入口，即顶角到半空间的入口和交叉棱角到棱角入口的入口。第三，提出了局部凸分解（LCD），将任意凹角分解为一组凸子角，使得该方法易于实现，并且与入射角的检测自然兼容。第四，将所提出的入射角法（EAM）应用于三维非连续变形分析（DDA）中，计算任意凹凸接触。最后，对基于EAM的三维DDA方法进行了验证，并将其应用于复杂多面体块体系统的非连续力学行为研究。总体而言，扩展的3-D DDA程序是充分发展，以满足复杂岩体工程的分析要求。
This study presents a novel angle-based contact detection method to address the concave contact problem of arbitrary polyhedra, including convex and concave polyhedra, those with cavities and/or holes, and likely their unions. First, the most important mathematical concept in this study, theangle, is introduced to represent a general polyhedron. Using angles, the topologies of the polyhedra can be far more complex and universal than those previously studied, allowing for the coplanarity of faces and collinearity of edges, and not limiting the polyhedra to simple homeomorphic to closed three-dimensional (3-D) spheres. Second, all the local entrances of two general angles, which are either vertex angle to half-space or crossing edge angle to edge angle entrances, are identified using the entrance formulas. Third, local convex decomposition (LCD) is proposed to decompose any arbitrarily concave angle into a set of convex subangles, making the method easy to implement and naturally compatible with detection of entrance angles. Fourth, the proposed entrance angle method (EAM) is implemented in 3-D discontinuous deformation analysis (DDA) to compute arbitrarily convex/concave contacts. Finally, the EAM-based 3-D DDA method is validated and then employed to investigate the discontinuous mechanical behaviors of complex polyhedral block systems. Overall, the extended 3-D DDA program is sufficiently developed to meet the analysis requirements of complex rock mass projects.
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