Functionally Graded Sandwich Plates Research Articles

Multi-Directional Functionally Graded Sandwich Plates: Buckling and Free Vibration Analysis with Refined Plate Models under Various Boundary Conditions

This study conducts buckling and free vibration analyses of multi-directional functionally graded sandwich plates subjected to various boundary conditions. Two scenarios are considered: a functionally graded (FG) skin with a homogeneous hard core, and an FG skin with a homogeneous soft core. Utilizing refined plate models, which incorporate a parabolic distribution of transverse shear stresses while ensuring zero shear stresses on both the upper and lower surfaces, equations of motion are derived using Hamilton’s principle. Analytical solutions for the buckling and free vibration analyses of multi-directional FG sandwich plates under diverse boundary conditions are developed and presented. The obtained results are validated against the existing literature for both the buckling and free vibration analyses. The composition of metal–ceramic-based FG materials varies longitudinally and transversely, following a power law. Various types of sandwich plates are considered, accounting for plate symmetry and layer thicknesses. This investigation explores the influence of several parameters on buckling and free vibration behaviors.

Thermo-mechanical vibration and buckling analysis of porous FG sandwich plates with geometric discontinuity based on physical neutral surface

The effect of thermo-mechanical load coupling and porosity distributions on vibration and buckling characteristics of Functionally Graded Sandwich Plates (FGSPs) with cutouts is investigated by Finite Element (FE) formulation. Two sandwich configurations are considered and physical neutral surface is incorporated due to material asymmetry. Novel dynamic approach is proposed to evaluate buckling loads. Results obtained are compared with experimental, numerical solutions in literature and revealed that the FGSP buckling capacity under thermomechanical loads improves on using ceramic with lower thermal expansion coefficient. Also, at higher temperature rises, buckling capacity increases due to increasing porosity content, whereas capacity reduces at lower temperature rises.

Magnetic Control of Vibrational Behavior of Smart FG Sandwich Plates with Honeycomb Core via a Quasi‐3D Plate Theory

Herein, vibrational behavior of functionally graded (FG) smart piezoelectric sandwich plates with honeycomb core resting on viscoelastic foundation under the effect of 2D magnetic field is presented. By varying the magnetic‐field magnitude and its direction, the vibrations can be controlled. The plate is composed of two FG piezoelectric layers bonded with honeycomb structure as a mid‐layer. Magnetic Lorentz force will be deduced via Maxwell's relations. A new quasi‐3D plate theory considering the shear and normal deformations is incorporated to evaluate the displacements. The governing equations of motion are introduced via Hamilton's principle. Galerkin technique is considered to solve the motion equations for different boundary conditions. Influences of the magnetic field, boundary conditions, electric voltage, and core thickness on the eigenfrequency of the FG sandwich piezoelectric plate are illustrated. It is found that considering the effect of the magnetic field on the smart devices increases their vibrations, which may lead to an increment in the energy harvested from them. Further, when the magnetic field is applied along the length of the rectangular plate, the vibrations are reduced and vice versa.

Influence of porosity and nonuniform in-plane edge loads on vibration and buckling response of power law and sigmoid function based FG sandwich plates with geometrical discontinuities

Porosity defects can emerge during the manufacturing process of Functionally Graded Sandwich Plates (FGSPs). In practice, FGSPs have geometric discontinuities/cutouts and are exposed to Nonuniform In-plane Edge Loads (NIELs). The presence of porosity, cutout and NIELs causes a significant reduction in the stiffness of the plate affecting its vibration and buckling behavior. Therefore, in this paper vibration and buckling results obtained using the Finite Element (FE) method hitherto not reported in the literature are presented for porous FGSPs with cutouts and subjected to NIELs. Four types of porosity distribution models are explored, and the porosity imperfections are modeled as the criteria of stiffness reduction. Porosity-dependent material properties of FGSPs are evaluated using modified power law and sigmoid function. The current study incorporates two distinct kinds of sandwich configuration in such a way that there is no material mismatch along the thickness direction. The application of different cases of NIELs on the plate with cutouts leads to the development of nonuniform stresses. Hence a novel dynamic approach has been proposed to evaluate buckling loads by implementing two sets of boundary conditions. The first set of boundary conditions calculates pre-buckling stress, while second set calculates critical buckling loads. The generated results from the current FE formulation are compared with existing results in the literature to ensure accuracy. Finally, the effect of porosity distribution, NIELs, cutout ratio and its positions, support conditions, volume fraction exponents and geometric parameters on the vibration and buckling response are studied and discussed to arrive at appropriate conclusion.

