全部

力学与实践 ›› 2011, Vol. 33 ›› Issue (5): 67-69.doi: 10.6052/1000-0879-lxysj2010-263

• 教育研究 • 上一篇    下一篇

对弹性静力学中外力功表达式及相关问题的探讨

白冰1,李小春2,石露3,姚华彦4   

  1. 1. 中国科学院武汉岩土力学研究所
    2. 武汉中国科学院武汉岩土力学研究所
    3. 国科学院岩土力学与工程国家重点试验室
    4.
  • 收稿日期:2010-06-21 修回日期:2011-09-08 出版日期:2011-10-15 发布日期:2011-11-07
  • 通讯作者: 白冰 E-mail:bai_bing2@126.com

Discussions on the expressions of external force work and its related problems

Bai Bing,Li Xiaochun,Shi Lu,Yao Huayan   

  • Received:2010-06-21 Revised:2011-09-08 Online:2011-10-15 Published:2011-11-07
  • Contact: Bai Bing E-mail:bai_bing2@126.com

摘要: 外力功、势能等概念是弹性力学能量原理的重要内容. 但笔者发现, 经典弹性理论著作中给 出的外力功、势能的表达式并非真实的功、真实势能值. 本文根据弹性静力学的基本假定和 应变能定理对此进行了论证, 并以一维弹簧受压问题进行了说明. 对总势能、外力势能、外 力功及保守力的定义及其相互关系进行了详细分析, 建议在介绍系统总势能定义的同时, 应 一方面说明它不是系统的真实总势能, 另一方面要补充介绍这样定义总势能的原因是保证最 小势能原理与平衡方程等价. 通过厘清上述概念之间的关系, 以期给弹性力学的初学者以明 晰的概念.

关键词: 弹性力学,外力功,势能,应变能,保守力

Abstract: Work of external forces and potential energy are key concepts in elastic mechanics of continuum. But it is found by the author that the expressions of these concepts listed in some classic textbooks are not real, which is verified using theorem of strain energy and then explained with an example of 1 dimension spring. Then the definitions and the relationships of total potential energy, potential energy / work of external forces and the reserved forces are analyzed, which make it easily for the primer students to understand these concepts clearly. At last, an advice is given that it is proper and necessary to tell clearly the fact that the expressions above are not real.

Key words: Elasticity