An electromechanical model for functionally graded porous plates attached to piezoelectric layer based on hyperbolic shear and normal deformation theory

2021 ◽  
pp. 114352
Author(s):  
Rabab A. Alghanmi ◽  
Ashraf M. Zenkour
Keyword(s):  
Piezoelectric Layer ◽  
Deformation Theory ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Electromechanical Model

A new higher-order shear and normal deformation theory for functionally graded sandwich beams

2015 ◽  
Vol 19 (3) ◽  
pp. 521-546 ◽  
Author(s):  
Riadh Bennai ◽  
Hassen Ait Atmane ◽  
Abdelouahed Tounsi
Keyword(s):  
Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Normal Deformation

FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

2013 ◽  
Vol 13 (01) ◽  
pp. 1350004 ◽  
Author(s):  
D. K. JHA ◽  
TARUN KANT ◽  
R. K. SINGH
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

2014 ◽  
Vol 60 ◽  
pp. 274-283 ◽  
Author(s):  
Zakaria Belabed ◽  
Mohammed Sid Ahmed Houari ◽  
Abdelouahed Tounsi ◽  
S.R. Mahmoud ◽  
O. Anwar Bég
Keyword(s):  
Functionally Graded Material ◽  
Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Graded Material

A New Trigonometric Higher-Order Shear and Normal Deformation Theory for Functionally Graded Plates

2016 ◽  
Author(s):  
Ankit Gupta ◽  
Mohammad Talha
Keyword(s):  
Boundary Conditions ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Normal Deformation ◽  
3 Dimensional

In the present study, a new trigonometric higher-order shear and normal deformation theory is proposed and implemented to investigate the free vibration characteristics of functionally graded material (FGM) plates. The present theory comprises the nonlinear variation in the in-plane and transverse displacement and accommodates, both shear deformation and thickness stretching effects. It also satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor. The governing equations are derived using the variational principle. The effective mechanical properties of FGM plates are assumed to vary according to a power law distribution of the volume fraction of the constituents. Poisson’s ratios of FGM plates are assumed constant. The numerical solution has been obtained using an efficient displacement based C0 finite element model with eight degrees of freedom per node. The computed results are compared with 3-dimensional and quasi-3-dimensional solutions and those projected by other well-known plate theories. Natural frequencies of the functionally graded plates with various side-to-thickness ratios, boundary conditions, and volume fraction index ‘n’ have been computed. It can be concluded that the proposed model is not only accurate but also simple in predicting the vibration behavior of functionally graded plates.

A new higher order shear and normal deformation theory for functionally graded beams

2015 ◽  
Vol 18 (3) ◽  
pp. 793-809 ◽  
Author(s):  
Mustapha Meradjah ◽  
Abdelhakim Kaci ◽  
Mohammed Sid Ahmed Houari ◽  
Abdelouahed Tounsi ◽  
S.R. Mahmoud
Keyword(s):  
Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation

A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets

2013 ◽  
Vol 15 (6) ◽  
pp. 671-703 ◽  
Author(s):  
Aicha Bessaim ◽  
Mohammed SA Houari ◽  
Abdelouahed Tounsi ◽  
SR Mahmoud ◽  
El Abbes Adda Bedia
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Normal Deformation

Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

2020 ◽  
Vol 234 (9) ◽  
pp. 1183-1202
Author(s):  
Mohammad Arefi ◽  
Amir Hossein Soltan Arani
Keyword(s):  
Electric Potential ◽  
Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Governing Equations ◽  
Normal Deformation ◽  
Transverse Deflection ◽  
Stretching Effect ◽  
Applied Electric Potential

Comprehensive nonlocal piezoelasticity relations are developed in this paper for a sandwich functionally graded nanoplate subjected to applied electric potential based on higher-order shear and normal deformation theory. To account thickness stretching effect, the higher-order shear and normal deformation theory is developed. Based on this theory, the transverse deflection is decomposed into bending, shear and stretching portions in which the third term is reflected variation of transverse deflection along the thickness direction. Size dependency is accounted in governing equations based on nonlocal elasticity theory. The sandwich nanoplate is made of a functionally graded core integrated with two piezoelectric layers. Distribution of material properties are assumed according to the power-law function in the thickness direction. The Hamilton’s principle is used to derive governing equations of motion. Navier’s technique is implemented to solve partial differential equation of motion. Accuracy and efficiency of the presented technique are verified by a comparison between obtained results and existing results in literature for two cases including and excluding thickness stretching effect. The comparison between the results with and without thickness stretching effect can justify necessity of present work. Large parametric analysis is organized to investigate effect of significant parameters such as external applied voltage, nonlocal parameter, non-homogeneous index, stretching effect, length-to-thickness, length-to-width and core-to-face sheet thickness ratios on the vibrational behavior of the system. As an important result of this study, one can conclude that accounting thickness stretching effect leads to decrease of natural frequencies in comparison with cases disregards thickness stretching.

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