This article aims to present comprehensive model and analytical solution to investigate the static bending behavior of regularly squared cutout perforated thin/thick nanobeams incorporating the coupled effect of the microstructure and surface energy for the first time. The perforation influence is considered to be deriving equivalent geometrical and material characteristics. The modified couple stress theory is adopted to incorporate the microstructure effect while the modified Gurtin–Murdoch surface elasticity model is employed to incorporate the surface stress effect in perforated nanobeams. A variational formulation based on minimization of the total potential energy principle is employed to derive the equilibrium equations of perforated nanobeams based on both Euler–Bernoulli and Timoshenko beams theories are developed to investigate the associated effect of the shear deformation due to perforation process. Additionally, Poisson’s effect is also incorporated. Analytical closed-form for the non-classical bending profiles as well as the rotational displacement are developed for both beam theories considering the simultaneous effect of both couple stress and surface stress for both uniformly distributed and concentrated loading patterns. The verification of the developed model is verified and compared with previous works, and an excellent agreement is obtained. The applicability of the developed model is demonstrated and applied to study and analyze the nonclassical bending behavior of regularly squared perforated simply supported beams under different loading conditions. Additionally, effects of the perforation configuration parameters, beam size as well as beam aspect ratio on the bending behavior of perforated beams in the presence of microstructure and surface stress effects are also investigated and analyzed. The obtained results reveal that both couple stress and surface stress significantly affect the bending behavior of regularly squared cutout perforated beam structures. Results obtained are supportive for the design, analysis and manufacturing of perforated NEMS applications.

中文翻译：

---

多孔纳米梁的静态弯曲，包括表面能和微结构效应

本文旨在提出综合模型和解析解，以研究首次结合微观结构和表面能耦合效应的规则平方切口穿孔薄/厚纳米梁的静态弯曲行为。穿孔影响被认为是导出等效的几何和材料特性。采用修正的耦合应力理论来结合微观结构效应，而采用修正的 Gurtin-Murdoch 表面弹性模型来结合穿孔纳米梁的表面应力效应。基于最小化总势能原理的变分公式用于推导基于欧拉-伯努利和铁木辛科梁理论的穿孔纳米梁的平衡方程，以研究穿孔过程引起的剪切变形的相关影响。此外，还包含泊松效应。考虑到对均匀分布和集中加载模式的耦合应力和表面应力的同时影响，为两种梁理论开发了非经典弯曲轮廓和旋转位移的解析闭合形式。对开发模型的验证进行了验证并与以前的工作进行了比较，获得了很好的一致性。证明了所开发模型的适用性，并将其应用于研究和分析不同载荷条件下规则方形穿孔简支梁的非经典弯曲行为。此外，还研究和分析了穿孔配置参数、梁尺寸以及梁纵横比在存在微观结构和表面应力效应的情况下对穿孔梁弯曲行为的影响。获得的结果表明，耦合应力和表面应力都显着影响规则方形切口穿孔梁结构的弯曲行为。获得的结果支持穿孔 NEMS 应用的设计、分析和制造。