Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory

2018 ◽  
Vol 41 (8) ◽  
pp. 1042-1062
Author(s):  
Attia Bachiri ◽  
Mohamed Bourada ◽  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Refined Plate Theory ◽  
Thermodynamic Effect ◽  
Bending Response

A Novel Refined Plate Theory for Free Vibration Analyses of Single-Layered Graphene Sheets Lying on Winkler-Pasternak Elastic Foundations

2019 ◽  
Vol 58 ◽  
pp. 151-164 ◽  
Author(s):  
Fatima Boukhatem ◽  
Aicha Bessaim ◽  
Abdelhakim Kaci ◽  
Abderrahmane Mouffoki ◽  
Mohammed Sid Ahmed Houari ◽  
...  
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Displacement Field ◽  
Scale Effects ◽  
Plate Theory ◽  
Small Scale ◽  
Graphene Sheets ◽  
Refined Plate Theory ◽  
Foundation Parameters

In this article, the analyses of free vibration of nanoplates, such as single-layered graphene sheets (SLGS), lying on an elastic medium is evaluated and analyzed via a novel refined plate theory mathematical model including small-scale effects. The noteworthy feature of theory is that the displacement field is modelled with only four unknowns, which is even less than the other shear deformation theories. The present one has a new displacement field which introduces undetermined integral variables, the shear stress free condition on the top and bottom surfaces of the plate is respected and consequently, it is unnecessary to use shear correction factors. The theory involves four unknown variables, as against five in case of other higher order theories and first-order shear deformation theory. By using Hamilton’s principle, the nonlocal governing equations are obtained and they are solved via Navier solution method. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all examined. From this work, it can be observed that the small-scale effects and elastic foundation parameters are significant for the natural frequency.

scholarly journals Flexure of Thick Plates Resting on Elastic Foundation Using Two-Variable Refined Plate Theory

2015 ◽  
Vol 62 (2) ◽  
pp. 181-203 ◽  
Author(s):  
Jafar Rouzegar ◽  
Reza Abdoli Sharifpoor
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Plate Thickness ◽  
Benchmark Problems ◽  
Shear Stresses ◽  
Rectangular Plates ◽  
Governing Equations ◽  
Thick Plates ◽  
Refined Plate Theory ◽  
Winkler Elastic Foundation

Abstract The two-variable refined plate theory is used in this paper for the analysis of thick plates resting on elastic foundation. This theory contains only two unknown parameters and predicts parabolic variation of transverse shear stresses. It satisfies the zero traction on the plate surfaces without using shear correction factor. Using the principle of minimum potential energy, the governing equations for simply supported rectangular plates resting on Winkler elastic foundation are obtained. The Navier method is adopted for solution of obtained coupled governing equations, and several benchmark problems under various loading conditions are solved by present theory. The comparison of obtained results with other common theories shows the excellent efficiency of this theory in modeling thick plates resting on elastic foundation. Also, the effect of foundation modulus, plate thickness and type of loading are studied and the results show that the deflections are decreased by increasing the foundation modulus and plate thickness

Refined plate theory and its variants

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 137-146 ◽  
Author(s):  
R. P. Shimpi
Keyword(s):  
Plate Theory ◽  
Refined Plate Theory
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