Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2016, Vol. 52 ›› Issue (4): 597-607.DOI: 10.13209/j.0479-8023.2016.076

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Lagrange Equation Applied to Continuum Mechanics

FENG Xiaojiu1, LIANG Lifu2   

  1. 1. School of Environmental and Safety Engineering, Changzhou University, Changzhou 213164
    2. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001
  • Received:2015-10-23 Revised:2016-04-02 Online:2016-07-20 Published:2016-07-20
  • Contact: LIANG Lifu, E-mail: lianglifu(at)


冯晓九1, 梁立孚2   

  1. 1. 常州大学环境与安全工程学院, 常州213164
    2. 哈尔滨工程大学航天与建筑工程学院, 哈尔滨 150001
  • 通讯作者: 梁立孚, E-mail: lianglifu(at)
  • 基金资助:


How to apply the Lagrange equation to the continuous medium mechanics has been a theoretical issue of academic circles. Using variational derivative concepts and operational rules, the properties of variational derivative in Lagrange equation are studied. The Lagrange equation is applied to linear elastic dynamics and nonlinear elastic dynamics, and some corresponding numerical examples are given. The result shows that it is a feasible way to solve the problem of the application of Lagrange equation to the mechanics of continuous media by using the variational integral calculus.

Key words: continuum mechanics, Lagrange equation, variational derivative, linear elastic dynamics, nonlinear elastic dynamics


如何将Lagrange 方程应用于连续介质力学, 一直是学术界关注的理论课题。应用变导的概念和运算法则, 研究Lagrange 方程中的求导的性质, 进而将Lagrange 方程应用于线性弹性动力学和非线性弹性动力学, 并且给出相应的算例。结果表明, 借鉴变积分学来解决将Lagrange 方程应用于连续介质力学的问题是可行的。

关键词: 连续介质力学, Lagrange 方程, 变导, 线性弹性动力学, 非线性弹性动力学

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