Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

Zenkour, Ashraf M.; Allam, M. N. M.; Sobhy, Mohammed

doi:10.1007/s00419-009-0396-9

Cited by 38 publications

(12 citation statements)

References 26 publications

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“…are of the form [14]: (12) where c = cosθ k and s = sin θ k and c ij are the (plane stress-reduced) material stiffness of the lamina: (13) in which E i are Young's moduli in the material principal directions, v ij are Poisson's ratios, and G ij are shear moduli.…”

Section: Closed-form Solutionmentioning

confidence: 99%

“…However, there are three specific co-ordinates transformations under which an orthotropic material retains monoclinic symmetry, namely, rotations about the axes , or . For example, if the material is orthotropic with respect to the old co-ordinate system, it follows under rotation through an angle about the -axis that the transformation formulae for the stiffnesses are of the form [14]: (12) where and and are the (plane stress-reduced) material stiffness of the lamina: (13) in which are Young's moduli in the material principal directions, are Poisson's ratios, and are shear moduli.…”

Section: Numerical Examples and Discus-sionmentioning

confidence: 99%

“…This article deals with the thermal bending of angleply laminated plates resting on elastic foundations. It is to be noted that, such problems of plates resting on elastic foundations are often encountered in the analysis of the foundations of buildings, highway and railroad structures, and of geotechnical structures in general [9][10][11][12]. The effects due to several parameters such as thermal loadings, foundations, aspect and side-to-thickness ratios, as well as the lamination angle are investigated.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermoelastic Bending Response of Angel-Ply Composite Plates Resting on Elastic Foundations

Zenkour

Abbas

2013

Advanced Composites Letters

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Different plate theories are presented to study the thermoelastic response of a multilayered angle-ply composite plate. The plate is subjected to a sinusoidal temperature and resting on different types of elastic foundations. The effects due to thermal loads and elastic foundations parameters as well as the variation of lamination angle are studied. Numerical results suggest that Pasternak's model should be used for such plates resting on elastic foundations.

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Section: Closed-form Solutionmentioning

confidence: 99%

Section: Numerical Examples and Discus-sionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermoelastic Bending Response of Angel-Ply Composite Plates Resting on Elastic Foundations

Zenkour

Abbas

2013

Advanced Composites Letters

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“…Thus, the two-parameter models of foundation taking into account its operation both in compression and in transverse shear were proposed in [4,9] and numerous problems were solved both for massive solids and for thin-walled structural elements. The subsequent development in this direction is described in [5,7,12,16]. In [1], in order to formulate the conjugation conditions in the tangential direction, the authors apply a second-order differential operator.…”

mentioning

confidence: 99%

A Generalized Model of Viscoelastic Interlayer or Coating Taking into Account its Transverse Shear Deformation

Skorodyns'kyi

Maksymuk

2014

J Math Sci

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A generalized model of viscoelastic anisotropic interlayer or coating operating in compression and in transverse shear is constructed and examined. We solve the problem of action of a time-dependent normal distributed load on the isotopic viscoelastic layer on the rigid substrate and study the case of concentrated forces acting at the origin of coordinates.In contemporary machine building, civil engineering, and transport, the mechanical contact between solid bodies fairly often is realized through thin interlayers or coatings with their own physicomechanical properties and characteristics. Among these objects are pavements and foundations, damping layers in transport and in laying of pipelines, etc. In the design of objects of this kind, it is necessary to take into account their physicomechanical behavior under loads of different types for various loading modes and guarantee the adequate choice of the proper mathematical model. In [2, 3, 6], a large number of contact problems for bodies with thin coatings and interlayers described by elastic and viscoelastic models, including the linear and nonlinear Winkler models, were solved within the framework of the theory of creep and aging [2,3]. The Winkler viscoelastic foundation was considered within the framework of the Voigt model in [14]. However, the Winkler model does not take into account the resistance of the foundation to transverse shear and, hence, the displacements outside the region of action of the load are equal to zero. Thus, the two-parameter models of foundation taking into account its operation both in compression and in transverse shear were proposed in [4,9] and numerous problems were solved both for massive solids and for thin-walled structural elements. The subsequent development in this direction is described in [5,7,12,16]. In [1], in order to formulate the conjugation conditions in the tangential direction, the authors apply a second-order differential operator. However, the models of elastic interlayer considered in the cited work are not two-parameter models. The generalizations of the two-parameter model of foundation to the viscoelastic case in the dynamic and quasistatic statements can be found in [8,15]. Note that the surveys of the results on the models of elastic and viscoplastic foundations together with a large body of cited literature can be found in [5,7,13].The aim of the present paper is to study a generalized model of viscoelastic interlayer or coating that takes into account its operation both in compression and in transverse shear, in particular, on the example of a problem of action of normal loads on the viscoelastic layer joined with the rigid foundation. A Generalized Model of Viscoelastic Interlayer (Coating)Within the framework of the Kelvin-Voigt model [11], the generalized thermomechanical conditions of conjugation of solid bodies via a thermoelastic anisotropic interlayer of thickness 2h operating in compression

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“…Since the governing equations as well as boundary conditions for thin plates have been established long ago, the main focus has been on the solutions, which has brought in a variety of solution methods for various plates. Most of these methods are approximate/numerical ones such as the finite difference method 1 2 , the finite strip method 3 4 , the finite element method (FEM) 5 6 , the boundary element method 7 8 , the differential quadrature method 9 10 , the discrete singular convolution method 11 12 13 14 , the meshless method 15 16 17 , the collocation method 18 19 20 , the Illyushin approximation method 21 22 , the Rayleigh-Ritz method and Galerkin method 23 .…”

mentioning

confidence: 99%

A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

Wang

et al. 2015

Sci Rep

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A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates. The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation. The main advantage of the developed approach is its wide applicability since no trial solutions are needed in the analysis, which is completely different from the other methods. Numerical examples for both static bending and free vibration plates are presented to validate the developed analytic solutions and to offer new numerical results. The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

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Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

Cited by 38 publications

References 26 publications

Thermoelastic Bending Response of Angel-Ply Composite Plates Resting on Elastic Foundations

Thermoelastic Bending Response of Angel-Ply Composite Plates Resting on Elastic Foundations

A Generalized Model of Viscoelastic Interlayer or Coating Taking into Account its Transverse Shear Deformation

A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

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