大变形非线性弹性力学的广义变分原理  

Generalized Variational Principles on Nonlinear Theory of Elasticity with Finite Displacements

作　　者：薛大为[1] 

机构地区：[1]北京理工大学

出　　处：《应用数学和力学》1991年第3期209-218,共10页Applied Mathematics and Mechanics

摘　　要：本文导出了大变形非线性弹性力学的两个具有σ_(ij),e_(ij),和u_i三类独立变量的广义变分原理,证明了当应力应变关系为约束条件时这两个广义变分原理是等价的.文中对某些特例也作了阐明.Two generalized vafiatinal principles on nonlinear theory of elasticity with finite displacements in which the σij, eij and ui are all three kinds of independent functions are suggested in this paper. It is proved that these two generalized varia-tional principles are equivalent to each other if the stress-strain relation is satisfied as constraint. Some special cases, i. e. generalized variational principles on nonlinear theory of elasticity with small deformation, on linear theory with finite deformation and on linear theory with small deformation together with the corresponding equivalent theorems are also obtained. All of them are related to the three kinds of independent variables.

关 键 词：非线性 弹性力学 广义 变分原理 

分 类 号：O343.5[理学—固体力学]