Free Vibration Analysis of Functionally Graded Sandwich Plates with a Homogeneous Core

The functionally graded (FG) sandwich plate has attained much attention in recent years due to its potential for exhibiting the merits of sandwich construction and FGM. Accordingly, intensive studies have focused on FG sandwich plates to investigate their mechanical behaviors. However, these mechanical behaviors are still in need of further investigation, particularly with respect to the major parameters. In this context, this paper intends to parametrically investigate the free-vibration behavior of the FG sandwich plate with a homogeneous core by developing a reliable and effective numerical method. This numerical method was based on hierarchical models, developed from the spectral model accuracy, and the 2-D natural element method (NEM). The hierarchical models were derived from the 3-D elasticity and the NEM was characterized by high smooth interpolation functions. From the verification experiments, the proposed method shows a good agreement with the reference and a uniform convergence to the 3-D elasticity. The free vibration characteristics of FG sandwich plates with a homogeneous core were investigated using the proposed numerical method. It was found that the calibrated fundamental frequency was significantly influenced by the type of material composing the core, the volume fraction index, the relative thickness and position of core layer, and the plate aspect ratio.

New finite modelling of the nonlinear static bending analysis of piezoelectric FG sandwich plates resting on nonlinear elastic foundations

This paper presents a new finite modelling of the nonlinear static bending analysis of piezoelectric functionally graded (FG) sandwich plates resting on nonlinear elastic foundations. Finite element formulations are derived by using the first-order shear deformation theory (FSDT) of Mindlin and the finite element method. The proposed theory and mathematical model of this work are verified by comparing the results with those of other methods, and they are in good agreement. A parameter study is conducted to investigate the effects of geometrical and physical properties such as nonlinear factors, volume fraction index, nonlinear foundation parameters, applied voltages, boundary conditions, etc., on the nonlinear mechanical behaviors of piezoelectric FG sandwich plates. The novel numerical results of this work are very important, and can be used as a good reference to examine related structures as well as of use in engineering practice.

Buckling analysis of functionally graded sandwich plates resting on Pasternak foundation using a novel refined quasi-3D third-order shear deformation theory

This study presents a numerical model for buckling analysis of the functionally graded sandwich plates (FGSP) laid on the elastic foundation through the Moving Kriging interpolation-based meshless method using a refined quasi-3D third-order shear deformation theory. The in-plane displacements encompassed a new third-order polynomial in terms of the thickness coordinate, will satisfy the natural vanishing of transverse shear stresses on the top and bottom surfaces. Furthermore, the displacement fields approximated by only four variables with accounting for the thickness stretching effect can lead to the reduction of computational time. Comparison investigations are studied to justify the accuracy of the present method. The influence of the aspect ratios, gradient index, and elastic foundation parameters on the normalized buckling load of FGSP is also studied and discussed.

Free vibration and sound insulation of functionally graded honeycomb sandwich plates

Based on the hyperbolic tangent shear deformation theory, free vibration and sound insulation of two different types of functionally graded (FG) honeycomb sandwich plates with negative Poisson’s ratio are studied in this paper. Using Hamilton’s principle, the vibration and vibro-acoustic coupling dynamic equations for FG honeycomb sandwich plates with simply supported edges are established. By applying the Navier’s method and fluid–solid interface conditions, the derived governing dynamic equations are solved. The natural frequencies and the sound insulation of FG honeycomb sandwich plates obtained in this work are compared with the numerical results by the finite element simulation. It is proven that the theoretical models for the free vibration and the sound insulation are accurate and efficient. Moreover, FG sandwich plates with different honeycomb cores are investigated and compared. The corresponding results show that the FG honeycomb core with negative Poisson’s ratio can yield much lower frequencies. Then, the influences of various geometrical and material parameters on the vibration and sound insulation performance are systematically analyzed.

