中文摘要：

基于Hamilton体系研究了Eringen的非局部线弹性本构关系。Eringen的非局部线弹性理论存在积分型和微分型两类本构关系。由于方程的形式简单,目前多采用微分型本构;而积分型本构方程是典型的积分-微分方程,数值求解较为困难。在分析结构力学中提出的界带分析方法,成功求解了时间滞后问题的积分-微分方程。根据分析动力学与分析结构力学的模拟关系,将界带分析方法引入到非局部理论的积分型本构方程,可以实现积分-微分方程的数值求解。通过杆件的振动分析算例验证了该套理论算法的准确性和可行性,也指出了辛体系算法在非局部力学问题中的潜力。

英文摘要：

Based on the Hamilton theory, the constitutive relation was investigated for the non- local linear elasticity originally proposed by Eringen. Eringen＇ s nonlocal equations can be writ- ten in the integral form and the differential form. The differential form with the relatively simple mathematical formulation, had been widely used in recent years. For the integral form of the nonlocal elastic theory, solving the integro-differential equations was challenging for numerical process. In the analytical structural mechanics, the integro-differential equations in time-delay problems had been solved with the inter-belt theory. According to the simulative relations be- tween the analytical dynamics and the analytical structural mechanics, the inter-belt theory was introduced into the integral-form constitutive equations of the nonlocal theory, and hence the integro-differential equations were numerically solved with high precision. Then the fundamental theory and computational algorithm were applied to dynamic problems of nonlocal rod vibra- tion. The numerical experiments demonstrate validity of the present method and potential of the symplectic system algorithm in solving nonlocal mechanics problems.