The application of the nonlocal theory and various shear strain theories for bending and free vibration analysis of organic nanoplates

Abstract

This is the first study of the static bending and free vibration response of organic nanoplates based on the combination of nonlocal theory with various shear strain theories, where the theory of shear deformation of the plate has the advantage of requiring no shear correction factor. The equilibrium equation of the plate is derived using Hamilton’s principle, the analytic solution is derived using the Navier solution form, and the finite element technique is implemented using a quadrilateral element with four nodes and six degrees of freedom for each node. Moreover, this is the first work to calculate for nanoplates with a nonlocal parameter whose value varies with plate thickness. This study’s credibility has been established by comparing it to previously published findings, which are utilized to validate the results of analytical and numerical calculations, respectively. In addition, the study investigates how a range of components impact the displacement and stress response of organic nanoplates. The findings of the study indicate that there are some circumstances in which it is not feasible to disregard the nonlocal parameter while doing calculations for organic nanostructures.