基于局部凸分解的一般多面体接触搜索方法
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摘要
为解决任意形状多面体非凸角接触不确定性问题,提出一种较易实现的多面体局部凸分解方案,沿各凹二面角的延伸平面角将任意角分解为凸子角集。采用该方案拓展的一般多面体进入面接触搜索方法具有普遍意义,实现了三维非连续变形分析法(DDA)一般多面体接触计算的功能。最后,拓展后的三维DDA程序展示了一般多面体局部凸分解、接触搜索与计算及碰撞接触力学行为分析方面的强大能力,验证了该方法的正确性和稳健性,表明拓展后的三维DDA程序可用于复杂的多面体块体系统力学行为分析。
To address the indeterminacy of contacts involving nonconvex angles of arbitrarily shaped polyhedron,an easy-to-implement local convex decomposition method(LCD),dividing any arbitrary angle along the extensive plane angle of concave dihedral angles into a set of convex angles,was proposed and employed to extend the entrance plane method(EPM). The LCD-EPM is a universal method for contact detection of general polyhedrons,and herein,enabled the use of a three-dimensional discontinuous deformation analysis(3-D DDA) to calculate contacts between general polyhedrons. Finally,the extended 3-D DDA program was used to illustrate the powerful ability of LCD including contact detection and calculation as well as an impact-contact behaviour analysis of general polyhedrons,which validates the correctness and robustness of the LCD-EPM. The extended 3-D DDA program can be applied in mechanical analyse of complex polyhedral block systems.
To address the indeterminacy of contacts involving nonconvex angles of arbitrarily shaped polyhedron,an easy-to-implement local convex decomposition method(LCD),dividing any arbitrary angle along the extensive plane angle of concave dihedral angles into a set of convex angles,was proposed and employed to extend the entrance plane method(EPM). The LCD-EPM is a universal method for contact detection of general polyhedrons,and herein,enabled the use of a three-dimensional discontinuous deformation analysis(3-D DDA) to calculate contacts between general polyhedrons. Finally,the extended 3-D DDA program was used to illustrate the powerful ability of LCD including contact detection and calculation as well as an impact-contact behaviour analysis of general polyhedrons,which validates the correctness and robustness of the LCD-EPM. The extended 3-D DDA program can be applied in mechanical analyse of complex polyhedral block systems.
引文
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[32]ZHANG H,LIU S G,ZHENG L,et al.Extensions of edge-to-edge contact model in three-dimensional discontinuous deformation analysis for friction analysis[J].Computers and Geotechnics,2016,71:261-275.
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[36]WANG W,ZHANG H,ZHENG L,et al.A new approach for modeling landslide movement over 3D topography using 3Ddiscontinuous deformation analysis[J].Computers and Geotechnics,2017,81:87-97.
[37]ZHU H H,WU W,CHEN J Q,et al.Integration of three dimensional discontinuous deformation analysis(DDA)with binocular photogrammetry for stability analysis of tunnels in blocky rock mass[J].Tunnelling and Underground Space Technology,2016,51:30-40.
[38]WU W,ZHU H H,LIN J S,et al.Tunnel stability assessment by 3DDDA-key block analysis[J].Tunnelling and Underground Space Technology,2018,71:210-214.
[39]LIU SG,LI ZJ,ZHANG H,et al.A 3-D DDA damage analysis of brick masonry buildings under the impact of boulders in mountainous areas[J].Journal of Mountain Science,2018,15(3):657-671.
[40]LI Z,LIU S,ZHANG H,et al.Simulating the damage extent of unreinforced brick masonry buildings under boulder impact using three-dimensional discontinuous deformation analysis(3-D DDA)[J].Engineering Failure Analysis,2018,93:122-143.
[41]HE L,AN X M,ZHAO Z Y.Development of contact algorithm for three-dimensional numerical manifold method[J].International Journal for Numerical Methods in Engineering,2014,97:423-453.
[42]ZHANG Q H,LIN S Z,DING X L,et al.Triangulation of simple arbitrarily shaped polyhedra by cutting off one vertex at a time[J].International Journal for Numerical Methods in Engineering,2018,114:517-534.
[2]GOODMAN R E,SHI G H.Block theory and its application to rock engineering[M].London:Prentice-Hall,1985:1-338.
