Angle-Based Contact Detection in Discontinuous Deformation Analysis
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ORIGINAL PAPER
Angle‑Based Contact Detection in Discontinuous Deformation Analysis Hong Zhang1 · Jing‑wen Zhang1 · Wei Wu1,3,4 · Xi Wang1 · Hehua Zhu1,3,4 · Jeen‑shang Lin5 · Jian‑gang Chen2 Received: 7 December 2019 / Accepted: 16 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract 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, the angle, 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. Keywords Rock mass · Concave polyhedron · Discontinuous deformation analysis · Contact detection · Entrance angle method · Local convex decomposition
1 Introduction * Wei Wu [email protected] * Xi Wang [email protected] 1
College of Civil Engineering, Tongji University, Shanghai 200092, People’s Republic of China
2
Key Laboratory of Mountain Hazards and Earth Surface Process, Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, People’s Republic of China
3
State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, People’s Republic of China
4
Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, People’s Republic of China
5
Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
Numerical tools must be developed in three dimensions (3-D) to be truly predictive in modern engineering design (Hart et al. 1988; Sukumar et al. 2000; Duarte et al. 2001; Shi 2001; Rabczuk and Belytschko 2007; Zhao et al. 2011; Temizer et al. 2012; He et al. 2013; Nadimi et al. 2016; Nguyen et al. 2017). These 3-D approaches are indispensable, p
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