A two variable refined plate theory for the bending analysis of functionally graded plates

2010 ◽  
Vol 26 (6) ◽  
pp. 941-949 ◽  
Author(s):  
Ismail Mechab ◽  
Hassen Ait Atmane ◽  
Abdlouahed Tounsi ◽  
Hichem Abdesselem Belhadj ◽  
El Abbas Adda Bedia
Keyword(s):  
Plate Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Bending Analysis

NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER PRESSURE LOADS USING A FOUR VARIABLE REFINED PLATE THEORY

2014 ◽  
Vol 11 (04) ◽  
pp. 1350062 ◽  
Author(s):  
MOHAMED ATIF BENATTA ◽  
ABDELHAKIM KACI ◽  
ABDELOUAHED TOUNSI ◽  
MOHAMMED SID AHMED HOUARI ◽  
KARIMA BAKHTI ◽  
...  
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Von Karman ◽  
Von Kármán

The novelty of this paper is the use of four variable refined plate theory for nonlinear analysis of plates made of functionally graded materials. The plates are subjected to pressure loading and their geometric nonlinearity is introduced in the strain–displacement equations based on Von–Karman assumptions. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The fundamental equations for functionally graded plates are obtained using the Von–Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for functionally graded plates are given in dimensionless graphical forms; and the effects of material properties on deflections and stresses are determined. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the CPT, but are almost comparable to those obtained using higher order theories having more number of unknown functions.

A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates

2016 ◽  
Vol 22 (3) ◽  
pp. 473-495 ◽  
Author(s):  
Habib Hebali ◽  
Ahmed Bakora ◽  
Abdelouahed Tounsi ◽  
Abdelhakim Kaci
Keyword(s):  
Plate Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Refined Plate Theory

Levy solution for buckling analysis of functionally graded plates based on a refined plate theory

2013 ◽  
Vol 227 (12) ◽  
pp. 2649-2664 ◽  
Author(s):  
Huu-Tai Thai ◽  
Brian Uy
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Neutral Surface ◽  
Functionally Graded Plates ◽  
Refined Plate Theory

This article presents analytical solutions for buckling analysis of functionally graded plate based on a refined plate theory. Based on the refined shear deformation theory, the position of neutral surface is determined and the governing stability equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The closed-form solutions of buckling load are obtained for rectangular plates with various boundary conditions. The accuracy of neutral surface-based model is verified by comparing the obtained results with those reported in the literature. Finally, parameter studies are carried out to study the effects of power law index, thickness ratio, and aspect ratio on the critical buckling load of functionally graded plates.

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