Perforated beam is essential structural element of Nano-Electro-Mechanical-Systems (NEMS), whose design needs appropriate modelling of size of holes, hole numbers, and scale effects. The current manuscript presents a comprehensive study and develops non-classical closed form solutions to predict the static bending behavior and buckling stability of perforated nanobeams (PNBs) incorporating the surface energy for different four beams theories, for the first time. Equivalent geometrical models for both bulk and surface characteristics are presented. The Gurtin–Murdoch surface elasticity model is modified and adopted to include the perforation in surface characteristics. To consider the warping shear effect on bending as well as critical buckling loads with the presence of surface stress effects, four different beams theories with shear deformation are considered. The non-classical equilibrium equations relevant to each PNB theory are developed in detail. Closed-form solutions are developed considering the different classical and non-classical boundary conditions as well as loading conditions. The proposed methodology is verified by comparing the obtained results with the available analytical solutions for fully filled beams and excellent agreement is observed. Effects of perforation characteristics as well as the surface effects on bending and buckling behaviors are investigated.

中文翻译：

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包括表面能在内的穿孔纳米梁的弯曲和屈曲响应，包括不同梁的理论

穿孔梁是纳米机电系统 (NEMS) 的基本结构元素，其设计需要对孔的大小、孔数和尺度效应进行适当的建模。当前的手稿提出了一项综合研究，并开发了非经典的封闭形式解决方案，以预测穿孔纳米梁 (PNB) 的静态弯曲行为和屈曲稳定性，首次结合不同四梁理论的表面能。提出了体积和表面特性的等效几何模型。对 Gurtin-Murdoch 表面弹性模型进行了修改和采用，以将穿孔包括在表面特征中。为了考虑弯曲的翘曲剪切效应以及存在表面应力效应的临界屈曲载荷，考虑了四种不同的剪切变形梁理论。详细开发了与每个 PNB 理论相关的非经典均衡方程。考虑到不同的经典和非经典边界条件以及加载条件，开发了封闭形式的解决方案。通过将获得的结果与可用的完全填充梁的解析解进行比较来验证所提出的方法，并观察到极好的一致性。研究了穿孔特性的影响以及表面对弯曲和屈曲行为的影响。通过将获得的结果与可用的完全填充梁的解析解进行比较来验证所提出的方法，并观察到极好的一致性。研究了穿孔特性的影响以及表面对弯曲和屈曲行为的影响。通过将获得的结果与可用的完全填充梁的解析解进行比较来验证所提出的方法，并观察到极好的一致性。研究了穿孔特性的影响以及表面对弯曲和屈曲行为的影响。