A comprehensive investigation of the bending and vibration behavior of size-dependent functionally graded nanoplates via an enhanced nonlocal finite element shear model

Abstract

This research paper conducts a comprehensive investigation into the linear bending and free vibration of size-dependent functionally graded (FG) nanoplates using an improved first-order shear deformation theory (IFSDT). The present IFSDT offers an enhanced representation and precise computation of normal and shear stresses across the thickness of the nanoplates. Notably, it not only ensures compliance with free conditions on both the upper and lower surfaces but also eliminates the need for a conventional correction factor commonly employed in the first-order shear deformation theory (FSDT). To transcend the assumptions of classical continuum mechanics and address the impacts of small-scale effects in discrete nanoplates, Eringen’s nonlocal elasticity theory is applied. The formulation of the governing equation for the bending and free vibration analyses of the FG nanoplates is achieved through the application of Hamilton’s principle. The proposed IFSDT is implemented with an efficient C0-continuous quadrilateral element which is suitable for analysis of structures with arbitrary shapes and complex forces. The model’s performance is showcased through a comparative evaluation against literature predictions, highlighting its high accuracy and rapid convergence. Additionally, the research scrutinizes the effects of various parameters, such as plate thickness, boundary conditions, aspect ratio, nonlocal parameter, different material compositions, and power-law index on the deflections, stresses, and naturel frequencies of the FG nanoplates. The results underscore the significant impact of size-dependent effects on the linear bending and vibration behaviors of the nanoplates.