【摘要】 表面效应对纳米结构的力学性能有重要影响。飞机上很多微纳尺度的结构可简化为悬臂梁。本工作分析表面效应对随从载荷作用下梯度多孔材料纳米悬臂梁在高温环境下非线性力学响应的影响。基于GurtinMurdoch表面弹性理论和非线性梁理论，建立梯度多孔材料梁在随从载荷以及温度场中的非线性控制微分方程。假定梯度多孔材料的性能在整个厚度范围内连续变化，且沿厚度呈两种余弦形式的非均匀孔隙率分布模式。采用打靶法求解梯度多孔材料悬臂纳米梁在热-随从载荷下的非线性力学响应。获得各种孔隙率系数和不同非均匀升温下悬臂纳米梁非线性力学响应的数值解，详细讨论材料表面弹性常数和表面应力对纳米悬臂梁力学响应的影响。结果表明：不同孔隙率系数和不同非均匀升温下梁的力学行为是不同的；纳米梁表现出十分显著的表面效应。更多还原

【Abstract】 The surface effect has an important influence on the mechanical properties of nanostructures. Many micro and nano-scale structures on aircraft can be simplified as cantilever beams. In this paper,the influence of surface effect on the nonlinear mechanical response of gradient porous material nano cantilever under follower load at high temperature was analyzed. Based on GurtinMurdoch’s surface elastic theory and nonlinear beam theory, the nonlinear governing differential equations of gradient porous material beam under follower load and temperature field were established. It was assumed that the properties of gradient porous materials change continuously in the entire thickness range,and there were two kinds of non-uniform porosity distribution patterns in cosine form along the thickness. The nonlinear mechanical response of the gradient porous material cantilever nanobeam under thermal follower load was solved by shooting method. The numerical solutions of the nonlinear mechanical response of the cantilever under various porosity coefficients and different non-uniform temperature rises were obtained. The effects of the material surface elastic constants and surface stresses on the mechanical response of the cantilever were discussed in detail. The results show that the mechanical behaviors of beams are different under different porosity coefficients and different non-uniform temperature rises. The nanobeams exhibit very significant surface effects.更多还原