力学与实践 ›› 2019, Vol. 41 ›› Issue (4): 483-487.DOI: 10.6052/1000-0879-18-051

• 力学纵横 • 上一篇    下一篇

一张纸最多能对折几次的力学分析 1)

曾凡林2)   

  1. 哈尔滨工业大学航天科学与力学系,哈尔滨 150001
  • 收稿日期:2018-01-29 出版日期:2019-08-27 发布日期:2019-08-26
  • 通讯作者: 曾凡林
  • 作者简介:2) 曾凡林,教授,主要研究方向为材料与结构的微纳尺度的力学与破坏行为。E-mail: zengfanlin@hit.edu.cn
  • 基金资助:
    1) 黑龙江省高等教育教学改革项目(SJGY20170626);国家自然科学基金项目资助(51873051)

A MECHANICAL ANALYSIS OF THE PROBLEM: HOW MANY TIMES CAN A SHEET OF PAPER BE FOLDED 1)

ZENG Fanlin2)   

  1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin 150001, China
  • Received:2018-01-29 Online:2019-08-27 Published:2019-08-26
  • Contact: ZENG Fanlin

摘要:

通过将纸张折叠问题简化为矩形截面简支梁在中段集中力作用下的三点弯曲问题,通过最大弯曲挠度和最小折叠载荷讨论了A4打印纸和八开报纸在普通人力作用下的最大对折次数问题。结果表明对于普通A4打印纸,一般成年人只能对折6次,最多也只能对折7 次。对于八开报纸,一般成年人能轻松对折7次,但是基本不可能对折8次。试验测试结果与理论预测结果吻合良好。

关键词: 纸张对折, 三点弯曲, 集中力, 挠度

Abstract:

In this paper, the paper folding problem is simplified to a three-point bending model of a simply supported beam with a rectangular cross section under the concentrated force acting on the middle position. The maximal folding times of a sheet of A4 printing paper and octavo newspaper under a normal human force are related with the maximum bending deflections and the minimum folding loads. The results show that for an ordinary A4 printing paper, an adult can only fold 6 times, or up to 7 times under extreme circumstances. For an octavo newspaper, an adult can easily fold 7 times, but not 8 times. The test results are in good agreement with the theoretical predictions.

Key words: paper folding, three-point bending model, concentrated force, deflections

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