非线性力学中的虚功率原理

导出非线性平衡方程和3种常用的非线性虚功率方程.在解非线性问题时,构型的选择和应力-应变率(或与变形有关的率)的选择是两个重要问题.构型包括两种:初始构型和变形构型.在选择应力-应变率(或与变形有关的率)的时候,要注意它们之间的配对,即要考虑功率共轭的问题.在变形构型下,选择Cauchy应力σij与变形率Dij;在初始构型下,可以选择名义应力Pji与变形梯度率.Fij,或者选择第二类Piola-Kirchhoff应力Sij与Green应变率E.ij.

Principle of Rate-of-Virtual Work in Nonlinear Mechanics

Nonlinear equilibrium equations are derived and three kinds of nonlinear rate-of-virtual work equations in common use are given.It is important to choose configuration and stress-strain rates（or rates related to deformation） in solving nonlinear problems.There are two kinds of configurations： initial configuration and deformed configuration.When selecting stress-strain rates（or rates related to deformation）,their counterparts,or rate-of-work conjugations need to be considered.Under deformed configuration,Cauchy stress σij and rate-of-deformation Dij are considered.Under initial configuration,nominal stress Pji and rate-of-deformation gradient ij may be considered;or second Piola-Kirchhoff stress Sij and rate-of-Green strain ij may be considered.