Bending analysis of functionally graded sandwich plates using the refined finite strip method

In this study, static analysis of functionally graded (FG) sandwich plates is performed using the finite strip method based on the refined plate theory (RPT). Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. Differential equations of FG sandwich plates are obtained using Hamilton's principle and stiffness and force matrices are formed using the finite strip method. The central deflection and the normal stress values are obtained for a sinusoidal loaded FG sandwich plate and the accuracy of the results are verified against those obtained from other theories such as the classical plate theory (CPT), the first-order shear deformation theory (FSDT), and the higher order shear deformation theory (HSDT). For the first time, this study presents a finite strip formulation in conjunction with the RPT to analyze FG Sandwich plates. While the proposed method is fast and simple, it is capable of modeling a variety of boundary conditions.

Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment

Wave propagation analysis of porous functionally graded (FG) sandwich plate in a hygro-thermal environment is presented in this paper. The sandwich plates’ composing materials change through three layers that are either homogeneous ceramic, homogeneous metal, or power-law-based functionally graded ceramic–metal. Six different porosity models are considered in the analysis to express the porosities’ distribution factor and uniformity. The study is conducted using a simple four-unknown integral higher-order shear deformation theory (HSDT). The effect of moisture and temperature on wave propagation in porous FG sandwich plates is investigated by considering their role on the materials’ expansion. The governing equations are derived for the wave propagation problem based on the presented theory via Hamilton’s principle. A generalized solution for wave propagation is applied to formulate the stiffness and mass matrix that describes the dispersion relations. The numerical results are obtained by solving an eigenvalue problem. The effects of core-to-thickness ratio, FGM power index, porosity volume fraction, temperature, and moisture change are illustrated and discussed. The presented results can be utilized as a benchmark for further studies on wave propagation in FGM plates.

Free Vibration Analysis of FG Porous Sandwich Plates under Various Boundary Conditions

In the present work, free vibration analysis of the square sandwich plate with functionally graded (FG) porous face sheets and isotropic homogenous core is performed under various boundary conditions. For this purpose, the material properties of the sandwich plate are supposed to vary continuously through the thickness direction according to the volume fraction of constituents defined with the modified rule of the mixture including porosity volume fraction with four different types of porosity distribution over the cross-section. Furthermore, a hyperbolic shear displacement theory is used in the kinematic relation of the FG porous sandwich plate, and the equations of motion are derived utilizing Hamilton’s principle. Analytical solutions are achieved for free vibration analysis of square sandwich plates with FG porous face sheets under various boundary conditions, i.e. combinations of clamped (C), simply supported (SS), and free (F) edges are presented. Several parametrical studies are conducted to examine the effects of porosity volume fraction, type of porosity distribution model, lay-up scheme, side to thickness ratio, and boundary conditions on the free vibration of the FG sandwich plates. Finally, it is concluded that the investigated parameters have significant effects on the free vibration of the FG sandwich plates and the negative effects of porosity may be reduced by adopting suitable values for said parameters, considerably.

Thermomechanical Bending Analysis of FG Sandwich Plates Using a Quasi-Three-Dimensional Theory

In the present article, a displacement-based polynomial-type quasi-three-dimensional plate theory is developed and applied to predict the accurate thermomechanical bending behavior of sandwich plates with functionally graded (FG) skins and a homogenous isotropic core. The theory considers the effects of transverse shear and normal stresses. The x-directional and y-directional displacements consist of extension, bending, and shear components expanded up to fifth-order polynomials in terms of the thickness coordinates. The z-directional displacement consists of a transverse normal effect up to a fourth-order polynomial in terms of the thickness coordinate. The governing equations are extracted using the principle of virtual work, and thermomechanical bending solution for simply supported plates is obtained using Navier’s solution technique. The present results are compared with the previously published results and are found to be in good agreement with them.

