Three-dimensional Analyses of Functionally Graded Multi-layered Systems

This paper presents an analytical solution for the free vibration of functionally graded material (FGM) sandwich plates in a thermal environment. An equivalent‐single‐layer (ESL) plate theory with four variables is used to obtain the solution. Two types of sandwich plates are examined in this study: one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets. The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method. The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature. The effects of volume fraction distribution, geometrical parameters, and temperature increments on the free vibration characteristics are discussed in detail.

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.

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened sandwich plate with functionally graded material (FGM) on elastic foundation using both of the first-order shear deformation plate theory and stress function with full motion equations (not using Volmir's assumptions). The thick sandwich plates are assumed to rest on elastic foundation and subjected to mechanical loads in thermal environment. Numerical results for dynamic response of the eccentrically stiffened thick sandwich plates are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, material properties, imperfections, the elastic foundations, eccentric stiffeners, mechanical loads and temperature on the nonlinear dynamic response and nonlinear vibration of functionally graded sandwich plates. The numerical results in this paper are compared with the results reported in other publications.

Three-dimensional free vibration analyses of functionally graded laminated shells under thermal environment by a hierarchical quadrature element method

2 - Sandwich Structures

In the present work, the inverse trigonometric shear deformation theory (ITSDT) is applied to analytically perform the free vibration and buckling analysis of functionally graded (FG) sandwich plate. The governing equations are derived using the principle of virtual work, incorporating linear structural kinematics and the generalized Hooke’s law. These equations are solved in closed form for simply supported boundary conditions to obtain the buckling and vibration response. For the analysis, two types of FG sandwich plates are considered i.e., Type – A and Type – B. For the Type – A plate, the core and face sheets of the FG sandwich plate are made up of Ceramic and FG material, respectively. Whereas in case of Type- B plate, the core is composed of FG material, while the top and bottom face sheets are made up of ceramic and metal, respectively. The power law is employed to vary the material properties in the FG material. The evaluated results for the FG sandwich Type – A plate are compared with the already reported results in the literature wherever possible and are found in good agreement. The influence of the various parameters such as span to thickness (a/h), aspect ratio (a/b), power law index (p) and core thickness (schemes) are investigated on the dimensionless fundamental frequency and dimensionless critical buckling load of the FG sandwich plate, on those basis, noteworthy conclusions are drawn.

Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

In this study, a curved sandwich beam with Functionally Graded Materials (FGM) face sheets and a homogeneous core under thermomechanical loads is investigated. The problem is studied numerically by the finite element method (FEM). Plane, eight nodes isoparametric elements are used, where the gradient of the material properties is incorporated into the formulation of the element. The effect of the thickness and volume fraction index (VFI) of the FGM face sheets on the stress and the temperature fields are studied. The results are valuable in the design of hydrogen mechanical applications, since the FGM sandwich curved beam could be a part of hydrogen storage tanks.

Based on the first order shear deformation plate theory (FSDT) in the present studie, static and dynamic behavior of carbon nanotube-reinforced composite sandwich plates has been analysed. Two types of sandwich plates, namely, the sandwich with face sheet reinforced and homogeneous core and the sandwich with homogeneous face sheet and reinforced core are considered. The face sheet or core plates are reinforced by single-walled carbon nanotubes with two types of distributions of uniaxially aligned reinforcement material which uniformly (UD-CNT) and functionally graded (FG-CNT). The analytical equations are derived and the exact solutions for bending and vibration analyses of such type’s plates are obtained. The mathematical models provided and the present solutions are numerically validated by comparison with some available results in the literature. Influence of Various parameters of reinforced sandwich plates such as aspect ratios, volume fraction, types of reinforcement and plate thickness on the bending and vibration analyses of carbon nanotube-reinforced composite sandwich plates are studied and discussed. The findings suggest that the (FG-CNT) face sheet reinforced sandwich plate has a high resistance against deflections compared to other types of reinforcement. It is also revealed that the reduction in the dimensionless natural frequency is most pronounced in core reinforced sandwich plate.

This study investigates the effects of fluid–structure and soil–structure interaction on the free vibration response of functionally graded sandwich plates. To this aim, an exemplary problem is analyzed, whereas a metal/ceramic sandwich plate is placed at the bottom of a tank filled in with fluid. Two cases are considered: (i) soft core, i.e., a sandwich plate with metal core and ceramic skins, and (ii) hard core, i.e., a sandwich plate with ceramic core and metal skins. In both cases, the skins are modelled as suitable functionally graded materials (FGMs). The soil is modelled as a Pasternak foundation. The free vibration analysis is carried out according to the extended higher order sandwich plate theory (EHSAPT). The fluid is assumed to be inviscid, incompressible, and irrotational. Hamilton’s principle is exploited to deduce the governing equations and the corresponding boundary conditions. The Rayleigh–Ritz method with two-variable orthogonal polynomials is used to compute the natural frequencies of the sandwich plate. The adopted approach is first validated through comparison with results published in the literature. Then, the effects are studied of several parameters on the dynamic response of the system.

Thermal buckling of various types of FGM sandwich plates

In this paper, transient response of functionally graded materials (FGM) rectangular sandwich plates subjected to thermal loading based on three-dimensional theory of elasticity is carried out. The facing layers are made of metal and ceramics whereas core layer is FGM with exponential function distribution. For the case of simply supported boundary conditions, obtained state space differential equations are solved analytically by using Fourier series expansions along the in-plane coordinates and Laplace transformation. For other edges, boundary condition semi-analytical method is used by applying differential quadrature method (DQM) along the in-plane direction and state space technique across the transverse coordinate. After carrying out the convergence of the present method, accuracy of this study is validated by comparing the numerical results with those reported in the literature. Finally, influences of the boundary conditions, length-to-thickness ratios, length-to-width ratios, time constant and the FGM graded index on elastic behavior of sandwich plate are examined.

Nonlinear vibration of sandwich plates with FG-GRC face sheets in thermal environments