二维Nonlocal线弹性理论的变分原理与对偶方程

基于Eringen提出的Nonlocal线弹性理论的微分形式本构关系,导出了相应的能量密度表达式,进而得到二维Nonlocal线弹性理论的变分原理.利用变分原理导出了对偶平衡方程和相应的边界条件.进而给出了非局部动力问题的Lagrange函数,并引入对偶变量和Hamilton函数,得到了对偶体系下的变分方程.在Hamilton体系下,通过变分得到了二维Nonlocal线弹性理论的对偶平衡方程和相应的边界条件.

VARIATIONAL PRINCIPLE AND DUAL EQUATIONS OF TWO-DIMENSIONAL NONLOCAL LINEAR ELASTICITY

The energy density expression was deduced using the constitutive equations in differential form of nonlocal elasticity, proposed by Eringen, and the corresponding variational principle of two-dimensional nonlocal linear elasticity was presented. Then, the equilibrium equations and the relevant boundary conditions were obtained from the established variational principle and the correlative Lagrangian for nonlocal dynamic problems was presented. After introducing Hamiltonian and duality variables, the variational principle was rewritten in the duality system, the duality equilibrium equations and relevant boundary conditions of two-dimensional nonlocal linear elasticity were derived from the variational equation in duality form.