• Wind and Structures
• /
• 제32권1호
• /
• pp.19-30
• /
• 2021

This study presents buckling analysis of a simply supported sandwich plate with functionally graded porous layers. In the kinematic relation of the plate, a hyperbolic shear displacement model is used. The governing equations of the problem are derived by using the principle of virtual work. In the solution of the governing equations, the Navier procedure is implemented. In the porosity effect, four different porosity types are used for functionally graded sandwich layers. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the critical buckling of the functionally graded sandwich plates are investigated.

• Structural Engineering and Mechanics
• /
• 제86권3호
• /
• pp.373-384
• /
• 2023

The main objective of this research work is to present analytical solutions for the thermoelastic bending analysis of sandwich plates made of functionally graded materials with an arbitrary gradient. The governing equations of equilibrium are solved for a functionally graded sandwich plates under the effect of thermal loads. The transverse shear and normal strain and stress effects on thermoelastic bending of such sandwich plates are considered. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. The results of the shear deformation theories are compared together. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated.

• Steel and Composite Structures
• /
• 제24권5호
• /
• pp.569-578
• /
• 2017

In this research work, a simple and accurate hyperbolic plate theory for the buckling analysis of functionally graded sandwich plates is presented. The main interest of this theory is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\not=}0$), the displacement field is composed only of 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 like in the well-known "higher order shear and normal deformation theories". Thus, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Governing equations are obtained by employing the principle of minimum total potential energy. Comparison studies are performed to verify the validity of present results. A numerical investigation has been conducted considering and neglecting the thickness stretching effects on the buckling of sandwich plates with functionally graded skins. It can be concluded that the present theory is not only accurate but also simple in predicting the buckling response of sandwich plates with functionally graded skins.

• Steel and Composite Structures
• /
• 제15권2호
• /
• pp.221-245
• /
• 2013

This paper presents an analytical solution to the thermomechanical bending analysis of functionally graded sandwich plates by using a new hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are investigated.

• Steel and Composite Structures
• /
• 제18권1호
• /
• pp.235-253
• /
• 2015

In this research, a simple but accurate sinusoidal plate theory for the thermomechanical bending analysis of functionally graded sandwich plates is presented. The main advantage of this approach is that, in addition to incorporating the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 as in the well-known conventional sinusoidal plate theory (SPT). The material properties of the sandwich plate faces are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is made of an isotropic ceramic material. Comparison studies are performed to check the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical behavior of functionally graded sandwich plates. The effect of side-to-thickness ratio, aspect ratio, the volume fraction exponent, and the loading conditions on the thermomechanical response of functionally graded sandwich plates is also investigated and discussed.

• Steel and Composite Structures
• /
• 제18권1호
• /
• pp.91-120
• /
• 2015

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

• Advances in materials Research
• /
• 제8권4호
• /
• pp.313-335
• /
• 2019

The objective of the present paper is to investigate the bending and free vibration behavior of functionally graded material (FGM) sandwich rectangular plates using an efficient and simple higher order shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The most interesting feature of this theory is that it does not require the shear correction factor. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Computers and Concrete
• /
• 제33권1호
• /
• pp.27-39
• /
• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Structural Engineering and Mechanics
• /
• 제77권6호
• /
• pp.797-807
• /
• 2021

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

• Structural Engineering and Mechanics
• /
• 제58권3호
• /
• pp.397-422
• /
• 2016

In the present work, a simple first-order shear deformation theory is developed and validated for a variety of numerical examples of the thermal buckling response of functionally graded sandwich plates with various boundary conditions. Contrary to the conventional first-order shear deformation theory, the present first-order shear deformation theory involves only four unknowns and has strong similarities with the classical plate theory in many aspects such as governing equations of motion, and stress resultant expressions. 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 thermal loads are considered as uniform, linear and non-linear temperature rises within the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates. Moreover, numerical results prove that the present simple first-order shear deformation theory can achieve the same accuracy of the existing conventional first-order shear deformation theory which has more number of unknowns.