Size-Dependent Buckling Analysis of Three-Layered Nano-plate on Orthotropic Foundation Using Surface Theory

Subject Areas : Mechanics of Solids

Amir Hossein Soltan Arani ¹ , Ali Ghorbanpour Arani ² , Zahra Khoddami Maraghi ³

1 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran---Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran
3 - Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran

Received: 2023-09-11 Accepted : 2024-06-24 Published : 2024-09-24

Keywords: Bi-axial buckling load, Neutral surface, Nonlocal strain gradient theory, Stretching effect, Surface effects,

Abstract :

In this paper, a refined plate theory including the stretching effect is extended for analysis of functionally graded nano-plate integrated with piezoelectric face-sheets resting on orthotropic foundation. According to this theory, the size-dependent buckling behavior of a simply supported rectangular nano-plate is studied using surface piezoelasticity theory in the framework of the nonlocal strain gradient theory. The properties of functionally graded nano-plate are assumed to be varied in the thickness direction based on a simple power-law distribution in terms of volume fraction. The governing equations are derived by employing the principle of minimum potential energy based on the neutral surface concept. Navier-type solution is used to obtain the analytical results of nano-plate subjected to an electric field. In order to check the accuracy and efficiency of the current model, a validation study is carried out based on the obtained results and available results in the previous literature. Numerical results show that the residual surface stress and neutral surface position have an undeniable influence on the critical buckling load of the nano-plate. It is expected that the results of current study to be utilized in designing micro/nano-electro-mechanical systems components based on smart nanostructures.

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