大学物理 ›› 2025, Vol. 44 ›› Issue (11): 50-.doi: 10.16854/j.cnki.1000-0712.250064

• 教学讨论 • 上一篇    下一篇

浅析本科力学课程体系中虚功原理的脉络

李永胜,闫晓鹏,李志刚,陈静   

  1. 1. 太原理工大学 航空航天学院力学与工程科学系,山西 太原030024;2. 太原理工大学 山西省力学基础学科研究中心,山西 太原030024;3. 太原理工大学 人工智能学院生物力学研究所,山西 晋中030600
  • 收稿日期:2025-02-11 修回日期:2025-03-11 出版日期:2026-01-19 发布日期:2026-01-20
  • 作者简介:李永胜(1981—),男,太原理工大学力学与工程科学系副教授,博士,主要从事固体力学的教学和科研工作.
  • 基金资助:
    山西省基础研究计划(202203021221076);山西省教学改革项目(J20220179)

Analysis of the context of virtual work principle in the mechanics curriculum of undergraduate

LI Yongsheng1,2, YAN Xiaopeng1,2, LI Zhigang1,2, CHEN Jing3   

  1. 1. Department of Mechanics and Engineering Science, College of Aeronautics and Astronautics,
    Taiyuan University of Technology, Taiyuan 030024, China; 
    2. Shanxi Research Center of Basic Discipline of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China; 
    3. Institute of Biomechanics, College of Artificial Intelligence, Taiyuan University of Technology, Jinzhong 030600, China
  • Received:2025-02-11 Revised:2025-03-11 Online:2026-01-19 Published:2026-01-20

摘要: 虚功原理是本科力学教学的重要内容,加深对该原理的理解对掌握固体力学的能量原理有重要意义.本文对不同课程阶段虚功原理的表达进行了归纳总结,给出了对该原理的若干认识,主要内容如下:(1) 给出了一种由质点系虚位移原理过渡到变形体的定性说明,厘清了内力虚功和虚应变能的关系;(2) 阐明了杆系结构与一般弹性体在虚功原理表达上的区别和联系,对现行教材中杆系结构虚功原理容易混淆的地方进行了辨析;(3) 从整个课程体系的角度总结了质点系和变形体的虚功原理,给出了课程体系中原理的总体脉络,最后通过简单例题对虚功原理的应用加以说明.本文旨在理清虚功原理在各课程阶段的关系,厘清一些相关的概念,以期有助于读者形成对虚功原理的总体认识,加深对该原理的理解.

关键词: 虚位移(虚功)原理, 虚力(余虚功)原理, 可能功原理, 内力虚功, 虚应变能

Abstract:

The principle of virtual work is an important part of undergraduate mechanics curriculum. Deepening the understanding of the principle is of great significance for mastering the energy principle of solid mechanics. In this paper, the expressions of virtual work principle in different courses are summarized, and some understandings of the principle are given. The main contents of this paper are as follows: (1) a qualitative description of the transition from virtual displacement principle of particle system to deformed body is given, and the relationship between virtual work of internal force and virtual strain energy is clarified; (2) The differences and correlation between the virtual work principle of rod structure and that of general elastic body are clarified, and the confusion of 

the virtual work principle of rod structure in the current textbooks is analyzed; (3) From the perspective of curriculum, the virtual work principle of particle system and deformable body is summarized, and the overall context of the principle in the curriculum is given. This paper aims to clarify the relationship of virtual work principle in each course stage and clarify some related concepts, so as to help readers form a general understanding of virtual work principle and deepen their understanding for the principle.

Key words: virtual displacement (virtual work) principle, virtual force (complementary virtual work) principle, principle of possible work, internal force virtual work, virtual strain energy