Application of Carrera unified formulation in conjunction with finite strip method in static and stability analysis of functionally graded plates
TL;DR: In this article, the static and mechanical buckling analysis of functionally graded (FG) plates was performed using Carrera's unified formulation (CUF) and the principle of virtual displace.
Abstract: This paper presents the static and mechanical buckling analyses of thick functionally graded (FG) plates. For this purpose, Carrera’s unified formulation (CUF) and the principle of virtual displace...
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TL;DR: In this paper, the hygrothermal response of free vibration of laminated composite plates is discussed, and the formulation of the nth-order shear deformation theory is modified to discuss the hydrastic response.
Abstract: The formulation of the nth-order shear deformation theory was modified to discuss the hygrothermal response of free vibration of laminated composite plates. Current theory has four unknown variable...
15 citations
TL;DR: In this paper, the dynamic instability of the hybrid fiber/nanocomposite-reinforced toroidal shells is investigated by using the approximation of Fourier series and applying the Galerkin method.
Abstract: Abstract In this article, the dynamic instability of the hybrid fiber/nanocomposite-reinforced toroidal shells is investigated. By using the approximation of Fourier series and applying the Galerkin method, a semi-analytical solution is achieved. The proposed method provides an accurate assessment of the dynamic stability of the shell with no computational costs in comparison to the numerical methods. By comparing the obtained results for some examples with those available in the present literature, the accuracy of present formulation is approved. In order to evaluate the effects of geometrical and mechanical specifications on the dynamic instability of the proposed shells, a comprehensive parametric study is performed, as well.
11 citations
TL;DR: In this paper, static analysis of functionally graded (FG) sandwich plates is performed using the finite strip method based on the refined plate theory (RPT) two types of common FG sandwich plates
Abstract: In this study, static analysis of functionally graded (FG) sandwich plates is performed using the finite strip method based on the refined plate theory (RPT) Two types of common FG sandwich plates
8 citations
TL;DR: In this paper, a four-node rectangular finite element with assumed natural shear strains, based on the exact neutral surface position and new higher-order shear deformation theory is employed.
Abstract: In the current work, a four-node rectangular finite element with assumed natural shear strains, based on the exact neutral surface position and new higher-order shear deformation theory is employed...
8 citations
TL;DR: In this article, an efficient finite element model based on conventional shell elements available in ABAQUS software was developed for free vibration analysis of FGM monolayer and sandwich flat panels.
Abstract: An efficient finite element model based on conventional shell elements available in ABAQUS software has been developed for free vibration analysis of FGM monolayer and sandwich flat panels. Applica...
6 citations
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TL;DR: In this paper, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates.
Abstract: Theoretical formulation, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The formulation accounts for the thermomechanical coupling, time dependency, and the von Karman-type geometric non-linearity. Numerical results of the linear third-order theory and non-linear first-order theory are presented to show the effect of the material distribution on the deflections and stresses. Copyright © 2000 John Wiley & Sons, Ltd.
1,460 citations
"Application of Carrera unified form..." refers methods in this paper
...Reddy [6] presented a finite element (FE) procedure using Navier’s solution [7] based on the third-order shear deformation theory for the analysis of rectangular FG plates....
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TL;DR: In this paper, the authors present an extension of Hooke's Law for determining the stability under stress of thin shells of isotropic elastic material, which they use to determine the equilibrium of an elementary volume of the substance by considering the forces acting upon it.
Abstract: The object of the present paper is to derive equations that are adequate to decide questions of the stability under stress of thin shells of isotropic elastic material. Equations for the same purpose have been given by R. V. Southwell, who used a method that is closely followed in a part of this paper. Such equations must contain terms that may be, and are, neglected in applications of the theory of elasticity to problems in which the stability of configurations is not considered. The truth of Kirchhoff's uniqueness theorem, which has reference to the ordinary equations of elasticity, in which powers of the displacement co-ordinates above the first are neglected, is sufficient proof of this statement. In practice it is generally sufficient to retain only the first and second order terms, and no terms of higher order are considered here. To obtain such equations an extended form of Hooke's Law is necessary; the extension made by Southwell is used in this paper. There are then two methods available for the derivation of the equations. Either we may obtain the three conditions for the equilibrium of an elementary volume of the substance by considering the forces acting upon it, or we may calculate the energy of strain correct to the third order of displacement co-ordinates, and deduce the equations by variation of this function. The first method has been used in one place here, as it would appear to be the simpler in the particular case of a plane plate, in which only one of the equations, and that the simplest, is required. However, the stability equations for a cylindrical shell are also obtained, and then all three equations are necessary. The derivation by the first method of each one of these is a laborious matter, while using the second method there is only one calculation, that of the strain energy function, to be made. Consequently, for this purpose, as in general, the second method seems to be preferable.
1,003 citations
Book•
01 Jan 1976
TL;DR: In this paper, the theory of the finite strip method and its application in structural engineering with special reference to slab and box girder bridges is introduced, and a discussion of the application of finite strip analysis in bridge construction is presented.
Abstract: This book introduces the theory of the finite strip method, and discusses its application in structural engineering with special reference to slab and box girder bridges. Separate chapters deal with :(1) finite strip method; (2) bending of plates and plate-beam systems with application to slab-beam bridges; (3) plane stress analysis; (4) analysis of folded plate structures with special reference to box girder bridges; (5) vibration and stability of plates and shells; (6) further developments in finite strip analysis; (7) finite layer method and finite prism method; and (8) computation methods and computer program. Author and subject indexes are appended. /TRRL/
644 citations
"Application of Carrera unified form..." refers methods in this paper
...The FSM was first introduced in 1976 by Chung [60] and was found to be one of the most efficient methods for the static and specifically buckling analysis of plates....
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...[14] S.-H. Chi and Y.-L. Chung, Mechanical behavior of functionally graded material plates under transverse load—Part II: Numerical results, Int....
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...Chi and Chung [13, 14] investigated the bending behavior of rectangular simply supported moderately thick FG plates subjected to transverse loading....
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...[13] S.-H. Chi and Y.-L. Chung, Mechanical behavior of functionally graded material plates under transverse load—Part I, Analysis....
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TL;DR: In this article, a higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia.
629 citations
TL;DR: In this article, the static response of a simply supported rectangular plate subjected to a transverse uniform load is presented for a simple supported functionally graded rectangular plate, where material properties of the plate 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.
508 citations
"Application of Carrera unified form..." refers methods in this paper
...Zenkour [9] performed the static analysis of a simply supported FG rectangular plate subjected to transverse loading using his generalized shear deformation theory....
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