Eur. Phys. J. Plus (2021) 136: 676
https://doi.org/10.1140/epjp/s13360-021-01667-7

Regular Article

Surface elastic-based nonlinear bending analysis of functionally graded nanoplates with variable thickness

¹ School of Science and Technology, The University of Georgia, 0171, Tbilisi, Georgia
² Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, North Cyprus via Mersin 10, Turkey
³ Institute of Continuum Mechanics, Leibniz Universitaet Hannover, 30823, Garbsen, Germany

^c aldakheel@ikm.uni-hannover.de

Received: 20 December 2020
Accepted: 22 May 2021
Published online: 20 June 2021

Abstract

In this investigation, the geometrically nonlinear bending behavior of functionally graded (FG) composite elliptical and sector nanoplates with variable thickness is analyzed in the presence of surface elasticity and surface residual stress coming from the low thickness to volume ratio at nanoscale. To this purpose, a quasi-3D plate model incorporating a sinusoidal transverse shear function in conjunction with a trigonometric normal function is established based upon the Gurtin–Murdoch theory. Hereby, three different patterns including linear, convex and concave ones are considered for the plate thickness variation. The nanoplate is graded continuously from top surface to bottom, as the properties of the atomic layers of free surfaces are considered based on the surface elasticity associated with specific crystallographic directions. To resolve the surface elastic-based flexural problem, the non-uniform rational B-spline type of isogeometric solution methodology is adopted to integrate accurately the geometric discerption. The model extracted deflection results are lower than those obtained by classical continuum elasticity, due to the stiffening character of the surface stress size effect coming from low surface to volume ratio at nanoscale, resulting with extra stiffness for the proposed FG nanoplate. Furthermore, it is revealed that by changing the pattern of the thickness variation from convex to linear type, and then from linear to concave type, the classical flexural stiffness enhances. This results with lower surface elastic-based flexural stiffness of FG nanoplates because of a higher value of the plate thickness average.