[3]SHI G H.Producing joint polygons,cutting joint blocks and finding key blocks for general free surfaces[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(11):2 161-2 170.
[4]石根华.接触理论及非连续形体的形成约束和积分[M].北京:科学出版社,2016:1-294.(SHI Genghua.Contact theory and constraint formation and integration of discontinuous body[M].Beijing:Science Press,2016:1-294.(in Chinese))
[5]李小凯,郑宏.基于线性互补的非连续变形分析[J].岩土力学,2014,35(6):1 787-1 794.(LI Xiaokai,ZHENG Hong.Discontinuous deformation analysis based on linear complementarity theory[J].Rock and Soil Mechanics,2014,35(6):1 787-1 794.(in Chinese))
[6]江巍,郑宏.非连续变形分析方法变分不等式提法的外梯度法[J].中国科学:技术科学,2014,44(11):1 222-1 232.(JIANG Wei,ZHENG Hong.Extra-gradient method for the variational inequality formulation of discontinuous deformation analysis[J].Science China:Technological Science,2014,44(11):1 222-1 232.(in Chinese))
[7]WILLIAMS JR,O?CONNOR R.A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries[J].Engineering Computations,1995,12(2):185-201.
[8]MUNJIZA A,ANDREWS K R F.NBS contact detection algorithm for bodies of similar size[J].International Journal for Numerical Methods in Engineering,1998,43(1):131-149.
[9]PERKINS E,WILLIAMS J R.A fast contact detection algorithm insensitive to object sizes[J].Engineering Computations,2001,18(1/2):48-61.
[10]WU W,ZHU H H,ZHUANG X Y,et al.A multi-shell cover algorithm for contact detection in the three dimensional discontinuous deformation analysis[J].Theoretical and Applied Fracture Mechanics,2014,72(1):136-149.
[11]CUNDALL P A.Formulation of a three-dimensional distinct element model-Part I.A scheme to detect and represent contacts in a system composed of many polyhedral blocks[J].International Journal of Rock Mechanics and Mining Sciences,1988,25(3):107-116.
[12]NEZAMI E G,HASHASH Y M A,ZHAO D,et al.A fast contact detection algorithm for 3D discrete element method[J].Computers and Geotechnics,2004,31(7):575-587.
[13]NEZAMI E G,HASHASH Y M A,ZHAO D,et al.Shortest link method for contact detection in discrete element method[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(8):783-801.
[14]CHANG S W,CHEN C S.A non-iterative derivation of the common plane for contact detection of polyhedral blocks[J].International Journal for Numerical Methods in Engineering,2008,74(5):734-753.
[15]ZHONG Z H,NILSSON L.A contact searching algorithm for general3-D contact-impact problems[J].Computers and Structures,1990,34(2):327-335.
[16]JELENI′C G,CRISFIELD M A.Non-linear master-slave relationships for joints in 3D beams with large rotations[J].Computer Methods in Applied Mechanics and Engineering,1996,135(3/4):211-228.
[17]LIU X L,LEMOS J V.Procedure for contact detection in discrete element analysis[J].Advances in Engineering Software,2001,32(5):409-515.
[18]陈文胜,郑宏,郑榕明,等.岩石块体三维接触判断的侵入边法[J].岩石力学与工程学报,2004,23(4):565-571.(CHEN Wensheng,ZHENG Hong,ZHENG Rongming,et al.Detection of 3D rock block contacts by penetration edges[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(4):565-571.(in Chinese))
[19]KENETI A R,JAFARI A,WU J H.A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis[J].Computers and Geotechnics,2008,35(5):746-759.
[20]BEYABANAKI S A R,MIKOLA R G,HATAMI K.Three-dimensional discontinuous deformation analysis(3D DDA)using a new contact resolution algorithm[J].Computers and Geotechnics,2008,35:346-356.
[21]AHN T Y,SONG J J.New contact-definition algorithm using inscribed spheres for 3D discontinuous deformation analysis[J].International Journal of Computational Methods,2011,8(2):171-191.
[22]BOON C W,HOULSBY G T,UTILI S.A new algorithm for contact detection between convex polygonal and polyhedral particles in the discrete element method[J].Computers and Geotechnics,2012,44:73-82.
[23]WANG J,LI S,FENG C.A shrunken edge algorithm for contact detection between convex polyhedral blocks[J].Computers and Geotechnics,2015,63:315-330.
