Analysing scale phenomena in nanostructures is crucial for modelling and optimizing modern nanotechnological devices. Notably, soft nanostructures can be effectively designed as basic components of smart electro-mechanical systems that require geometrically nonlinear analyses as their structural parts undergo large deflection. Adoption of non-conventional approaches for accurate assessment of size effects is thus needed. The paper investigates the elastostatic behaviour of small-scale beams experiencing large displacements exploiting a consistent model of integral gradient elasticity. An iterative analytical solution procedure is proposed to address the geometrically nonlinear problem of soft nanobeams. The presented nonlocal stress gradient methodology is able to capture both stiffening and softening size-dependent nonlinear responses, thus generalizing the outcomes contributed by Vaccaro (2022). Effectiveness of the proposed approach for modelling and designing next-generation smart devices is finally shown by solving applicative nanomechanical problems. The presented methodology can be further extended to nonlinear analyses of three-dimensional nanocontinua to capture size effects of arbitrarily shaped structures undergoing large configuration changes.

中文翻译：

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非局部梯度悬臂梁的大挠度


分析纳米结构中的尺度现象对于建模和优化现代纳米技术设备至关重要。值得注意的是，软纳米结构可以有效地设计为智能机电系统的基本组件，这些系统需要几何非线性分析，因为其结构部件会发生较大的挠度。因此，需要采用非常规方法来准确评估尺寸效应。本文利用积分梯度弹性的一致模型研究了经历大位移的小尺寸梁的弹性静态行为。提出了一种迭代解析求解程序来解决软纳米束的几何非线性问题。提出的非局部应力梯度方法能够捕获刚度和软化与尺寸相关的非线性响应，从而概括了 Vaccaro （2022） 贡献的结果。最终通过解决应用纳米力学问题，证明了所提出的建模和设计下一代智能设备的方法的有效性。所提出的方法可以进一步扩展到三维纳米连续体的非线性分析，以捕获经历较大构型变化的任意形状结构的尺寸效应。