大变形非线性弹性力学的广义变分原理

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Generalized Variational Principles on Nonlinear Theory of Elasticity with Finite Displacements

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.
- 大变形 /
- 非线性弹性力学 /
- 广义变分原理 /
- 三类独立变量
Abstract: Two generalized variational principles on nonlinear theory of elasticity with finite displacements in which the σ_ij_i e_ij and u_i are all three kinds of independent functions are suggested in this paper. It is provedthat these two generalized variational 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.
- finite displacement /
- nonlinear theory of elasticity /
- generalized variational principle /
- three kinds of independent variables

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