Closed-form elasticity solution for three-dimensional deformation of functionally graded micro/nano plates on elastic foundation

H Salehipour,A.R Shahidi,H Nahvi

doi:10.1590/1679-78251398

Abstract

This paper addresses the static deformation of simply supported rectangular micro/nano plates made of functionally graded (FG) materials based on the three-dimensional nonlocal elasticity theory of Eringen. The plates are assumed to be simply supported and rested on a Winkler-Pasternak elastic foundation. Elasticity modulus is assumed to obey an exponential law along the thickness direction of the micro/nano plate. Using the Fourier series, a displacement field is defined that satisfies simply supported boundary condition and reduces three elasticity equations to two independent equations. The closed-form bending response is achieved by exerting boundary conditions of the lateral surfaces. Numerical results are presented to investigate the influences of the gradient index of the material properties, nonlocal parameter and stiffness of elastic foundation on the mechanical behavior of the plates.

Highlights

Micro- and nano-scaled plates are very important new type of structures that are utilized in different engineering applications such as micro- and nano-electro mechanical systems (MEMS and NEMS), atomic force microscopes, solar cells and many others
functionally graded (FG) materials are used in structures such as MEMS and NEMS (Witvrouw et al, 2005; Lee et al, 2006) to increase their thermal resistance
Ansari et al (2011) proposed a size-dependent model for bending and free vibration of Timoshenko microbeams made of FG materials based on the modified strain gradient elasticity theory

Summary

Introduction

Micro- and nano-scaled plates are very important new type of structures that are utilized in different engineering applications such as micro- and nano-electro mechanical systems (MEMS and NEMS), atomic force microscopes, solar cells and many others. Lu et al (2009) considered the surface effects to develop classic and Mindlin plate theories for nano-scaled FG circular films They evaluated cylindrical bending for supported boundary conditions to demonstrate the stability of the developed theories. Reddy and Kim (2012) presented a nonlinear size-dependent thirdorder plate theory based on the modified couple stress theory using nonlinear strains of von Karman and power-law distribution for FG material along the thickness direction. They utilized the linear form of this theory to observe mechanical behavior of supported rectangular plates (2013). Salehipour et al (2015) has presented analytical closed-form solution for free vibration of nonlocal FG plates based on the three-dimensional elasticity theory

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Conclusion