The size-dependent bending of perfectly/imperfectly bonded multilayered/stepwise functionally graded nanobeams, e.g. multiwalled carbon nanotubes with weak van der Waals forces, with any arbitrary numbers of layers, exhibiting different material, geometrical, and length-scale properties, is studied through a layerwise formulation of the stress-driven nonlocal theory of elasticity and the Bernoulli-Euler beam theory. The formulation is also valid for the continuously graded nanobeams, where the through-the-thickness material gradation with any arbitrary distribution is approximated in a stepwise manner through many layers. The size-dependency of each layer is accounted for through nonlocal constitutive relationships, which define the strains at each point as the output of integral convolutions in terms of the stresses in all the points of the layer and a kernel. Linear elastic uncoupled interfacial laws are implemented to model the mechanical response of the interfaces. The size-dependent system of equilibrium equations governing the deformations of the layers are derived and subjected to the variationally consistent edge boundary conditions and the constitutive boundary conditions associated with the stress-driven integral convolution. The formulation is applied to multilayered and sandwich nanobeams and the effects of the interfacial imperfections on the displacement fields and the interfacial displacement jumps are studied. It is found that the interfacial imperfections have greater impact on the field variables of multilayered nanobeams than that of the multilayered beams with the large-scale dimensions.

通过以下方法研究了完美/不完美结合的多层/逐步功能梯度纳米束（例如具有弱范德华力的多壁碳纳米管，具有任意数量的层，表现出不同的材料，几何形状和长度尺度特性）的尺寸依赖性弯曲应力驱动的非局部弹性理论和Bernoulli-Euler梁理论的分层表示。该配方对于连续分级的纳米束也是有效的，在纳米束中，具有任意分布的整个厚度的材料渐变通过多个层以逐步方式进行近似。每层的尺寸相关性是通过非局部本构关系解决的，根据层和内核所有点的应力，将每个点的应变定义为积分卷积的输出。实施线性弹性非耦合界面定律以对界面的机械响应进行建模。推导了控制层变形的尺寸方程平衡方程组，该方程受应力一致积分卷积的变化一致边缘边界条件和本构边界条件的影响。该配方应用于多层和三明治纳米束，研究了界面缺陷对位移场和界面位移跳跃的影响。