SBFE analysis of nano-scale elastic layer with consideration of surface energy effects

摘要

This paper presents an efficient and accurate numerical technique for determining the mechanical response of an infinite elastic layer under surface loading and surface stress effects.The governing equation of the bulk is formulated from the classical linear elasticity theory via a SBFE technique whereas that of the material surface is obtained from a complete version of Gurtin-Murdoch surface elasticity theory.By enforcing the continuity at the interface of the material surface and the bulk,it leads to a system of linear non-homogenous ordinary differential equations governing the nodal functions.A general solution of the resulting system of ODEs is constructed via standard procedures and then used together with the boundary conditions to form a system of linear algebraic equations governing nodal degrees of freedom.To investigate the accuracy and convergence of the proposed method,selected scenarios are solved and obtained numerical results are reported and discussed.