非线性弹性力学广义变分原理

GENERALIZED VARIATIONAL PRINCIPLES IN NONLINEAR ELASTICITY WITH SMALL DEFORMATION

本文利用Legendre变换,给出了小变形非线弹性力学最小势能/余能原理的新提法;在最小势能/余能原理新提法的基础上,用线性Lagrange乘子法,解除应力—应变/应变—应力关系在内的全部约束条件,建立了新的三类变量广义势能/余能原理;推导了相应的线性弹性力学广义势能/余能原理及其广义杂交元模型,为工程应用提供了新的理论基础。

In this paper,a new proposition of the principle of minimum potential/complementary en- ergy in nonlinear elasticity with small deformation was presented.Based on the proposition,applying linear lagrange multiplier method to release all the constraint conditions,three field principle of gener- alized potential/complementary energy was founded.A corresponding principle of generalized poten- tial/complementary enregy,and its generalized hybrid element models were duduced,which provides new theoretical basis to engineering applications.