Abstract

A novel mathematical formulation is presented for the applications of the stress-driven nonlocal theory of elasticity to engineering nano-scale problems requiring longitudinal discretization. Specifically, a differential formulation accompanied with novel constitutive continuity conditions is provided for determining exact closed-form solutions of nonlocal Euler-Bernoulli beams with loading discontinuities, i.e. points of discontinuity for external loads and internal forces. Constitutive continuity conditions have to be satisfied in interior points where a loading discontinuity occurs and contain integral convolutions of the stress over suitable parts of the nonlocal beam. Several results show the effectiveness of the proposed method.

摘要

提出了一种新的数学公式，用于将应力驱动的非局部弹性理论应用于需要纵向离散化的工程纳米级问题。具体而言，提供了一种带有新的本构连续性条件的微分公式，用于确定具有加载不连续性的非局部 Euler-Bernoulli 梁的精确闭合形式解决方案，即外载荷和内力的不连续点。在发生加载不连续的内部点必须满足本构连续性条件，并且在非局部梁的适当部分上包含应力的积分卷积。几个结果表明了所提出方法的有效性。