A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates

In this paper, an efficient and simple higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

In this paper, a new quasi-three-dimensional (3D) hyperbolic shear deformation theory for the bending and free vibration analysis of functionally graded plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, the number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only five, as against six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory.

New Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates

A review of theories for the modeling and analysis of functionally graded plates and shells

Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review

A new first-order shear deformation theory is developed for bending and dynamic behaviors of functionally graded plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The equations governing the axial and transverse deformations of functionally graded plates are derived based on the present first-order shear deformation plate theory and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. To examine accuracy of the present formulation, several comparison studies are investigated. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented 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. 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. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

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, ie 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

https://jacm.scu.ac.ir/article_16055_37a403565b15edb2690dca5a737c7958.pdf

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

Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory

This paper presents a new nonlocal Hyperbolic Shear Deformation Beam Theory (HSDBT) for the free vibration of porous Functionally Graded (FG) nanobeams. A new displacement field containing integrals is proposed which involves only three variables. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect and its account for shear deformation by a hyperbolic variation of all displacements through the thickness without using the shear correction factor. It has been observed that during the manufacture of Functionally Graded Materials (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the free vibration analysis of FG beams taking into account the influence of these imperfections is established. Four different porosity types are considered for FG nanobeam. Material characteristics of the FG beam are supposed to vary continuously within thickness direction according to a power-law scheme which is modified to approximate material characteristics for considering the influence of porosities. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio, and the porosity types on the dynamic responses of the nanobeam are discussed.

Lazreg Hadji

Papers

Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

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

Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory

Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory