• Structural Engineering and Mechanics
• /
• v.75 no.2
• /
• pp.157-174
• /
• 2020

In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

• Journal of the Korean Society of Safety
• /
• v.17 no.4
• /
• pp.31-37
• /
• 2002

This paper demonstrates the analyses of the interlaminar shear stress of laminated composite plates subjected to transversely impact. For this purpose, a plate finite element model based on the higher order shear deformation plate theory in conjunction with static contact laws is developed. Test materials were CFRP with cross-ply laminate $[O_4/{\theta}_4]_S$, $[90_4/{\theta}_4]_S$ stacking sequences and angle-ply laminate $[{\theta}_4/-{\theta}_4]_S$, $[{\theta}_4/-{\theta}_4]_S$ stacking deguences with $2^t{\times}40^w{\times}100^l(mm)$ dimension. As a result, stacking seguence and fiber orientation were found to have a significant effect on the interlaminar stresses in composite laminates.

• Structural Engineering and Mechanics
• /
• v.6 no.6
• /
• pp.583-612
• /
• 1998

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.

• Wind and Structures
• /
• v.28 no.1
• /
• pp.49-62
• /
• 2019

In this paper, an analytical analysis for the study of vibratory behavior and wave propagation of functionally graded plates (FGM) is presented based on a high order shear deformation theory. The manufacture of these plates' defects can appear in the form of porosity. This latter can question and modify the global behavior of such plates. A new shape of the distribution of porosity according to the thickness of the plate was used. The field of displacement of this theory is present of indeterminate integral variables. The modulus of elasticity and the mass density of these plates are assumed to vary according to the thickness of the plate. Equations of motion are derived by the principle of minimization of energies. Analytical solutions of free vibration and wave propagation are obtained for FGM plates simply supported by integrating the analytic dispersion relation. Illustrative examples are given also to show the effects of variation of various parameters such as(porosity parameter, material graduation, thickness-length ratio, porosity distribution) on vibration and wave propagation of FGM plates.

• Steel and Composite Structures
• /
• v.26 no.1
• /
• pp.1-15
• /
• 2018

This study reported, the effect of random variation in system properties on bending response of single wall carbon nanotube reinforced composite (SWCNTRC) plates subjected to transverse uniform loading is examined. System parameters such as the SWCNT armchair, material properties, plate thickness and volume fraction of SWCNT are modelled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behaviour of the SWCNTRC composite plate. A C0 finite element method in conjunction with the first order perturbation technique procedure developed earlier by the authors for the plate subjected to lateral loading is employed to obtain the mean and variance of the transverse deflection of the plate. The performance of the stochastic SWCNTRC composite model is demonstrated through a comparison of mean transverse central deflection with those results available in the literature and standard deviation of the deflection with an independent First Order perturbation Technique (FOPT), Second Order perturbation Technique (SOPT) and Monte Carlo simulation.

• Steel and Composite Structures
• /
• v.35 no.1
• /
• pp.1-12
• /
• 2020

This article deals with the buckling analysis in the plates containing carbon nanotubes (CNTs) subject to axial load. In order to control the plate smartly, a piezoelectric layer covered the plate. The plate is located in elastic medium which is modeled by spring elements. The Mori-Tanaka low is utilized for calculating the equivalent mechanical characteristics of the plate. The structure is modeled by a thick plate and the governing equations are deduced using Hamilton's principle under the assumption of higher-order shear deformation theory (HSDT). The Navier method is applied to obtain the bulking load. The effects of the applied voltage to the smart layer, agglomeration and volume percent of CNT nanoparticles, geometrical parameters and elastic medium of the structure are assessed on the buckling response. It has been demonstrated that by applying a negative voltage, the buckling load is increased significantly.

• Coupled systems mechanics
• /
• v.9 no.3
• /
• pp.237-264
• /
• 2020

This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

• Coupled systems mechanics
• /
• v.10 no.1
• /
• pp.61-77
• /
• 2021

The porosity of functionally graded materials (FGM) can affect the static and dynamic behavior of plates, which is important to take this aspect into account when analyzing such structures. The present work aims to study the effect of the distribution shape of porosity on the free vibration response of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is expanded to study the influence of the distribution shape of porosity on the free vibration behavior of FG plates. The findings showed that the distribution shape of porosity significantly influences the free vibration behavior of thick rectangular FG plates for small values of Winkler-Pasternak elastic foundation parameters.

• Structural Engineering and Mechanics
• /
• v.40 no.6
• /
• pp.783-800
• /
• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• Structural Engineering and Mechanics
• /
• v.60 no.2
• /
• pp.271-299
• /
• 2016

In this article, based on the higher-order shear deformation plate theory, buckling analysis of a rectangular plate made of functionally graded piezoelectric materials and its effective parameters are investigated. Assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for the buckling analysis of an FGP rectangular plate are established. In addition to the Maxwell equation, all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. Considering double sine solution (Navier solution) for displacement field and electric potential, an analytical solution is obtained for full simply supported boundary conditions. The accurate buckling load of FGP plate is presented for both open and closed circuit conditions. It is found that the critical buckling load for open circuit is more than that of closed circuit in all loading conditions. Furthermore, it is observed that the influence of dielectric constants on the critical buckling load is more than those of others.