Experimental study on structure optimization of functionally graded sandwich plates under ballistic impact

In this study, the ballistic performance of Al6061-SiC functionally graded sandwich plate (FGSP) with varying number of layers and volume fractions was examined experimentally. For this purpose, the two outmost layers of the FGSP were designed to be aluminum and the volume fraction of remaining constituents was gradually changing in intermediate layers through the plate thickness. The specimen plates were manufactured via powder stacking-hot pressing method. Ballistic tests of specimens were conducted with a single-stage gas gun, shooting 0.3 caliber fragment simulated projectiles onto specimens. After the ballistic tests, deformation and damage mechanisms in the front and rear surfaces were examined and ballistic performance evaluation was carried out in terms of depth of penetration of the projectile measurements. Results showed that the composition of the projectile impact surface, which was beneath the top aluminum layer, had a considerable effect on ballistic resistance capability. A volume fraction of ceramic constituent greater than 60% in the projectile impact surface reduced the ballistic performance of the specimen. Likewise, a decreasing volume fraction of ceramic constituent of projectile impact surface below 60% increased projectile penetration. Furthermore, increasing the number of layers within the functionally graded region did not have a significant effect on the ballistic resistance of the FGSPs.

Free vibration and damping analysis of porous functionally graded sandwich plates with a viscoelastic core

Free vibration and damping analysis of porous functionally graded (FG) sandwich plates are presented based on a modified Fourier-Ritz method. The sandwich plate is composed of a viscoelastic core and two porous FG face layers. A complex elasticity modulus is employed to describe the viscoelastic core. Material properties of the porous FG face layer are described continuously across each face thickness according to a volume fraction index and a porosity coefficient. The distribution of porosities within the face layers is formulated either evenly or unevenly. The displacements are constructed by the first-order shear deformation theory combined with the modified Fourier method. The free vibration and damping analysis of a porous single-layered plate and a non-porous sandwich plate are then conducted to exhibit the capability and accuracy of the developed method. The obtained results are in good agreement with those in literature. Finally, a series of parametric analyses are investigated in detail, in which boundary condition, power-law index, porosity coefficient, geometricdimension and material loss factor are taken into consideration. It is noted that the porosities within the FG face layers have significant effects on the natural vibrationand damping performance of porous FG sandwich plates.

Free vibration of FG sandwich plates partially supported by elastic foundation using a quasi-3D finite element formulation

Free vibration of functionally graded (FG) sandwich plates partially supported by a Pasternak elastic foundation is studied. The plates consist of three layers, namely a pure ceramic hardcore and two functionally graded skin layers. The effective material properties of the skin layers are considered to vary in the plate thickness by a power gradation law, and they are estimated by Mori--Tanaka scheme. The quasi-3D shear deformation theory, which takes the thickness stretching effect into account, is adopted to formulate a finite element formulation for computing vibration characteristics. The accuracy of the derived formulation is confirmed through a comparison study. The numerical result reveals that the foundation supporting area plays an important role on the vibration behavior of the plates, and the effect of the layer thickness ratio on the frequencies is governed by the supporting area. A parametric study is carried out to highlight the effects of material distribution, layer thickness ratio, foundation stiffness and area of the foundation support on the frequencies and mode shapes of the plates. The influence of the side-to-thickness ratio on the frequencies of the plates is also examined and discussed.

Thermo-elastoplastic analysis of functionally graded sandwich plates using a three-dimensional meshless model

In this paper, for the first time, three-dimensional (3D) thermo-elastoplastic bending analysis of functionally graded (FG) sandwich plates with FG face sheets and FG/homogeneous core subjected to combined thermal and mechanical loads is performed. It is assumed that the functionally graded material (FGM) is composed of two different constituents (metal-ceramic) whose volume fractions vary continuously in the thickness direction according to a power law. The von-Mises yield criterion and isotropic strain hardening rule are employed, while temperature-dependent thermal and mechanical properties of the materials are taken into account. A complete 3D meshless numerical model based on the local radial point interpolation method (LRPIM) is developed and used in all analyses. Several numerical examples for temperature, deflection and stress analysis of FG sandwich plates are presented considering different material gradients, layer thickness ratios, thickness-to-length ratios, and boundary conditions. The numerical results are compared with the existing results of 3D, quasi-3D, and 2D shear deformation theories and an excellent agreement is observed.

