基于显式时间积分的球颗粒DDA计算方法  

Explicit time integration based spherical DDA calculation method

作　　者：赵强[1,2] 焦玉勇 张秀丽 谢壁婷[1,2] 王龙 黄刚海 ZHAO Qiang;JIAO Yu-yong;ZHANG Xiu-li;XIE Bi-ting;WANG Long;HUANG Gang-hai(State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,Hubei 430071,China;University of Chinese Academy of Sciences,Beijing 100049,China;Engineering School,China University of Geosciences,Wuhan,Hubei 430074,China;State Grid Electric Power Company Economic and Technological Research Institute of Shandong,Jinan,Shandong 250021,China;School of Civil Engineering,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China)

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北武汉430071 [2]中国科学院大学,北京100049 [3]中国地质大学(武汉)工程学院,湖北武汉430074 [4]国家电网山东省电力公司经济技术研究院,山东济南250021 [5]湖南科技大学土木工程学院,湖南湘潭411201

出　　处：《岩土力学》2019年第11期4515-4522,共8页Rock and Soil Mechanics

基　　金：国家重点基金项（No.41731284）;国家自然科学基金面上资助项目（No.11672360）~~

摘　　要：非连续变形分析方法(DDA)是一种平行于有限元法的新型数值计算方法,该方法基于最小势能原理,把每个离散块体的变形、运动和块体之间的接触统一到平衡方程中进行隐式求解。然而,传统DDA方法在计算过程中需组装整体刚度矩阵并联立求解方程组,在用于大型岩土工程问题的三维数值模拟时占用内存较大、耗时较长、计算效率极低。因此,提出一种基于显式时间积分的三维球颗粒DDA方法。该方法在求解过程中不需要组装整体刚度矩阵,在求解加速度时,由于质量矩阵为对角矩阵,可存储为一维向量占用内存较少,且可分块逐自由度求解,效率较高,在接触判断上采用最大位移准则简化了接触算法,采用较小的时步,保证了计算的精确性;通过几个典型算例验证了该方法的准确性及计算效率。Discontinuous deformation analysis(DDA) is a new numerical method parallel to the finite element method. Based on the principle of minimum potential energy, the method unifies the deformation, motion and contact of each discrete block into the equilibrium equation for implicit solution. However, the traditional DDA method requires assembling the whole stiffness matrix to solve the equations in parallel, which occupies a large amount of memory, takes a long time and has a very low computational efficiency in the three-dimensional numerical simulation of large geotechnical engineering problems. Therefore, a three-dimensional spherical DDA method based on explicit time integration is proposed. This method does not require assembling the whole stiffness matrix. Because of the mass matrix is diagonal matrix, it can be stored as a one-dimensional vector with less memory, and can be solved block by block with higher efficiency in the acceleration solving process. The maximum displacement criterion is used to simplify the contact algorithm in the contact judgment, and the smaller time step ensures the accuracy of calculation. Finally, the accuracy and efficiency of the method are verified by several classical examples.

关 键 词：非连续变形分析 显式时间积分 质量矩阵 最大位移准则 岩土工程 

分 类 号：O242[理学—计算数学]