As a basic element of the micro/nanodevices, nanobeams have remarkable physical properties and have attracted considerable attention in the previous studies. However, previous publications did not study the large deformation problem of nanobeams under follower loading when the surface effect becomes significant and especially for the influence of surface effect on mechanical behaviors of the nanobeams under follower loading remains unclear. In this paper, we investigated the large deformation behavior of nanobeams subjected to follower loads in consideration of the surface effects. The mechanical model of large deflection of extensible cantilever nanobeams under follower loading is presented in combination with the surface elasticity and residual surface stress, and then a MATLAB program of shooting method with a technique for determining the initial value was developed to solve the problems. The results indicate that the surface effects have an important influence on the large deflection of nanobeams under follower loading: when the surface residual stress is positive, the maximums of displacement in horizontal and vertical directions and the rotation angle of the free end become lager, but the corresponding follower force related to those maximums becomes smaller. When the residual surface stress is negative, the results are the opposite. In addition, the influence of the cross-sectional dimension of the nanobeams under follower loading on surface effects was discussed. This work is beneficial to understand the mechanism of large deformation of nanobeams with surface effects subjected to follower loads, and can also provide inspirations to design advanced nanomaterials and nanoscaled devices.

中文翻译：

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受随动载荷作用下纳米束大挠度的表面效应

作为微/纳米器件的基本元件，纳米束具有显着的物理特性，在以往的研究中引起了相当大的关注。然而，当表面效应变得显着时，以前的出版物没有研究纳米梁在随动载荷下的大变形问题，特别是表面效应对随动载荷下纳米梁力学行为的影响仍不清楚。在本文中，我们在考虑表面效应的情况下研究了承受随动载荷的纳米梁的大变形行为。结合表面弹性和残余表面应力，提出了随动载荷下可延伸悬臂纳米梁大挠度的力学模型，然后开发了带有初始值确定技术的射击法MATLAB程序来解决这些问题。结果表明，表面效应对随动加载下纳米梁的大挠度有重要影响：当表面残余应力为正时，水平和垂直方向的最大位移和自由端的旋转角度变大，但与这些最大值相关的相应从动力变小。当残余表面应力为负时，结果相反。此外，还讨论了随动载荷下纳米束的横截面尺寸对表面效应的影响。这项工作有助于理解具有表面效应的纳米束在受随动载荷作用下的大变形机理，