MULTI-LAYERED ELASTIC MEDIUM UNDER AXISYMMETRIC LOADING AND SURFACE ENERGY EFFECTS

Abstract

Multi-layered nano-scale structures have been found in a wide range of applications these days. Since the surface energy effect is presented at the nano-scale level, a novel calculation scheme is required to accurately capture the mechanical behaviors of such structures. In this study, a solution scheme for analysis of a multi-layered elastic medium with influence of surface energy effects subjected to axisymmetric loading by adopting Gurtin-Murdoch surface elasticity theory is presented. The standard Love’s representation and Hankel integral transform are employed to derive the general solutions, and the obtained solutions are employed in the determination of the stiffness matrix for each elastic layer. The global stiffness equation of a multi-layered system is assembled by considering the continuity of traction and displacements at each layer interface. The numerical solutions to the global equation yield displacements and stresses at the interfaces of the layered medium under axisymmetric loading. The obtained results reveal that the elastic fields are significantly influenced by the surface elastic properties, the loading radius and the elastic material properties of each layer. The proposed solution scheme can be used to examine a variety of practical problems, and the solutions can also be used as benchmark solutions in the development of FEM and BEM for more complicated problems related to multi-layered systems with the influence of surface energy effects.