面向杆系结构的离散元异步长计算方法

doi:10.19596/j.cnki.1001-246x.8427

摘要/Abstract

摘要：

为了提升离散元法处理连续介质问题的计算效率, 提出一种基于重叠颗粒的离散元分区异步长计算方法来处理连续介质问题。该方法采用颗粒分割将连续介质划分为若干子分区, 各分区采用velocity-Verlet积分格式求解运动方程。相邻分区通过重叠颗粒构成局部耦合区域, 边界数据传递过程中不涉及插值和截断过程。数值算例表明, 该方法在保证高精度的同时有效地降低了计算时间。在实际应用中可以有针对性地将连续介质划分为不同尺度颗粒的分区, 根据问题规模及分区颗粒尺度特性采用不同时间步长, 节省存储空间且大幅提升计算效率。

关键词: 离散元方法, 连接键, 重叠颗粒, 异步长, 连续介质

Abstract:

To improve computational efficiency of discrete element method(DEM), referring to domain decomposition method and sub-cycle method in finite element method, a discrete element partition asynchronous time step computing method based on overlapping particles was proposed to deal with continuous medium problems. In the method, the continuum is divided into sub-domains. The velocity-Verlet integral scheme is used to solve the motion equation in sub-domains. Local action regions are formed with overlapping particles in adjacent sub-domains. Interpolation and truncation are not involved in transfer process of boundary data. Numerical examples show that accuracy of the method is high and the computation time is reduced effectively. In practical application, continuous media could be divided into several sub-domains with different particles size, and different time steps are adopted according to particle size characteristics of the sub-domains, with which storage space could be saved and computing efficiency improved greatly.

Key words: discrete element method, linked bar, overlapping particles, asynchronous step, continuous medium

李佟, 王倩, 金先龙. 面向杆系结构的离散元异步长计算方法[J]. 计算物理, 2022, 39(4): 395-402.

Tong LI, Qian WANG, Xian-long JIN. A Multi-time-step Discrete Element Method for Bar Structures[J]. Chinese Journal of Computational Physics, 2022, 39(4): 395-402.

图/表 10

图1 连接键模型(a)球形颗粒连接键；(b)球形颗粒等效接触面积

Fig.1 Model of linked bar (a) linked bar of spherical particles; (b) equivalent contact area of spherical particles

图2 (a) 重叠边界颗粒划分及(b) 边界数据更新传递

Fig.2 (a) Particle division with overlapping boundaries and update and (b) transfer of boundary data

图3 不同分区多时间步长计算流程

Fig.3 Multi-time step calculation flow of different partitions

图4 边界颗粒数据更新顺序

Fig.4 Update order of boundary particles data

图5 等截面杆颗粒离散划分及颗粒之间相互作用

Fig.5 Region division of a uniform cross section rod and interaction between pairs of adjacent particles i and j

图6 不同方法计算的细长杆应力波传播

Fig.6 Stress-wave propagation through a slender rod calculated with different methods

图7 不同方法计算的自由端轴向位移曲线

Fig.7 Axial displacement curves of free end calculated with different methods

图8 阶梯杆受轴向集中载荷(a)阶梯杆区域划分及右端点P轴向载荷；(b)弹性杆颗粒离散及区域划分

Fig.8 A step-cross section rod subjected to axial concentrated load (a) Region division of rod and axial load of point P; (b) Particle partition of elastic rod

图9 不同方法计算的阶梯杆自由端轴向位移响应

Fig.9 Axial displacement response of the free end of a step-cross section rod calculated with different methods

表1 不同步长比计算时间

Table 1 Computational times with different time step ratios

计算方法		求解时间/s	时间比率/%
Newmark		216.2	100
同步长		176.4	81.6
异步长	η=3	117.4	54.3
	η=5	62.9	29.1
	η=8	55.6	25.7
	η=10	47.3	21.9
	η=12	12.3	5.7

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