Finite Difference Method for Biaxial and Uniaxial Buckling of Rectangular Silver Nanoplates Resting on Elastic Foundations in Thermal Environments Based on Surface Stress and Nonlocal Elasticity Theories

Abstract

In this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the Gurtin-Murdoch's theory. Using the principle of virtual work, the governing equations considering small scale for both nanoplate bulk and surface are derived. The influence of important parameters including, the Winkler and shear elastic moduli, boundary conditions, in-plane biaxial and uniaxial loads, and width-to-length aspect ratio, on the surface stress effects are also studied. The finite difference method, uniaxial buckling, nonlocal effect for both nanoplate bulk and surface, silver material properties, and below-mentioned results are the novelty of this investigation. Results show that the effects of surface elastic modulus on the uniaxial buckling are more noticeable than that of biaxial buckling, but the influences of surface residual stress on the biaxial buckling are more pronounced than that of uniaxial buckling.