In the present work, a displacement-based high-order shear deformation theory is introduced for the static response of functionally graded plates. The present theory is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced a and hence makes them simple to use. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The equilibrium equations of a functionally graded plate are given based on the higher order shear deformation theory. The numerical results presented in the paper are demonstrated by comparing the results with solutions derived from other higher-order models found in the literature and the present numerical results of Finite Element Analysis (FEA). In the numerical results, the effects of the grading materials, lay-up scheme and aspect ratio on the normal stress, shear stress and static deflections of the functionally graded Sandwich plates are presented and discussed. It can be concluded that the proposed theory is accurate, elegant and simple in solving the problem of the bending behavior of functionally graded plates.

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This paper presents an efficient higher-order theory for analyzing the dynamic behavior of two types of Sandwich plates: functionally graded Sandwich plates (FGSPs) and four-parameter functionally graded plates (FPFGPs). The FGSP consists of two functionally graded (FG) face sheets and a ceramic core. For FGSPs, the variation follows a power-law distribution, while for FPFGPs; it adheres to Tornabene's model. To ensure that transverse shear stresses vanish at the top and bottom surfaces of the FGSP, a trigonometric shear deformation theory is employed. This theory incorporates four displacement field variables with indeterminate integral terms. The governing equations are derived using Hamilton's principle and solved using the Navier solution method for simply supported boundary conditions. Validation results demonstrate excellent agreement between the proposed theory and existing literature. Additionally, a detailed parametric study highlights the influence of key geometric and mechanical parameters, including the power-law index, side-to-thickness ratio, and aspect ratio, on the dynamic behavior of the plates.

For the first time, by applying a modified high order Sandwich plates theory, vibration behaviour of two types of porous FG circular Sandwich plates are investigated. In the first type, the face sheets and in the second one, the core is made of FGM which is modelled by power law rule that is modified by considering two types of porosity distributions. All materials are temperature dependent and uniform temperature distribution is used to model the effect of the temperature changing in the Sandwiches. Governing equations are obtained by the Hamilton's energy principle and solved by Galerkin method for a clamped boundary condition. To verify the results, they are compared with FEM results obtained by Abaqus software and for special cases with the results in literatures.

The main aim of this paper is to investigate bending behavior in Sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets with considering the effects of carbon nanotube (CNT) aggregation. The Sandwich plates are assumed resting on Winkler-Pasternak elastic foundation and a mesh-free method based on first order shear deformation theory (FSDT) is developed to analyze the deflection of Sandwich plates. In the face sheets, volume fraction of CNTs and their clusters are considered to be changed along the thickness. To estimate the material properties of the nanocomposite, Eshelby-Mori-Tanaka approach is applied. In the mesh-free analysis, moving least squares (MLS) shape functions are employed to approximate the displacement field and transformation method is used for imposition of essential boundary conditions. The effects of CNT volume fraction, distribution and degree of aggregation, and also boundary conditions and geometric dimensions are investigated on the bending behavior of the Sandwich plates. It is observed that in the same value of cluster volume, FG distribution of clusters leads to less deflection in these structures.

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 three 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.

In this paper, supersonic flutter analysis of cantilevered trapezoidal plates composed of two functionally graded face sheets and an isotropic homogeneous core is presented. Using Hamilton’s principle, the set of governing equations and external boundary conditions are derived. A transformation of coordinates is used to convert the governing equations and boundary conditions from the original coordinates into the new dimensionless computational ones. Generalized differential quadrature method (GDQM) is employed as a numerical method and critical aerodynamic pressure and flutter frequencies are derived. Convergence, versatility, and accuracy of the presented solution are confirmed using numerical and experimental results presented by other authors. The effect of power- law index, thickness of the core, total thickness of the plate, aspect ratio and angles of the plate on the flutter boundaries are investigated. It is concluded that any attempt to increase the critical aerodynamic pressure leads to a decrease in lift force or rise in total weight of the plate.