| 宋来忠,廖大乾.矩形区域不等圆形随机堆放的数值模拟[J].计算力学学报,2017,34(1):62~67 |
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| 矩形区域不等圆形随机堆放的数值模拟 |
| The numerical simulation of unequal circles random stacking of rectangular regions |
| 投稿时间：2015-11-06 修订日期：2016-02-24 |
| DOI：10.7511/jslx201701008 |
| 中文关键词: NP难问题 圆形Packing问题 随机堆放 数值模拟 有限元 |
| 英文关键词:NP hard problem circle Packing problem random stacking numerical simulation finite element |
| 基金项目:国家自然科学基金（11171181）资助项目 |
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| 中文摘要: |
| 将若干待堆放的圆形堆放到一个给定矩形区域，是一类特殊的Packing问题。针对这一具有NP难度的困难问题，提出一种快速的数值模拟方法以及模拟力学检验的方法。该方法将圆形堆放的力学平衡规律化为几何形体相互接触的几何条件，把大量的圆形按级配及分布律等约束条件，随机堆放形成空间区域。按此方法得到的圆形堆体，在不加外力的情形下即可保持自身的稳定。使用该方法，在边长为15 cm的正方形区域内，取圆形的直径范围为0.5 cm~4 cm，模拟了孔隙率小于25%（面积比）的圆形堆体。最后，将所模拟的圆形堆体试件进行了有限元网格划分及力学加载试算，结果表明该堆体是稳定的。为进一步在细观层次研究圆形堆体提供了一个快速的数值模拟方法。 |
| 英文摘要: |
| A number of circles stacked to be stacked to a given rectangular region,is a special class of Packing problems.Aiming at the problem of NP difficult,a fast numerical simulation method and the method of simulating mechanical test are presented.In this method,the stacked circle mechanical equilibrium rule of geometric conditions for the geometric contact with each other,a number of circles according to the gradation,the distribution law of constraint conditions of randomly stacked form a region of space.By this method get circle stacking,in the case of no external force to maintain its own stability.Using this method,at length 15 cm square,circle diameter range for 0.5 cm~4 cm,simulated the porosity is lower than 25%(area ratio) of circles stack.Finally,the finite element mesh and the mechanical loading test are carried out.The results show that it is stable.A fast numerical simulation method is provided for the further study circles stack on the meso-level |
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