纳米开关结构是纳机电系统(Nano-Electromechanical System，NEMS)中广泛应用的重要控制元件，吸合特性是纳米开关的重要特征，纳米开关的吸合特性决定了纳米开关的工作性能。弯曲变形是纳米开关工作中时常发生的力学行为。当纳米开关结构的特征尺寸减小到纳米级时，表面效应凸显，将对纳米开关的力学性能产生影响。因此，表面效应对纳米开关力学行为影响的研究具有重要意义。本文通过理论推导和数值计算研究考虑表面效应的纳米开关结构线性弯曲、非线性弯曲行为及其吸合失稳特性。具体内容包含以下四部分：

(1) 研究考虑表面效应的纳米开关线性弯曲行为。基于表面弹性理论和“核壳”模型，通过等效弹性刚度和表面能模型引入表面效应。分析表面效应、静电力、分子间作用力(Casimir力)对纳米开关线性弯曲行为及其吸合稳定性的影响。通过最小势能原理推导控制方程，并通过同伦摄动法求解。具体计算四种边界条件下纳米开关结构，结果表明：表面效应对纳米开关吸合稳定性有显著影响。表面效应使纳米开关变形减小，吸合电压增大，随纳米开关结构尺寸增大，表面效应影响减弱，随电极间距增大，表面效应影响增大。Casimir力和电场边缘效应均使纳米开关吸合电压减小。纳米开关吸合电压值与已有文献中的数据吻合较好。

(2) 研究温度载荷下纳米开关线性弯曲行为及其吸合稳定性。根据热弹性力学理论计算温度应变能，分析表面效应、温度、静电力、分子间作用力(热修正Casimir力)对纳米开关线性弯曲行为及其吸合稳定性的影响。计算结果表明：温度对纳米开关吸合稳定性有显著影响。温度增加使纳米开关吸合电压减小，随纳米开关结构尺寸增大，温度对纳米开关吸合电压的影响几乎不变。热修正Casimir力和电场边缘效应均使纳米开关吸合电压减小。随电极间距增大，温度和电场边缘效应对纳米开关吸合电压影响增大。

(3) 研究纳米开关非线性弯曲行为。基于Von Karman 几何非线性理论，分析表面效应、几何非线性、静电力、分子间作用力(Casimir力)对纳米开关非线性弯曲行为及其吸合稳定性的影响。具体计算四种边界条件下纳米开关结构，结果表明：表面效应对纳米开关非线性弯曲及其吸合稳定性有显著影响。表面效应使纳米开关吸合电压增大，吸合位移减小，随纳米开关结构尺寸增大，表面效应影响减小。对比分析线性理论与非线性理论结果，线性理论的吸合电压比非线性理论吸合电压小。几何非线性的影响随纳米开关结构尺寸增大而增大，随电极间距增大而增大，随纳米开关结构长高比增大而减小。纳米开关非线性弯曲吸合电压值与已有文献中的数据吻合较好。

(4) 研究温度载荷下纳米开关非线性弯曲行为及其吸合稳定性。根据热弹性力学理论计算温度应变能，分析表面效应、温度、几何非线性、分子间作用力(热修正Casimir力)对纳米开关非线性弯曲及其吸合稳定性的影响。计算结果表明：随温度增加，纳米开关吸合电压减小，吸合位移增大。随纳米开关结构尺寸增大，温度对纳米开关吸合电压的影响几乎保持不变，对纳米开关吸合位移影响减小。

本文研究表面效应、几何尺寸、温度、电场边缘效应以及分子间作用力(Casimir力)对四种边界条件纳米开关线性弯曲、非线性弯曲行为及其吸合失稳特性的影响，为纳机电系统中纳米开关结构的优化设计与实际应用提供理论依据。

Nanomechanical switch structures are vital control elements extensively utilized in Nano-Electromechanical Systems (NEMS), with their pull-in characteristics significantly determining performance. Bending deformation is a mechanical behavior that often occurs in the operation of nano-switches. As dimensions of such structures diminish to the nanoscale, surface effects emerge, impacting mechanical properties. Hence, examining surface effects on the mechanical behavior of nano-switches is crucial. This paper investigates the linear bending, nonlinear bending, and pull-in instability of nano-switch structures considering surface effects through theoretical derivation and numerical calculations, comprising four parts:

(1) Investigating linear bending behavior of nano-switches considering surface effects. Employing surface elasticity theory and the "core-shell" model, surface effects are introduced via equivalent elastic stiffness and surface energy models. The influence of surface effects, electrostatic forces, and intermolecular forces (Casimir force) on the pull-in stability of linear bending behavior is analyzed. The governing equation is derived using the principle of minimum potential energy and solved through the homotopy perturbation method. Results for four boundary conditions indicate that surface effects significantly impact pull-in stability, reducing deformation and increasing pull-in voltage. As the size of the nano-switches structure increases, the surface effect is weakened, and as the electrode spacing increases, the surface effect increases. Both the Casimir force and the electric field edge effect reduce the pull-in voltage of the nano-switches. The pull-in voltage of the nano-switches is in good agreement with the data in the existing literature.

(2) Examining the linear bending behavior and pull-in stability of nano-switches under temperature load. Temperature-induced strain energy is calculated using thermoelasticity theory, analyzing the influence of surface effects, temperature, electrostatic forces, and intermolecular forces (thermally corrected Casimir force) on pull-in stability. Results reveal that temperature substantially impacts pull-in stability, with increasing temperatures decreasing pull-in voltage. As the size of the nano-switches structure increases, the effect of temperature on the pull-in voltage of the nano-switches is almost unchanged. Both the thermally corrected Casimir force and the electric field edge effect reduce the pull-in voltage of the nano-switches. With the increase of electrode spacing, the influence of temperature and electric field edge effect on the pull-in voltage of nano-switches increases.

(3) Investigating nonlinear bending behavior of nano-switches considering surface effects. The effects of surface effect, geometric nonlinearity, electrostatic force, and intermolecular force (Casimir force) on the pull-in stability of nonlinear bending behavior of nano-switches are analyzed. The von Karman geometric nonlinear theory is employed. The nano-switches structures under four boundary conditions are calculated. Results reveal that the surface effect has a significant effect on the nonlinear bending pull-in stability of the nano-switches. The surface effect increases the pull-in voltage of the nano-switches and decreases the pull-in displacement. With the increase of the size of the nano-switches structure, the surface effect decreases. Comparing linear and nonlinear theory results, the linear theory pull-in voltage is smaller than that of the nonlinear theory. The influence of geometric nonlinearity increases with the increase of the size of the nano-switches structure, increases with the increase of the electrode spacing, and decreases with the increase of the aspect ratio of the nano-switches structure. The nonlinear bending pull-in voltage of the nano-switches is in good agreement with the data in the existing literature.

(4) Studying the nonlinear bending behavior and pull-in stability of nano-switches under temperature load. The influence of surface effects, temperature, geometric nonlinearity, and intermolecular forces (thermally corrected Casimir force) on pull-in stability is analyzed. Results demonstrate that increasing temperature decreases pull-in voltage and increases pull-in displacement. As the size of the nano-switches structure increases, the effect of temperature on the pull-in voltage of the nano-switches remains almost unchanged, and the effect on the pull-in displacement of the nano-switches decreases.

This research examines the impact of surface effects, geometric dimensions, temperature, electric field edge effects, and intermolecular forces (Casimir force) on the pull-in instability characteristics of linear and nonlinear bending behavior for four boundary condition nano-switches models, providing a theoretical basis for the optimization and practical application of nano-switch structures in NEMS.