scholarly journals Buckling Analysis of Functionally Graded Sandwich Plates under Both Mechanical and Thermal Loads

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7194
Author(s):  
Dongdong Li ◽  
He Zhu ◽  
Xiaojing Gong
Keyword(s):  
Mechanical Load ◽  
Plate Theory ◽  
Single Layer ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Sandwich Plates ◽  
Thermal Loads ◽  
Linear Temperature ◽  
Simply Supported ◽  
Temperature Increment

This paper presents an analytical solution for the thermomechanical buckling of functionally graded material (FGM) sandwich plates. The solution is obtained using a four-variable equivalent-single-layer (ESL) plate theory. Two types of sandwich plates are included: one with FGM facesheets and homogeneous core, and vice versa for the other. The governing equations are derived based on the principle of minimum total potential energy. For simply supported boundary conditions, these equations are solved via the Navier method. The results on critical buckling load and temperature increment of simply supported FGM sandwich plates are compared with the available solutions in the literature. Several results are presented considering various material and geometrical parameters as well as their effect on the thermomechanical buckling response of FGM sandwich plates. The relationship between the mechanical load and the temperature increment for uniform/linear temperature rise of FGM sandwich plates under combined mechanical and thermal loads is studied.

THE EFFECT OF TRANSVERSE SHEAR AND NORMAL DEFORMATIONS ON THE THERMOMECHANICAL BENDING OF FUNCTIONALLY GRADED SANDWICH PLATES

2009 ◽  
Vol 01 (04) ◽  
pp. 667-707 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Shear Deformation ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Power Law Distribution ◽  
Equilibrium Equations

A thermomechanical bending analysis for a simply supported, rectangular, functionally graded material sandwich plate subjected to a transverse mechanical load and a through-the-thickness thermal load is presented using the refined sinusoidal shear deformation plate theory. The present shear deformation theory includes the effect of both shear and normal deformations and it is simplified by enforcing traction-free boundary conditions at the plate faces. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The equilibrium equations of different sandwich plates are given based on various plate theories. A number of examples are solved to illustrate the numerical results concern thermo-mechanical bending response of functionally graded rectangular sandwich plates. The influences played by transversal shear and normal deformations, plate aspect ratio, side-to-thickness ratio, volume fraction distributions, and thermal and mechanical loads are investigated.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates

2016 ◽  
Vol 32 (5) ◽  
pp. 539-554 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
A. Shahabodini
Keyword(s):  
Size Effect ◽  
Nonlinear Equations ◽  
Forced Vibration ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Continuation Method ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Governing Equations ◽  
First Order

AbstractIn this paper, a non-classical plate model capturing the size effect is developed to study the forced vibration of functionally graded (FG) microplates subjected to a harmonic excitation transverse force. To this, the modified couple stress theory (MCST) is incorporated into the first-order shear deformation plate theory (FSDPT) to account for the size effect through one length scale parameter, only. Strong form of nonlinear governing equations and associated boundary conditions are obtained using Hamilton's principle. The solution process is implemented on two domains. The generalized differential quadrature (GDQ) method is first employed to discretize the governing equations on the space domain. A Galerkin-based scheme is then applied to extract a reduced set of the nonlinear equations of Duffing-type. On the second domain, through a time differentiation matrix operator, the set of ordinary differential equations are transformed into the discrete form on time domain. Eventually, a system of the parameterized nonlinear equations is acquired and solved via the pseudo-arc length continuation method. The frequency response curve of the microplate is sketched and the effects of various material and geometrical parameters on it are evaluated.

On the High-Temperature Free Vibration Analysis of Elastically Supported Functionally Graded Material Plates Under Mechanical In-PlaneForce Via GDQR

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Roshan Lal ◽  
Rahul Saini
Keyword(s):  
Mechanical Properties ◽  
Plate Theory ◽  
Elastic Equilibrium ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Axisymmetric Vibration ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature

In this article, the effect of Pasternak foundation on free axisymmetric vibration of functionally graded circular plates subjected to mechanical in-plane force and a nonlinear temperature distribution (NTD) along the thickness direction has been investigated on the basis of classical plate theory. The plate material is graded in thickness direction according to a power-law distribution and its mechanical properties are assumed to be temperature-dependent (TD). At first, the equation for thermo-elastic equilibrium and then equation of motion for such a plate model have been derived by Hamilton's principle. Employing generalized differential quadrature rule (GDQR), the numerical values of thermal displacements and frequencies for clamped and simply supported plates vibrating in the first three modes have been computed. Values of in-plane force parameter for which the plate ceases to vibrate have been reported as critical buckling loads. The effect of temperature difference, material graded index, in-plane force, and foundation parameters on the frequencies has been analyzed. The benchmark results for uniform and linear temperature distributions (LTDs) have been computed. A study for plates made with the material having temperature-independent (TI) mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

2011 ◽  
Vol 32 (7) ◽  
pp. 925-942 ◽  
Author(s):  
L. Hadji ◽  
H. A. Atmane ◽  
A. Tounsi ◽  
I. Mechab ◽  
E. A. Adda Bedia
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Plate Theory
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