一种考虑域边界的密实圆形颗粒高效生成算法  

An efficient algorithm for dense discs packing considering domain boundaries

作　　者：徐鑫 夏明[1,2] XU Xing;XIA Ming(Hunan Key Laboratory of Geomechanics and Engineering Safety,Xiangtan University,Xiangtan 411105,China;College of Civil Engineering,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学岩土力学与工程安全湖南省重点实验室,湖南湘潭411105 [2]湘潭大学土木工程学院,湖南湘潭411105

出　　处：《湘潭大学学报（自然科学版）》2023年第2期18-28,共11页Journal of Xiangtan University(Natural Science Edition)

基　　金：湖南省自然科学基金(2022JJ30567);湖南省教育厅优秀青年项目(20B557);湖湘高层次人才聚集工程创新团队(2019RS1059)。

摘　　要：在计算域内生成密实圆形颗粒集合体是离散单元法模拟中的一个重要问题.颗粒生成算法中,波前法(包括closed型和open型)作为一种纯几何算法,由于其高效性得到了广泛应用.然而,波前法生成的颗粒集合体在域边界上存在较大的间隙,从而导致边界的非光滑性.为克服这一问题,将closed型波前法中处理外域边界方法拓展到open型波前法.该算法通过Netwon-Raphson迭代方法得到颗粒的中心坐标和半径,从而保证新生成的颗粒与域边界相切,最终消除了边界间隙和凹凸性.针对open型波前法在堆积过程中出现的右端抬升问题,给出了解决方法,消除了潜在的优势结构面,进一步提高了计算效率.结果表明:提出的closed型和open型算法对不同的内外域边界都有很好的适用性.相比其他颗粒生成算法,open型算法效率非常高,其效率分别是离散元模拟软件和closed型的20500倍和4.4倍.在考虑域边界情况下,open型波前法在2.3 GHz的笔记本电脑上生成410万密实圆形颗粒集合体只需0.9 s.The generation of dense and stable disc assemble in domains is a major problem in the discrete element modeling.Among particle generation algorithms,the advancing front approach(including closed form and open form),which is a geometric constructive method,becomes more and more popularly due to its high efficiency.However,the disadvantage of this approach is that there are relatively large gaps around domain boundaries,resulting in non-smooth of domain boundaries.To overcome this problem,the corresponding algorithm considering outer domain boundaries initially proposed for closed form is extended to open form.This algorithm can generate a disc with certain position and radius through the Netwon-Raphson iterative method,which can guarantee the new disc tangent to domain boundary.Then non-smooth of boundary and the gaps between assemble and boundary can be eliminated.The corresponding tacking issue is given to overcome the right part increasing problem in the discs packing with the open form.Then the potential discontinuity is eliminated,while the computational efficiency is further improved.The results show that proposed algorithms(closed form and open form)are very suitable to tackle inner and outer domain boundaries.Compared with other packing algorithms,the proposed algorithm with open form is highly efficiency.Its computational efficiency is 20500 and 4.4 times than that of PFC software and closed form,respectively.The numerical example with consideration of domain boundaries demonstrated that it takes only 0.9 s for the proposed open form algorithm to generate 4.1 million discs on a laptop with a one 2.3 GHz processor.

关 键 词：岩石力学 离散单元法 颗粒堆积 波前法 内外域边界 边界处理 

分 类 号：TU45[建筑科学—岩土工程]