BUCKLING OF CIRCULAR SANDWICH PLATES OF VARIABLE CORE THICKNESS AND FGM FACE SHEETS

2011 ◽  
Vol 11 (02) ◽  
pp. 273-295 ◽  
Author(s):  
S. K. JALALI ◽  
M. H. NAEI ◽  
A. POORSOLHJOUY
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Sheet Thickness ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Sandwich Plates ◽  
Radial Compression ◽  
Core Thickness ◽  
Circular Sandwich Plates

Presented herein is the buckling response of circular sandwich plates with a homogenous core of variable thickness and constant thickness functionally graded material (FGM) face sheets whose material properties are assumed to be graded in the thickness direction according to a simple power law. The plate is modeled using the first order shear deformation plate theory and subjected to a uniform radial compression. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, by employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved numerically to evaluate the critical buckling load. Numerical solutions are presented for both clamped and simply supported plates and for linear and parabolic core thickness distributions. The results show that the buckling behavior is significantly influenced by the thickness variation profile, the aspect ratio, the volume fraction index, and the core-to-face sheet thickness ratio. Comparison studies demonstrate that the results obtained using the current method compare very well with those available in the literature.

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.

Experimental and numerical investigation on the anti-penetration performance of metallic sandwich plates for marine applications

2019 ◽  
Vol 22 (2) ◽  
pp. 494-522 ◽  
Author(s):  
Na Zhao ◽  
Renchuan Ye ◽  
Ali Tian ◽  
Jie Cui ◽  
Peng Ren ◽  
...  
Keyword(s):  
Aluminum Foam ◽  
Failure Modes ◽  
Sheet Thickness ◽  
Face Sheet ◽  
Sandwich Plates ◽  
Ballistic Limit ◽  
Ballistic Performance ◽  
Core Thickness ◽  
Protective Structures ◽  
Constitutive Parameters

To predict the anti-penetration performance of protective structures, the ballistic performance of sandwich plates with steel face-sheet and aluminum foam core, the quasi-static compressive experiments of four different aluminum foam are performed and analyzed. The failure mechanism, mechanical parameters, and modified constitutive model are obtained. The virtual tests using numerical simulation were carried out in different penetration velocities based on quasi-static experimental constitutive parameters. Influence of projectile shape, face-sheet thickness, core thickness, and core densities on the residual velocity and plastic deformation of sandwich plates are discussed, while typical penetration failure modes and deformation mechanism are presented and analyzed. The failure modes of sandwich plates are different for hemisphere- and blunted-nosed projectile and the projectile shape influence is significant for ballistic performance when the penetration velocity approaches ballistic limit. The ballistic limit increases with increase of face-sheet or core thickness, core density and which shows an approximate linear relationship.

Free Vibration and Buckling Analysis of Sandwich Beams with Functionally Graded Carbon Nanotube-Reinforced Composite Face Sheets

2015 ◽  
Vol 15 (07) ◽  
pp. 1540011 ◽  
Author(s):  
Helong Wu ◽  
Sritawat Kitipornchai ◽  
Jie Yang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Micromechanical Model ◽  
Sandwich Beam ◽  
Sheet Thickness ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Reinforced Composite

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.

Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation

2017 ◽  
Vol 24 (11) ◽  
pp. 2327-2343 ◽  
Author(s):  
Rasool Moradi-Dastjerdi ◽  
Hamed Momeni-Khabisi
Keyword(s):  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Free And Forced Vibrations ◽  
Mesh Free ◽  
Pasternak Elastic Foundation

In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

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.

Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates

2017 ◽  
Vol 21 (3) ◽  
pp. 895-916 ◽  
Author(s):  
Sid Ahmed Belalia
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Material ◽  
Large Amplitude ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Nonlinear Frequency ◽  
Graded Material

In this paper, the geometrically nonlinear formulation based on von Karman’s assumptions is employed to study the large amplitude free vibrations of functionally graded materials sandwich plates. The functionally graded material sandwich plate is made up of two layers of power-law functionally graded material face sheet and one layer of ceramic homogeneous core. A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange’s equations. Employing the harmonic balance method, the equations of motion are converted from time domain to frequency domain and then solved iteratively using the linearized updated mode method. Results for linear and nonlinear frequency parameters of the simply supported functionally graded material sandwich plates are computed and compared with the published values, and an excellent agreement was found. The influence of the mechanical properties of the functionally graded material, thickness ratio of FGM layers, and volume fraction exponent on the backbone curves and on the nonlinear frequency parameters are investigated. The effects of the material properties of two different types of ceramics on the large amplitude vibration behaviors of the functionally graded material sandwich plates is also presented and discussed for the first time.

