Mechanistic models for nanobeams with surface stress effects

Abstract

In this paper, a mechanistic model for nanobeams with surface energy effects is developed by using a variational formulation. Thiswork is motivated by the unusual response of nanocantilevers predicted by models based on the Young-Laplace equation for surface stress.The governing equation and boundary conditions derived from the variational methods are compared with the governing equations andboundary conditions used in the Young-Laplace models and other formulations. A key difference in the shear force boundary condition isnoted. Analytical solutions for simply supported, cantilevered, and fixed-fixed beams are reexamined. It is shown that the unusual behavior ofnanocantilevers predicted by the Young-Laplace models is due to the shear force boundary condition used. The current formulation leads toconsistent solutions for beams under different boundary conditions.DOI:10.1061/(ASCE)EM.1943-7889.0001520.© 2018 AmericanSociety of Civil Engineers