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关于变形体虚功原理的若干认识

SOME PERSPECTIVES TO THE PRINCIPLE OF VIRTUAL WORK FOR DEFORMABLE BODIES

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【作者】 王国砚

【Author】 WANG Guoyan;School of Aerospace Engineering and Applied Mechanics, Tongji University;

【机构】 同济大学航空航天与力学学院

【摘要】 变形体虚功原理是变形体力学中的重要基本原理之一,在结构力学、弹性力学等课程都有广泛应用,但是关于其表述和理解在不同课程和不同文献并不完全一致。笔者分析了一些主要教科书和相关文献中的内容,针对变形体虚功原理的两个核心问题:(1)变形体与质点系之间的关系问题,(2)内力虚功的定义和计算问题,给出若干认识;据此认为质点系虚功原理和变形体虚功原理是辩证统一的;通过两个算例演示了本文的分析过程。希望本文的认识有助于深化对变形体虚功原理的理解,并有助于形成从质点系到变形体的一致的虚功原理描述体系。

【Abstract】 The principle of virtual work for deformable bodies is one of the important fundamental principles in deformable body mechanics. It is widely used in the courses of structural mechanics, elasticity, and etc. However, the statement and the understanding of it are not consistent among different courses and different references. The relative context in some typical references were analyzed and some perspectives are given in this paper to the two essential problems related to the principle of virtual work for deformable bodies, that is:(1) the relationship between deformable bodies and particle systems,(2) the definition and calculation of the virtual work done by internal force. Based on the analysis of this paper, it can be concluded that there is a dialectical unification between the principle of virtual work for deformable bodies and the principle of virtual work for particle systems. Two examples are given to demonstrate the analysis processes in this paper. Hopefully the perspectives in this paper can help to deepen the understanding of the principle of virtual work for deformable bodies and form a consistent description for the principle of virtual work from particle systems to deformable bodies.

  • 【文献出处】 物理与工程 ,Physics and Engineering , 编辑部邮箱 ,2022年03期
  • 【分类号】O347
  • 【下载频次】133
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