The stress-driven nonlocal continuum theory is a well-established integral elasticity formulation. Modelling the elastic strain via a convolution integral between stress and an averaging kernel, the theory leads to an integro-differential structural problem for arbitrary 3D nonlocal solids. Integral elasticity solutions are mainly available for 1D solids by adopting a bi-exponential kernel and reverting the boundary-value integro-differential problem to an equivalent differential formulation involving both classical and constitutive boundary conditions. A general computational framework to implement the stress-driven theory for 3D nonlocal solids is still missing. This paper tackles this issue, solving the relevant integro-differential problem by a two-field finite-element approach involving displacements and stresses. The approach can handle the dynamics of complex small-size structures of arbitrary shape. Focusing on free vibration responses, two examples are presented: a 2D rectangular plate, serving as benchmark to demonstrate size effects captured by stress-driven nonlocal elasticity, and a 3D solid modelling a typical dual microcantilever resonator with overhang.

应力驱动的非局部连续统理论是一种行之有效的整体弹性公式。通过应力和平均核之间的卷积积分对弹性应变进行建模，该理论导致了任意 3D 非局部实体的积分微分结构问题。积分弹性解主要适用于一维固体，方法是采用双指数核并将边界值积分微分问题恢复为涉及经典和本构边界条件的等效微分公式。仍然缺少实现 3D 非局部实体的应力驱动理论的通用计算框架。本文解决了这个问题，通过涉及位移和应力的两场有限元方法解决了相关的积分微分问题。该方法可以处理任意形状的复杂小尺寸结构的动力学。以自由振动响应为重点，给出了两个示例：一个 2D 矩形板，作为基准来展示由应力驱动的非局部弹性捕获的尺寸效应，以及一个 3D 实体，它对典型的带有悬垂的双微悬臂梁谐振器进行建模。