重力作用下软球壳堆积结构的有限元分析

doi:10.19596/j.cnki.1001-246x.8578

摘要/Abstract

摘要：

基于结构力学的有限元方法, 采用软球的面积和相邻球数分布研究重力作用下软球壳的二维堆积结构, 并分析堆积结构的填充率、势能等特性。研究表明: 软球壳堆积过程是无序的, 并没有取向偏好。堆积结构有不同的类型, 且不同类型对应不同的面积和相邻球数分布, 其呈现多分散特征。堆积结构的面积变化率与堆积结构的势能正相关, 面积变化率越大, 势能越大, 且结构类型的势能随着模量增大而减少。对于具有不同半径的双分散软球壳的堆积结构, 软球的面积与相邻球数之间, 呈现出近似线性关系, 且结构中半径较大的软球数量越多, 结构所具有的势能越大。本研究有助于提高对细胞等软物质堆积结构的几何和拓扑性质的理解, 为分析软球壳等活组织和材料提供了计算依据。

关键词: 堆积结构, 软球壳, 有限元, 势能, 重力

Abstract:

Based on the finite element method of structural mechanics, the two-dimensional stacking structure of soft spherical shells under gravity is studied by using the area of soft spheres and the distribution of the number of adjacent spheres, and the filling rate and potential energy of the stacking structure are analyzed. The results show that the soft spherical shell stacking process is disordered and has no orientation preference. There are different types of stacking structures, and different types correspond to different areas and distributions of adjacent spheres, which exhibit polydispersity characteristics. The area change rate of the stacking structure is positively correlated with the potential energy of the stacking structure. The greater the area change rate results the greater the potential energy, and the potential energy of the structure type decreases with the increase of the modulus. For the stacking structures of bidisperse soft spheres with different radii, there is an approximate linear relationship between the area of the soft spheres and the number of adjacent spheres, and the more number of soft spheres with bigger radii in the structure results in the greater potential energy of the structure. This study helps to improve the understanding of the geometric and topological properties of soft matter packing structures such as cells, and provides a computational basis for the analysis of living tissues and materials with soft spherical shells.

Key words: stacked structure, soft sphere, finite element, potential energy, gravity

麦兴鸿, 陈巧悦, 丁明明. 重力作用下软球壳堆积结构的有限元分析[J]. 计算物理, 2023, 40(3): 359-368.

Xinghong MAI, Qiaoyue CHEN, Mingming DING. Finite Element Analysis of the Stacked Structure of Soft Spherical Shells Under Gravity[J]. Chinese Journal of Computational Physics, 2023, 40(3): 359-368.

图/表 17

图1 重力场下的软球壳堆积模型示意图

Fig.1 Schematic diagram of soft spherical shell accumulation model under gravity field

图2 200 Pa的堆积结构类型 (a)堆积结构A类; (b) 堆积结构B类; (c) 堆积结构C类

Fig.2 Stacking structure type of 200 Pa (a) stacking structure type A; (b) stacking structure type B; (c) stacking structure type C

图3 同一类型的软球面积分布

Fig.3 Soft sphere area distribution of the same type

图4 同一类型的软球相邻球数分布

Fig.4 Soft sphere area distribution of the same type

图5 同一类型软球壳堆积结构的势能

Fig.5 Potential energy of the same type of soft spherical shell stacking structure

图6 同一类型软球壳堆积结构的面积变化率

Fig.6 Area change rate of stacking structure of the same type of soft spherical shell

图7 同一类型软球壳堆积结构的填充率

Fig.7 Filling rate of the same type of soft spherical shell stacking structure

图8 A类堆积结构的势能与模量关系

Fig.8 Relationship between potential energy and modulus of type A stacked structure

图9 A类堆积结构的面积变化率与模量关系

Fig.9 Relationship between area change rate and modulus of type A stacked structure

图10 A类堆积结构的填充率与模量关系

Fig.10 Relationship between filling rate and modulus of type A stacked structure

图11 双分散软球壳堆积结构的势能与大小球数量比例的关系

Fig.11 Relationship between the potential energy of double dispersed soft spherical shell stacking structure and the proportion of big and small spheres

图12 双分散软球壳堆积结构的面积变化率与大小球数量比例的关系

Fig.12 Relationship between the area change rate of double dispersed soft spherical shell stacking structure and the proportion of big and small spheres

图13 双分散软球壳堆积结构的面积分布

Fig.13 Area distribution of double dispersed soft spherical shell stacking structure

图14 双分散软球壳堆积结构的相邻球数分布

Fig.14 Adjacent sphere number distribution of double dispersed soft spherical shell stacking structure

图15 双分散软球壳堆积结构的势能图

Fig.15 Potential energy diagram of double dispersed soft spherical shell stacking structure

图16 双分散软球壳堆积结构的填充率

Fig.16 Filling rate of double dispersed soft spherical shell stacking structure

图17 软球平均面积与其相邻球数的关系

Fig.17 The relationship between the average area of soft balls and the number of adjacent balls

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