Nishiura Daisuke, Sakaguchi Hide, Aikawa Akira
Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Kanagawa 236-0001, Japan.
Railway Dynamics Division, Railway Technical Research Institute, Tokyo 185-8540, Japan.
Materials (Basel). 2017 Jun 3;10(6):615. doi: 10.3390/ma10060615.
Simulation of a large number of deformable bodies is often difficult because complex high-level modeling is required to address both multi-body contact and viscoelastic deformation. This necessitates the combined use of a discrete element method (DEM) and a finite element method (FEM). In this study, a quadruple discrete element method (QDEM) was developed for dynamic analysis of viscoelastic materials using a simpler algorithm compared to the standard FEM. QDEM easily incorporates the contact algorithm used in DEM. As the first step toward multi-body simulation, the fundamental performance of QDEM was investigated for viscoelastic analysis. The amplitude and frequency of cantilever elastic vibration were nearly equal to those obtained by the standard FEM. A comparison of creep recovery tests with an analytical solution showed good agreement between them. In addition, good correlation between the attenuation degree and the real physical viscosity was confirmed for viscoelastic vibration analysis. Therefore, the high accuracy of QDEM in the fundamental analysis of infinitesimal viscoelastic deformations was verified. Finally, the impact response of a ballast and sleeper under cyclic loading on a railway track was analyzed using QDEM as an application of deformable multi-body dynamics. The results showed that the vibration of the ballasted track was qualitatively in good agreement with the actual measurements. Moreover, the ballast layer with high friction reduced the ballasted track deterioration. This study suggests that QDEM, as an alternative to DEM and FEM, can provide deeper insights into the contact dynamics of a large number of deformable bodies.
大量可变形体的模拟通常很困难，因为需要复杂的高级建模来处理多体接触和粘弹性变形。这就需要联合使用离散单元法（DEM）和有限元法（FEM）。在本研究中，开发了一种四重离散单元法（QDEM），用于粘弹性材料的动态分析，其算法比标准有限元法更简单。QDEM很容易纳入离散单元法中使用的接触算法。作为迈向多体模拟的第一步，研究了QDEM在粘弹性分析中的基本性能。悬臂弹性振动的振幅和频率几乎与标准有限元法得到的结果相等。将蠕变恢复试验与解析解进行比较，结果显示二者吻合良好。此外，在粘弹性振动分析中，衰减程度与实际物理粘度之间具有良好的相关性。因此，验证了QDEM在微小粘弹性变形基本分析中的高精度。最后，作为可变形多体动力学的一个应用，使用QDEM分析了铁路轨道上道砟和轨枕在循环荷载作用下的冲击响应。结果表明，有砟轨道的振动在定性上与实际测量结果吻合良好。此外，具有高摩擦力的道砟层可减少有砟轨道的劣化。本研究表明，作为离散单元法和有限元法的替代方法，QDEM可以更深入地洞察大量可变形体的接触动力学。
