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Steel and Composite Structures
  Volume 33, Number 2, October25 2019 , pages 307-318
DOI: https://doi.org/10.12989/scs.2019.33.2.307
 


Nonlinear bending analysis of porous FG thick annular/circular nanoplate based on modified couple stress and two-variable shear deformation theory using GDQM
Amirmahmoud Sadoughifar, Fatemeh Farhatnia, Mohsen Izadinia and Sayed Behzad Tal

 
Abstract
    This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.
 
Key Words
    nonlinear bending; FG porous; annular and circular nanoplates; modified couple stress theory; Kerr medium
 
Address
(1) Amirmahmoud Sadoughifar, Fatemeh Farhatnia, Mohsen Izadinia, Sayed Behzad Tal:
Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran, 8514143131, Iran;
(2) Fatemeh Farhatnia:
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Isfahan, Iran, 8418148499, Iran;
(3) Sayed Behzad Talaeitaba:
Department of Civil Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Isfahan, Iran.
 

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