scholarly journals Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT

2014 ◽  
Vol 229 (5) ◽  
pp. 818-839 ◽  
Author(s):  
A Asanjarani ◽  
S Satouri ◽  
A Alizadeh ◽  
MH Kargarnovin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Conical Shell ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Graded Material ◽  
Truncated Conical Shell

Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

Bending Analysis of Piezoelectric Functionally Graded Material Plates Using HSDT

2019 ◽  
Vol 969 ◽  
pp. 116-121
Author(s):  
Ch. Naveen Reddy ◽  
M. Bhargav ◽  
T. Revanth
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Analytical Formulation ◽  
Simply Supported ◽  
Graded Material

This work investigates the complete analytical solution for functionally graded material (FGM) plates incorporated with smart material. The odjective of the present work is to determine bending characteristics of piezoelectric FGM plates with different geometrical parameters, voltages and boundary conditions for electro-mechanical loading. In this work an analytical formulation based on higher order shear deformation theory (HSDT) is presented for the piezoelectric FGM plates. The solutions are obtained in closed from using Navier’s technique for piezoelectric FGM plates a specific type of simply supported boundary conditions and pc code have been developed to find out the deflections and stresses for various parameters. All the solutions are plotted against aspect proportion, side to thickness proportion as a function of material variety parameter (n) and thickness coordinate for different voltages. The significant trends from the results are obtained.

scholarly journals Three new hybrid quasi-3D and 2D higher-order shear deformation theories for free vibration analysis of functionally graded material monolayer and sandwich plates with stretching effect

2020 ◽  
Vol 29 ◽  
pp. 096369352094186
Author(s):  
Y Belkhodja ◽  
D Ouinas ◽  
H Fekirini ◽  
JA Viña Olay ◽  
M Touahmia
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Functionally Graded Material ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Graded Material

The present investigation brings to the readers three new hybrid higher-order shear deformation theory (HSDT) models and analyses the functionally graded material (FGM) plates. The major objective of this work is to develop three HSDTs in a unique formulation by polynomial–hyperbolic–exponential and polynomial–trigonometric forms, propose the three new HSDT models, investigate the effect of thickness stretching by considering a quasi-three-dimensional theory and analyse the free vibration of isotropic and FGM monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as softcore) plates to demonstrate the models ability. Therefore, the Hamilton’s principle is exploited to develop equations of motion based on a displacement field of only five unknowns, of which three of them distinguished the transverse displacement membranes through the plate thickness (bending, shear and stretching displacements). In addition, the analytical solutions are found by applying the Navier approach for a simply supported boundary conditions type. The theory also considered that transverse shear deformation effect satisfied the stress-free boundary conditions on the plate-free surfaces without any requirement of shear correction factors. The used mechanical properties followed the power law and the Mori–Tanaka scheme distributions through the plate thickness. The determined results explained the effects of different non-dimensional parameters, and the proposed HSDTs predict the proper responses for monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as softcore) FGM plates in comparison with other different plates’ theories solutions found in the literature references, thus the reliability and accuracy of the present approach are ascertained. It is obtained that the present formulations of polynomial–hyperbolic–exponential and polynomial–trigonometric forms can be further extended to all existing HSDTs models, for numerous problems related to the shear deformable effect.

Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory

2018 ◽  
Vol 233 (6) ◽  
pp. 2056-2073 ◽  
Author(s):  
S Parida ◽  
SC Mohanty
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Material

In the present article, a higher order shear deformation theory is used to develop a finite element model for the free vibration analysis of a rotating functionally graded material plate in the thermal environment. The model is based on an eight-noded isoparametric element with seven degrees-of-freedom per node. The material properties are temperature dependent and graded along its thickness according to a simple power law distribution in terms of volume fraction of the constituents. The general displacement equation provides C0 continuity, and the transverse shear strain undergoes parabolic variation through the thickness of the plate. Therefore, the shear correction factor is not used in this theory. The obtained results are compared with the published results in the literature to determine the accuracy of the method. The effects of various parameters like hub radius, rotation speed, aspect ratio, thickness ratio, volume fraction index, and temperature on the frequency of rotating plate are investigated.

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

2020 ◽  
Vol 234 (18) ◽  
pp. 3667-3688
Author(s):  
Ismail Bensaid ◽  
Ahmed Amine Daikh ◽  
Ahmed Drai
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material

The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

scholarly journals Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Nguyen Thi Hong
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Third Order ◽  
Aspect Ratios ◽  
Graded Material ◽  
Nonlinear Static

Bidirectional functionally graded material (2D-FGM) plates have mechanical properties that vary continuously in both the thickness and one-edge directions; these plates are more and more widely used in design and engineering applications. When these structures are subjected to strong loads, they can be largely deformed; therefore, nonlinear calculations, in this case, are necessary. In this paper, nonlinear static bending and nonlinear free vibration behaviors of 2D-FGM plates are studied by using the finite element method based on the third-order shear deformation theory; the Newton-Raphson method is used to solve this problem. The accuracy of this approach is confirmed by comparing the results with respect to other papers. The effects of some numerical aspect ratios such as volume fraction index and thickness-to-length ratio on nonlinear static bending and free vibration of the plates are explored. This study shows that there is a big difference between the numerical results obtained from the nonlinear problem and those from the linear one.

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