Temperature dependent thermomechanical bending response of functionally graded sandwich plates

A higher-order shear deformation plate theory (HSDT) is applied in this work to study the thermomechanical bending behavior of sandwich plates composed of functionally graded (FG) face sheets and fully ceramic core. Material properties of the FG sandwich plate are dependent on temperature and supposed to be graded continuously across the sandwich plate thickness direction. Power-law model is adopted to describe continuous variation of material properties of FG sandwich plate. Temperature variation along the thickness direction is obtained by solving the one-dimensional heat conduction equation. An accurate solution of temperature variation along the thickness direction is employed by taking into account the thermal conductivity, the inhomogeneity parameter and the sandwich schemes. The governing equations of simply-supported FG sandwich plates are derived by means of the Hamilton’s variational principle combined with the Navier’s solutions. Numerical results indicate the impact of volume fraction index, temperature difference and side-to-thickness ratio on the deflections and stresses are carried out. The accuracy of the proposed five-order shear deformation theory is validated by comparing it with some available solutions in the literature. The present model is simple and can theoretically cover the existing polynomial models.

Aeroelastic analysis of cantilever non-symmetric FG sandwich plates under yawed supersonic flow

In this paper, a numerical solution is presented for supersonic flutter analysis of cantilever non-symmetric functionally graded (FG) sandwich plates. The plate is considered to be composed of two different functionally graded face sheets and an isotropic homogeneous core made of ceramic. Based on the first order shear deformation theory (FSDT) and linear piston theory, the set of governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and solved numerically using generalized differential quadrature method (GDQM) and critical velocity and flutter frequencies are calculated. For various values of the yaw angle, effect of different parameters like aspect ratio, thickness of the plate, power law indices and thickness of the core on the flutter boundaries are investigated. Numerical examples show that wings and tail fins with larger length and shorter width are more stable in supersonic flights. It is concluded for FG sandwich plates made of Al-Al2O3 that increase in volume fraction of ceramic (Al2O3) increases aeroelastic stability of the plate. Presented study confirms that improvement of aeroelastic behavior and weight of wings and tail fins of aircrafts are not consistent items. It is shown that value of the critical yaw angle depends on aspect ratio of the plate and other parameters including thickness and variation of properties have no considerable effect on it. Results of this paper can be used in design and analysis of wing and tail fin of supersonic airplanes.

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

Free vibration and mechanical buckling of porous functionally graded (FG) sandwich plates is studied in this paper by using a new and simple higher-order shear deformation theory (SHSDT). The present theory accounts for the distribution of transvers shear stresses that satisfy the free transverse shear stress conditions on the upper and lower surfaces of the sandwich plate. The FG sandwich plate is composed of three layers, an isotropic core and two FG face layers. Four porosities distribution and new model of FG sandwich plates based on a sigmoid function are presented. The boundary conditions for the FG sandwich plate are assumed to be simply-supported. Navier’s solution is used to obtain the closed-form solutions of FG sandwich plates. The effect of porosity, sandwich plate geometry and inhomogeneity parameter on the buckling and free vibration of FG sandwich plate is investigated.

A 3D full layer-wise method for yield achievement in Functionally Graded Sandwich Plates with general boundary conditions

The onset of yielding in Functionally Graded Sandwich Plates (FGSP) with ceramic core and Functionally Graded (FG) face sheets is presented in this paper. Full layer-wise theory which has been proved to be accurate and computationally efficient is developed for static analysis of these plates. The volume fraction of the ceramic phase is assumed to vary via a power-law function in the thickness direction of FG face sheets. TTO model which indicates the initials of the names of the authors who firstly introduced it as well as Rule of Mixture (ROM) are employed to determine the material properties variation through the FGSPs. The results associated with central deflection, and stress distribution through these structures were found to be significantly influenced by the utilized material models. After obtaining the stress fields, Von Mises yield criterion is implemented to find the first node(s) at which the yielding of FGSPs initiates. According to the final results, depending on the type of boundary conditions and core to face sheet thickness ratio, the yielding commencement could occur at the enriched metal or enriched ceramic surfaces. Power-law exponent however found to have no influence on the area at which yielding initiation occurs. Nevertheless, decreasing this parameter results in FGSPs with higher strength and postpones the yielding initiation of these structures. A comparison study is also presented which demonstrates how FGSPs are capable of undergoing bending loads, before yielding, up to twice as large as conventional Functionally Graded Plates (FGPs) while having the same weight and material constituents.