Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory

Abstract

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried out. An analytical solution for static analysis of rectangular plates is obtained to solve the governing equations and boundary conditions. The suggested model is justified by a very good agreement between the results given by the present model and available data. Additionally, the effects of different parameters such as internal length scale parameter, length to thickness ratio and aspect ratio on the numerical results are also investigated. It is hoped that the present methodology lead to other models for static and dynamic analysis of rectangular nano structures with considering small scale effects.