SBFE analysis of surface loaded elastic layered media with influence of surface/interface energy

A numerical technique, based upon a scaled boundary finite element (SBFE) method, is proposed for the analysis of a two-dimensional, infinite, elastic, layered medium under arbitrary surface loads and surface energy effects. The governing equations of the bulk layers and the material surface/interfaces were formulated from linear elasticity and Gurtin-Murdoch surface elasticity theories, respectively. The SBFE formulation was established in a general context to handle both homogenous and functionally graded bulk materials. Enforcing the continuity of the displacements and tractions along the material interfaces together with the surface/interface equations resulted in a system of non-homogeneous, linear, ordinary differential equations (ODEs) governing the unknown nodal functions of the layer medium. A general solution of the final system of ODEs was constructed via a standard procedure and then used to form a system of linear algebraic equations governing the nodal boundary data. To facilitate the treatment of surface loads over a finite region, the subdomain technique was applied to obtain the governing equations for the whole layered medium. A selected set of results is reported to demonstrate the accuracy, convergence, and performance of the proposed technique.