In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven integral formulation of elasticity. The present research extends the treatment in Barretta, Čanađija, Luciano, and de Sciarra (2018b) confined to elastically homogeneous nano-scopic structures. It is shown that the non-locality leads to a complex coupling between axial and transverse elastic displacements. Such a size-dependent phenomenon makes the solution of the relevant nonlocal thermoelastostatic problem, governed by a system of two ordinary differential equations with ten standard boundary conditions and non-classical constitutive boundary conditions, significantly more involved with respect to treatments in literature. Thus, a novel solution methodology, based on Laplace transforms, is proposed and illustrated by examining simple structural schemes of current applicative interest in Nanomechanics and Nanotechnology.

本文研究了非等温环境下多层小梁的力学行为。比例现象是通过数学上适当定位和实验上一致的应力驱动的弹性积分公式建模的。本研究扩大了Barretta，Čanađija，Luciano和de Sciarra（2018b）的治疗范围，仅限于弹性均质的纳米结构。结果表明，非局部性导致轴向和横向弹性位移之间的复杂耦合。这种大小相关的现象解决了相关的非局部热弹性问题，它由两个常微分方程组和十个标准边界条件和非经典本构边界条件共同决定，与文献治疗有关的更多。因此，通过研究当前在纳米力学和纳米技术中有兴趣的简单结构方案，提出并说明了一种基于拉普拉斯变换的新颖的解决方法。