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1、A new hyperbolic shear deformation theory for bending andfree vibration analysis of isotropic, functionally graded,sandwich and laminated composite platesAmale Mahia, El Abbas Adda Bediab, Abdelouahed TounsibaLaboratoire des Sciences Aronautiques, Universit de Blida 1, BP 270, 09000 Blida, AlgeriabL
2、aboratoire des Matriaux et Hydrologie, Universit de Sidi Bel Abbes, BP 89 Ben Mhidi, 22000 Sidi Bel Abbes, Algeriaa r t i c l ei n f oArticle history:Received 15 March 2013Received in revised form 29 June 2014Accepted 17 October 2014Available online 20 November 2014Keywords:Functionally graded plate
3、FG sandwich plateLaminated composite plateBendingFree vibrationShear deformation plate theorya b s t r a c tA new hyperbolic shear deformation theory applicable to bending and free vibrationanalysis of isotropic, functionally graded, sandwich and laminated composite plates is pre-sented. This new th
4、eory has five degrees of freedom, provides parabolic transverse shearstrains across the thickness direction and hence, it does not need shear correction factor.Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plateare satisfied rigorously. The energy functional of th
5、e system is obtained using Hamiltonsprinciple. Analytical solutions of deflection and stresses are obtained using Navier-typeprocedure. Free vibration frequencies are then accurately calculated using a set of bound-ary characteristic orthogonal polynomials associated with Ritz method. Numerical comp
6、ar-isons are conducted to verify and to demonstrate the accuracy and efficiency of the presenttheory. Excellent agreement with the known results in the literature has been obtained.? 2014 Elsevier Inc. All rights reserved.1. IntroductionFunctionally graded materials (FGMs) are a new kind of inhomoge
7、neous composite materials which have a smooth andcontinuous variation of material properties along one or more directions. At each interface, the material is chosen accordingto specific applications and environment loadings. Gradually varying the material properties can prevent from interfacecrackin
8、g, disbonding and residual stresses and thus maintain structural integrity to a desirable level. These highly heteroge-neous materials are also used as thermal barrier, wear coating and corrosion resistant coating in many engineeringapplications.In 19841985, a group of Japanese scientist proposed, f
9、or the first time, the concept of FGM. Five years later, the firstinternational conference 1 was held at Sendai-City in Japan. The interest was such that a rapid progress of FGM researchin Japan was noticed from 1984 to 1996 2. Since then, the increased attention given by many industrial engineers a
10、ndresearchers to these new composite materials was motivated by the real possibilities of improvement that can be achievedfor the mechanical properties of composites to overcome problems arising in composite structures such as delamination dueto high thermal gradients. Nowadays, these innovative mat
11、erials are increasingly being used in the manufacture of aerospaceand aeronautical components designed to support high temperature environments. They are also used in the manufacture ofhttp:/dx.doi.org/10.1016/j.apm.2014.10.0450307-904X/? 2014 Elsevier Inc. All rights reserved.Corresponding author.E
12、-mail address: (A. Mahi).Applied Mathematical Modelling 39 (2015) 24892508Contents lists available at ScienceDirectApplied Mathematical Modellingjournal homepage: that serve critical functions in aircrafts, space rockets, launchers and space shuttles. Further extensive applica-tions of FGMs can be f
13、ound in nuclear reactors, chemical plants, and in other applications such as biomechanical, optical,automotive, electronic, mechanical, civil, and shipbuilding industries.FGMs are typically made of a ceramic because of its thermal stability, good thermal shock resistance, mechanical strength,high-te
14、mperature creep resistivity, low density, excellent chemical resistance, good stiffness-to-weight ratio, and a metalbecause of its good fracture toughness. The functional association of these two high performance materials provides to avi-ation and aerospace manufacturers the ability to face success
15、fully a growing demand in achieving optimal performancewhile satisfying stringent safety standards. A good overview of the concept of FGMs, their processing, and their applicationscan be found in Refs. 35.In order to solve problems of structures composed of structural elements it is necessary to fin
16、d the right theory thatdescribes correctly the static and dynamic behaviors of the structure. This has led many researchers to develop more theoriesas well as new and effective methods of resolution.On basis of EulerBernoulli beam theory that relies on plane cross-sections hypothesis Kirchhoff 6 built a new theory forthin plates in 1850, on the assumption that normals to the undeformed midplane remain straight and normal to thedeformed midplane and unstretched in length. It was then extended to
