Finite-Element Solution to Nonlocal Elasticity and Scale Effect on Frequency Behavior of Shear Deformable Nanoplate Structure

Abstract

In this article, the eigenfrequency responses of a nanoplate structure are evaluated numerically via a novel higher-order mathematical model and finite-element method including nonlocal elasticity theory. A new computer program has been prepared based on the present model to compute the frequencies of the nanoplate structure. The accuracy of the numerical solutions has been checked through proper convergence and comparison with available published data by evaluating an adequate number of examples. The conclusions related to the capability of solving nanoplate structural problem and subsequent accuracy of the current higher-order finite-element model have been demonstrated by solving several illustrations. Also, the numerical examples are solved by considering the nonlocal elasticity as well as the scale effect and other geometrical and material parameters (aspect ratio, size, and nonlocal parameter) that may directly affect the final solutions are discussed.