弹性力学的Lagrange形式:用Routh方法建立弹性有限变形问题的基本方程

数学物理学报 ›› 1998, Vol. 18 ›› Issue (1): 78-88.

弹性力学的Lagrange形式:用Routh方法建立弹性有限变形问题的基本方程

沈惠川

中国科学技术大学基础物理中心合肥 230006

收稿日期:1996-05-21 修回日期:1996-12-17 出版日期:1998-03-26 发布日期:1998-03-26

Lagrange Formalism of Elasticity:Building the Basic Equations on Finite-Deformation Problems by Routh's Method

Shen Huichuan

China Universtiy of Sci, Tech, Fundamental Physics Center, Hefei 230026

Received:1996-05-21 Revised:1996-12-17 Online:1998-03-26 Published:1998-03-26

摘要/Abstract

摘要： 将弹性有限变形问题纳入Lagrange力学的理论体系中,并用经典力学中业已存在的Routh方法构建了有限变形平面应变问题和有限变形平面应力问题的基本微分方程,讨论了有限变形大挠度问题von kármán方程中存在的矛盾进而提出了两种改进方案.

关键词: Lagrange方程, Routh方法, 弹性力学, 有限变形问题, 平面应变, 平面应力, 大挠度

Abstract: The elastic finite-deformation problems be bring into the theoretical system of Lagrangian mechanics, the basic equations of finite-deformation for plane-strain problems and plane-stress problems be builded by the Routh method in classical mechanics,the contradiction in von Kármán equation of finite-deformation large-deflection problems be disussed, and thenew plan be proposed in this paper.

Key words: Lagrange formalism, Routh's method, Finite-Deformation problems

沈惠川. 弹性力学的Lagrange形式:用Routh方法建立弹性有限变形问题的基本方程[J]. 数学物理学报, 1998, 18(1): 78-88.

Shen Huichuan. Lagrange Formalism of Elasticity:Building the Basic Equations on Finite-Deformation Problems by Routh's Method[J]. Acta mathematica scientia,Series A, 1998, 18(1): 78-88.

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