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.

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

2013 ◽  
Vol 5 (1) ◽  
pp. 90-112 ◽  
Author(s):  
S. Jafari Mehrabadi ◽  
B. Sobhaniaragh ◽  
V. Pourdonya
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Effective Material Properties

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

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.

scholarly journals Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

2019 ◽  
Vol 69 (4) ◽  
pp. 9-24 ◽  
Author(s):  
Chikh Abdelbaki
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Power Law ◽  
Material Properties ◽  
Scale Effects ◽  
Plate Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Simply Supported ◽  
Shear Deformation Plate Theory

AbstractThis paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature.

Axisymmetric Solutions of Functionally Graded Circular and Annular Plates Using Second-Order Shear Deformation Plate Theory

2006 ◽  
Author(s):  
Ali Reza Saidi ◽  
Shahab Sahraee
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Second Order ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Classical Plate Theory ◽  
Maximum Displacement ◽  
Shear Deformation Plate Theory ◽  
Axisymmetric Bending

In this paper, axisymmetric bending and stretching of functionally graded solid circular and annular plate is studied based on the second-order shear deformation plate theory (SST). The solutions for deflections, force and moment resultants of the second-order theory are presented in terms of the corresponding quantities of the isotropic plates based on the classical plate theory from which one can easily obtain the SST solutions for axisymmetric bending of functionally graded circular plates. It is assumed that the mechanical properties of the functionally graded plates vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. Numerical results for maximum displacement are presented for various percentages of ceramic-metal volume-fractions and have been compared with those obtained from first-order shear deformation plate theory (FST).

Elastic Analysis of Carbon Nanotube-Reinforced Composite Plates with Piezoelectric Layers Using Shear Deformation Theory

2017 ◽  
Vol 09 (01) ◽  
pp. 1750011 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Tahereh Taghizadeh ◽  
Saeed Jafari Mehrabadi ◽  
Saeed Herasati
Keyword(s):  
Carbon Nanotube ◽  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Composite Plates ◽  
Third Order ◽  
Reinforced Composite ◽  
Shear Deformation Plate Theory ◽  
Piezoelectric Layers

This paper investigates the deflection and stress behavior of composite plates reinforced by single-walled carbon nanotubes (SWCNTs) with piezoelectric layers which are under transverse mechanical load. Two kinds of carbon nanotube-reinforced composite (CNTRC) plates, namely uniformly distributed (UD) and functionally graded (FG) along the plate thickness, are considered. The extended rule of mixture approach is used to estimate the effective material properties. The governing equations are derived using the Hamilton approach based on the first-order shear deformation plate theory (FSDT) and third-order shear deformation plate theory (TSDT). In addition, the Navier technique is employed to obtain the deflection and stress response of the nanocomposite plates. The results of present work are also compared with those available in the literature and show good agreement. The effects of applied force, volume fraction of CNT, distribution of CNT, thickness of piezoelectric layer, thickness to width ratio and aspect ratio on the static behavior are studied. In previous studies, deflection and stress analysis of nanocomposite plate with piezoelectric layers based on third-order shear deformation plate theory has not investigated.

Thermomechanical postbuckling analysis of eccentrically stiffened FGM sandwich plates with general Sigmoid and power laws based on TSDT

2016 ◽  
Vol 20 (8) ◽  
pp. 907-945 ◽  
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Power Laws ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Temperature Dependent ◽  
Third Order ◽  
Shear Deformation Plate Theory

The buckling and postbuckling behaviors of eccentrically stiffened sandwich plates on elastic foundations subjected to in-plane compressive loads, thermal loads, or thermomechanical loads are presented analytically by using the Reddy’s third-order shear deformation plate theory with von Karman geometrical nonlinearity. Four cases of general Sigmoid and power laws are considered. The material properties of the facesheets, the core layer, and stiffeners are assumed to be temperature-dependent. Theoretical formulations based on the smeared stiffeners technique and third-order shear deformation plate theory are derived. The expressions of thermal parameters are found in the analytical form. Applying the Galerkin method, the expressions for determination of the critical buckling load and analysis of the postbuckling mechanical and thermal load–deflection curves are obtained. The iterative algorithm is presented for the case of temperature-dependent plate material properties. In addition, the influences of thermal element, functionally graded material stiffeners, the facesheet thickness to total thickness ratio, initial imperfection, and foundations are clarified in detail.

BENDING BEHAVIOR OF SIMPLY SUPPOTED METALLIC SANDWICH PLATES WITH DIMPLED CORES

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6179-6184 ◽  
Author(s):  
DAE-YONG SEONG ◽  
CHANG GYUN JUNG ◽  
DONG-YOL YANG ◽  
DONG GYU AHN
Keyword(s):  
High Precision ◽  
Sandwich Plate ◽  
Sheet Thickness ◽  
Radius Of Curvature ◽  
Sandwich Plates ◽  
Collapse Load ◽  
Forming Process ◽  
Simply Supported ◽  
Bending Behavior ◽  
Sandwich Core

Metallic sandwich plates are lightweight structural materials with load-bearing and multi-functional characteristics. Previous analytic studies have shown that the bendability of these plates increases as the thickness decreases. Due to difficulty in the manufacture of thin sandwich plates, dimpled cores (structures called egg-box cores) are employed as a sandwich core. High-precision dimpled cores are easily fabricated in a sectional forming process. The cores are then bonded with skin sheets by multi-point resistance welding. The bending characteristics of simply supported plates were observed by the defining measure, including the radius ratio of the small dimple, the thickness of a sandwich plate, and the pattern angle (0°/90°, 45°). Experimental results revealed that sandwich plates with a thickness of 2.2 mm and a pattern angle of 0°/90° showed good bendability as the punch stroke under a collapse load was longer than other cases. In addition, the gap between attachment points was found to be an important parameter for the improvement of the bendability. Finally, sandwich plates with dimpled cores were bent with a radius of curvature of 330 mm for the sheet thickness of 2.2 mm using an incremental bending apparatus.

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