Thermal stability of functionally graded sandwich plates using a simple shear deformation theory

A refined and simple shear deformation theory for thermal buckling of solar functionally graded plate (SFGP) resting on two-parameter Pasternak's foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. It is assumed that the material properties of the plate vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the present plate theory based on exact neutral surface position is employed to derive the governing stability equations. The nonlinear strain-displacement relations are also taken into consideration. The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. The effects of the foundation parameters, plate dimensions, and power law index are presented comprehensively for the thermal buckling of solar functionally graded plates.

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Vibro-Acoustic Formulation of Elastically Restrained Shear Deformable Orthotropic Plates Using a Simple Shear Deformation Theory

Journal of Modern Mechanical Engineering and Technology ◽

10.15377/2409-9848.2014.01.02.2 ◽

2014 ◽

Vol 1 (2) ◽

pp. 49-57 ◽

Cited By ~ 2

Author(s):

T.Y. Kam ◽

◽

A. Nayan

Keyword(s):

Shear Deformation ◽

Simple Shear ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Orthotropic Plates ◽

Simple Shear Deformation ◽

Elastically Restrained ◽

Shear Deformable

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A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

Journal of Sandwich Structures & Materials ◽

10.1177/1099636217727577 ◽

2017 ◽

Vol 21 (6) ◽

pp. 1906-1929 ◽

Cited By ~ 49

Author(s):

Abdelkader Mahmoudi ◽

Samir Benyoucef ◽

Abdelouahed Tounsi ◽

Abdelkader Benachour ◽

El Abbas Adda Bedia ◽

...

Keyword(s):

Boundary Conditions ◽

Shear Deformation ◽

Elastic Foundation ◽

Deformation Theory ◽

Three Dimensional ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Sandwich Plates ◽

Refined Theory ◽

Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

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On the buckling of advanced composite sandwich rectangular plates

Journal of Sandwich Structures & Materials ◽

10.1177/1099636220925084 ◽

2020 ◽

pp. 109963622092508 ◽

Cited By ~ 2

Author(s):

Atteshamuddin S Sayyad ◽

Yuwaraj M Ghugal

Keyword(s):

Shear Deformation ◽

Power Law ◽

Analytical Solutions ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Skin Thickness ◽

Sandwich Plates ◽

Rectangular Plates ◽

Aspect Ratios

In this paper, higher order closed-formed analytical solutions for the buckling analysis of functionally graded sandwich rectangular plates are obtained using a unified shear deformation theory. Three-layered sandwich plates with functionally graded skins on top and bottom; and isotropic core in the middle are considered for the study. The material properties of skins are varied through the thickness according to the power-law distribution. Two types of sandwich plates (hardcore and softcore) are considered for the detail numerical study. A unified shear deformation theory developed in the present study uses polynomial and non-polynomial-type shape functions in terms of thickness coordinate to account for the effect of shear deformation. In the present theory, the in-plane displacements consider the combined effect of bending rotation and shear rotation. The parabolic shear deformation theory of Reddy and the first-order shear deformation theory of Mindlin are the particular cases of the present unified formulation. The governing differential equations are evaluated from the principle of virtual work. Closed-formed analytical solutions are obtained by using the Navier’s technique. The non-dimensional critical buckling load factors are obtained for various power-law coefficients, aspect ratios and skin-core-skin thickness ratios.

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Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory

Materials Research Express ◽

10.1088/2053-1591/ab48a9 ◽

2019 ◽

Vol 6 (11) ◽

pp. 115707 ◽

Cited By ~ 8

Author(s):

Ahmed Amine Daikh ◽

Ashraf M Zenkour

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Power Law ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Higher Order ◽

Functionally Graded ◽

Sandwich Plates

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Computational Development of a 4-Unknowns Trigonometric Quasi-3D Shear Deformation Theory to Study Advanced Sandwich Plates and Shells

International Journal of Applied Mechanics ◽

10.1142/s1758825116500496 ◽

2016 ◽

Vol 08 (04) ◽

pp. 1650049 ◽

Cited By ~ 6

Author(s):

J. L. Mantari

Keyword(s):

Boundary Conditions ◽

Shear Deformation ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Sandwich Plates ◽

Sandwich Plates And Shells ◽

Plates And Shells ◽

First Time ◽

Stretching Effect

In this paper, a simple and accurate sinusoidal trigonometric theory (STT) for the bending analysis of functionally graded single-layer and sandwich plates and shells is presented for the first time. The principal feature of this theory is that models the thickness stretching effect with only 4-unknowns, even less than the first order shear deformation theory (FSDT) which as it is well-known has 5-unknowns. The governing equations and boundary conditions are derived by employing the principle of virtual work. Then, a Navier-type closed-form solution is obtained for functionally graded plates and shells subjected to bi-sinusoidal load for simply supported boundary conditions. Consequently, numerical results of the present STT are compared with other refined theories, FSDT, and 3D solutions. Finally, it can be concluded that: (a) An accurate but simple 4-unknown STT with thickness stretching effect is developed for the first time. (b) Optimization procedure (described in the paper) appear to be of paramount importance for 4-unknown higher order shear deformation theories (HSDTs) of this gender, so deserves a lot of further research. (c) Transverse shear stresses results are sensitive to the theory and need carefully attention.

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