Influence of surface effect on mechanical properties of thermo-mechanical porous cantilever nanobeams

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 Gurtin-Murdoch'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.

Keywords

• graded porous materials
• cantilever beam
• follower force
• surface residual stress
• surface effect