摘要
为了从力学角度解释"一张打印纸平着立不起来,而弯曲一定弧度后就可以"这一现象,本文通过数学手段对两种状态下横截面几何性质进行演算,得到了截面形心主惯性矩的计算公式,并结合计算机分析进行验证,证明了公式的适用性。通过对纸张稳定性的讨论,把该问题抽象为自重状态下的压杆稳定性分析,发现弯曲弧度对于稳定性影响很大,当弧度为2.52时,圆柱面状A4纸均布轴向载荷的临界值约为平面状A4纸的3.7×105倍。
In order to explain the phenomenon that "a sheet of printing paper cannot be erected, while a certain degree curved one can" in terms of mechanics, the geometric properties of the cross section under two different states are analyzed to form a formula for the principal centroidal moments of inertia, which is verified by numerical simulations. The stability of the sheet of paper or a curved one is reduced into the stability of a column under its own weight. It is found that the curvature of the arc has a great influence on the stability.When the arc is 2.52, the critical value of the evenly distributed axial load of the cylindrical A4 paper is about 3.7 × 105 times of that of the planar one.
作者
黄可
郭昱均
郝泱
李栋栋
范钦珊
HUANG Ke;GUO Yujun;HAO Yang;LI Dongdong;FAN Qinshan(Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Department of Engineering Mechanics,School of Aerospace Engineering,Tsinghua University,Beijing 100084,China)
出处
《力学与实践》
北大核心
2021年第5期801-805,共5页
Mechanics in Engineering
基金
江苏高校优势学科建设工程资助项目。
关键词
打印纸
惯性矩
稳定性分析
printing paper
moment of inertia
stability analysis
