Eur. Phys. J. Plus (2020) 135: 493
https://doi.org/10.1140/epjp/s13360-020-00504-7

Regular Article

Nonlocal mixed variational formula for orthotropic nanoplates resting on elastic foundations

¹ Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
² Department of Mathematics, Kafrelsheikh University, 33516, Kafrelsheikh, Egypt
³ Department of Mathematics and Statistics, Higher Institute of Management and Information Technology, Nile for Science and Technology, 33514, Kafrelsheikh, Egypt

^a zenkour@kau.edu.sa

Received: 4 April 2020
Accepted: 3 June 2020
Published online: 13 June 2020

Abstract

This paper deals with the examination of orthotropic nanoplates utilizing nonlocal mixed variational formula. For this model, the displacement and stress fields are considered to be arbitrary and it includes the impact of transverse normal stress which does not exist in numerous theories. The orthotropic nanoplates are thought to be refreshed on elastic foundations. The mixed theory is utilized to get the governing differential equations as per Eringen’s nonlocal elasticity model. The governing equations incorporate the small-scale effect as well as foundations and mechanical impacts. Analytical solutions of bending response for simply supported orthotropic nanoplates are derived. The present outcomes are compared well with those being in the literature. The effects played by elastic foundation parameters, small-scale parameter, aspect and thickness nanoplate ratios are examined. The present study can be used as benchmarks for future comparisons with other investigators applying models containing the transverse shear and normal strains.