MECHANICAL VIBRATION AND BUCKLING ANALYSIS OF FGM PLATES AND SHELLS USING A FOUR-NODE QUASI-CONFORMING SHELL ELEMENT

2008 ◽  
Vol 08 (02) ◽  
pp. 203-229 ◽  
Author(s):  
SUNG-CHEON HAN ◽  
GILSON RESCOBER LOMBOY ◽  
KI-DU KIM
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Mechanical Vibration ◽  
Shear Deformation Theory ◽  
Homogeneous Element ◽  
Shell Element ◽  
Functionally Graded ◽  
Sigmoid Function ◽  
Rectangular Plates ◽  
Plates And Shells

In this paper, we investigate the natural frequencies and buckling loads of functionally graded material (FGM) plates and shells, using a quasi-conforming shell element that accounts for the transverse shear strains and rotary inertia. The eigenvalues of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but the Poisson ratios of the FGM plates and shells are assumed to be constant. The expressions for the membrane, bending and shear stiffness of FGM shell elements are more a complicated combination of material properties than a homogeneous element. In order to validate the finite element numerical solutions, the Navier solutions for rectangular plates based on the first order shear deformation theory are also presented. The present numerical solutions for composite and sigmoid FGM (S-FGM) plates and shells are verified by the Navier solutions and various examples of composite and FGM structures. The present results are in good agreement with the Navier theoretical solutions.

Effect of porosity and skew edges on transient response of functionally graded sandwich plates

2021 ◽  
pp. 030932472110626
Author(s):  
Abhilash Karakoti ◽  
Mahesh Podishetty ◽  
Shashank Pandey ◽  
Vishesh Ranjan Kar
Keyword(s):  
Finite Element ◽  
Transient Response ◽  
Volume Fraction ◽  
Pure Metal ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Skew Angle ◽  
Wide Range

This work for the first time presents the effect of porosity and skew edges on the transient response of functionally graded material (FGM) sandwich plates using a layerwise finite element formulation. Two configurations of FGM sandwich plates are considered. In the first configuration, the top and the bottom layers are made of the FGM and the core is made of pure metal, whereas in the second configuration, the bottom, core and the top layers are made of pure metal, FGM and pure ceramic, respectively. Four micromechanics models based on the rule of mixture are used to model porosity for these two configurations of FGM sandwich plates. A layerwise theory based on a first-order shear deformation theory for each layer that maintains the displacement continuity at the layer interface is used for the present investigation. An eight-noded isoparametric element with nine degrees of freedom per node is used to develop the finite element model (FEM). The governing equations for the present investigation are derived using Hamilton’s principle. A wide range of comparison studies are presented to establish the accuracy of the present FEM formulation. It has been shown here that the parameters like skew angle, porosity coefficient, volume fraction index, core to facesheet thickness ratio and boundary conditions have a significant effect on the transient response of FGM sandwich plates. Also, the present finite element formulation is simple and accurate.

Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators

2011 ◽  
Vol 22 (18) ◽  
pp. 2093-2102 ◽  
Author(s):  
Yiming Fu ◽  
Jianzhe Wang ◽  
Yiqi Mao
Keyword(s):  
Active Control ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Sensors And Actuators ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Layers

Employing higher order shear deformation theory, geometric nonlinear theory, and Hamilton’s principle, a set of nonlinear governing equations for the functionally graded beams with surface-bonded piezoelectric layers is derived. Then, the negative velocity feedback algorithm coupling the direct and inverse piezoelectric effect is used to control the piezoelectric functionally graded beams actively. Using the finite difference method and Newmark method synthetically, the numerical solutions for the nonlinear dynamic equations of functionally graded beams with piezoelectric patches are obtained iteratively. In the numerical examples, the effects of the volume fraction exponent on the nonlinear dynamic responses and amplitude–frequency curves are investigated, and the active control responses of the functionally graded beams with piezoelectric layers under different control gains and volume fraction exponents are analyzed. Some meaningful solutions have been presented.

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