SBFE analysis of layered elastic media with consideration of surface energy effect

Abstract

This thesis presents an efficient and accurate numerical technique for determining mechanical response of a two-dimensional, infinite, elastic, layered medium under arbitrary surface loading and surface stress effects. Governing equations of a generic bulk layer are formulated from the classical linear elasticity theory via a SBFE technique whereas those of the generic material surface are obtained from a full version of Gurtin-Murdoch surface elasticity theory. The formulation is established sufficiently general allowing both homogenous and functionally graded bulk materials to be treated for each layer. By enforcing the continuity at the interface of the material surface and the bulk, it leads to a system of non-homogenous, linear, ordinary differential equations governing the nodal functions of the layered medium. A general solution of the resulting system of ODEs is then constructed via standard procedures and then used to form a system of linear algebraic equations governing nodal boundary data. To facilitate the treatment of surface loading over a finite region, a SBFE subdomain technique is applied to establish a final system of governing equations for the whole layered medium. To fully investigate the accuracy, convergence, and capability of the proposed method, selected scenarios are solved and obtained numerical results are reported and discussed.