[24]刘新根,朱合华,刘学增,等.三维块体接触检索算法改进研究[J].岩石力学与工程学报,2015,34(3):489-497.(LIU Xingen,ZHUHehua,LIU Xuezeng,et al.Improvement of contact detection algorithm of three-dimensional blocks[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):489-497.(in Chinese))
[25]WILLIAMS J,LU Y,TRINKLE J C.A geometrically exact contact model for polytopes in multirigid-body simulation[J].Journal of Computational and Nonlinear Dynamics,2017,12(2):021001.
[26]FAN H,ZHENG H,WANG J.A generalized contact potential and its application in discontinuous deformation analysis[J].Computers and Geotechnics,2018,99:104-114.
[27]SHI G H.Contact theory[J].Science China:Technological Sciences,2015,58(9):1 450-1 498.
[28]ZHANG P,ZHENG H.Generalized contributing vertices-based method for Minkowski sum outer-face of two polygons[C]//Proceedings of International Conference on Image and Graphics.Cham:Springer,2015:333-346.
[29]ZHANG H,LIU S G,HAN Z,et al.A new algorithm to identify contact types between arbitrarily shaped polyhedral blocks for three-dimensional discontinuous deformation analysis[J].Computers and Geotechnics,2016,80:1-15.
[30]ZHANG H,CHEN G,ZHENG L,et al.Detection of contacts between three-dimensional polyhedral blocks for discontinuous deformation analysis[J].International Journal of Rock Mechanics and Mining Sciences,2015,78:57-73.
[31]ZHANG H,LIU S G,ZHENG L,et al.Method for resolving contact indeterminacy in three-dimensional discontinuous deformation analysis[J].International Journal of Geomechanics,2018,18(10):04018130.
[32]ZHANG H,LIU S G,ZHENG L,et al.Extensions of edge-to-edge contact model in three-dimensional discontinuous deformation analysis for friction analysis[J].Computers and Geotechnics,2016,71:261-275.
[33]ZHANG H,LIU S G,CHEN G Q,et al.Extension of threedimensional discontinuous deformation analysis to frictional-cohesive materials[J].International Journal of Rock Mechanics and Mining Sciences,2016,86:65-79.
[34]ZHANG H,LIU S G,WANG W,et al.A new DDA model for kinematic analyses of rockslides on complex 3-D terrain[J].Bulletin of Engineering Geology and the Environment,2018,77(2):555-571.
[35]WANG W,CHEN G Q,ZHANG H,et al.Analysis of landslidegenerated impulsive waves using a coupled DDA-SPH method[J].Engineering Analysis with Boundary Elements,2016,64:267-277.
[36]WANG W,ZHANG H,ZHENG L,et al.A new approach for modeling landslide movement over 3D topography using 3Ddiscontinuous deformation analysis[J].Computers and Geotechnics,2017,81:87-97.
[37]ZHU H H,WU W,CHEN J Q,et al.Integration of three dimensional discontinuous deformation analysis(DDA)with binocular photogrammetry for stability analysis of tunnels in blocky rock mass[J].Tunnelling and Underground Space Technology,2016,51:30-40.
[38]WU W,ZHU H H,LIN J S,et al.Tunnel stability assessment by 3DDDA-key block analysis[J].Tunnelling and Underground Space Technology,2018,71:210-214.
[39]LIU SG,LI ZJ,ZHANG H,et al.A 3-D DDA damage analysis of brick masonry buildings under the impact of boulders in mountainous areas[J].Journal of Mountain Science,2018,15(3):657-671.
[40]LI Z,LIU S,ZHANG H,et al.Simulating the damage extent of unreinforced brick masonry buildings under boulder impact using three-dimensional discontinuous deformation analysis(3-D DDA)[J].Engineering Failure Analysis,2018,93:122-143.
[41]HE L,AN X M,ZHAO Z Y.Development of contact algorithm for three-dimensional numerical manifold method[J].International Journal for Numerical Methods in Engineering,2014,97:423-453.
[42]ZHANG Q H,LIN S Z,DING X L,et al.Triangulation of simple arbitrarily shaped polyhedra by cutting off one vertex at a time[J].International Journal for Numerical Methods in Engineering,2018,114:517-534.