Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory

Kant, Tarun; Swaminathan, K.

doi:10.1016/s0263-8223(00)00180-x

Cited by 331 publications

(135 citation statements)

References 42 publications

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“…Analytical solutions were also derived by Kant et al ([10], [11]) and Zhen and Wanji [12] to study vibration and buckling of composite beams. By using the method of power series expansion of displacement components, Matsunaga [13] analysed the natural frequencies and buckling stresses of composite beams.…”

Section: Introductionmentioning

confidence: 99%

Vibration and buckling of composite beams using refined shear deformation theory

Thai

2012

International Journal of Mechanical Sciences

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Vibration and buckling analysis of composite beams with arbitrary lay-ups using refined shear deformation theory is presented. The theory accounts for the parabolical variation of shear strains through the depth of beam. Three governing equations of motion are derived from the Hamilton's principle.The resulting coupling is referred to as triply coupled vibration and buckling. A two-noded C 1 beam element with five degree-of-freedom per node which accounts for shear deformation effects and all coupling coming from the material anisotropy is developed to solve the problem. Numerical results are obtained for composite beams to investigate effects of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads and corresponding mode shapes.

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Section: Introductionmentioning

confidence: 99%

Vibration and buckling of composite beams using refined shear deformation theory

Thai

2012

International Journal of Mechanical Sciences

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“…In order to overcome the drawbacks of FSDT, HSDTs were developed which involved higher order terms in the displacements in the thickness coordinate. Remarkable among them are Reddy [14], Zenkour [15][16][17], Kant and Co-workers [18][19][20][21][22][23], Kadkhodayan [24], Matsunaga [25,26], Xiang [27] and Ferreira [28]. The buckling, vibration, linear and nonlinear bending behaviors of FG-CNT reinforced composite structures have drawn much concentration from researchers [29] because of the capability of FG-CNT reinforced composites to control deformation, dynamic response, wear, corrosion etc.…”

Section: Introductionmentioning

confidence: 99%

Static Bending Behavior of FG-CNT Reinforced Composite Plates Using Higher Order Shear Deformation Theory

Akurathi¹

2017

IJRASET

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The analytical formulations and solutions for the bending behavior of simply supported functionally graded carbon nanotube reinforced composite plates (FG-CNT Plates) are presented in this paper. Higher Order Shear Deformation Theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate is used for the analysis. Two types of carbon nanotube (CNT) distributions are analyzed in this investigation. It is assumed that through the thickness, the material properties of the plate are varied. The governing equations of motion and boundary conditions are derived based on the principle of virtual work. Solutions are obtained for FG-CNT Plates in closed-form using Navier's technique. The deflections and stresses are shown for simply supported boundary conditions. The effect of side-to-thickness ratio, aspect ratio, the volume fraction, and through-the-thickness on the deflections and stresses are studied in this paper. The obtained results are compared with the available FSDT solutions in the literature for deflections. This research also shows that the volume fraction of CNT has little effect on stresses. A computer program in C is developed for determining deflections and stresses. Keywords: Static Bending Behavior, FG-CNT Plates, Effective Material Properties, HSDT, Navier's Method. I. INTRODUCTIONIn 1987, Niino and co-workers proposed initially the concept of functionally graded materials(FGMs) [1]. Functionally graded materials available in nature as bones, teeth etc. [2], that are designed by nature to meet their expected service requirements. This concept is reproduced from nature to solve an engineering problem. Functionally graded materials (FGMs) are gaining interest from researchers during recent years since these are advanced materials which show improvement in properties like thermal, mechanical, light-weight, dimensional stability, barrier properties, flame retardancy, heat resistance and electrical conductivity [3][4]. Initially, FGMs were utilized as thermal barrier materials for aerospace structural applications and fusion reactors [5]. FGMs also found significance in structural components functioning under very high-temperature environments [6]. As the content of reinforcement in FGMs varies gradually in some direction leads to gradation in properties through the thickness of plate thus eliminates interface problems and reduces stress concentrations [7]. The carbon nanotubes have great stiffness and axial strength due to carbon-carbon Sp2 bonding. They are the excellent stiff materials [8] with Young's modulus of 1.4 TPa and tensile strength well above 100 GPa. The CNT reinforced functionally graded composite materials(FGCM) having a wide variety of applications in different technological areas such as aerospace, defence, energy, automobile, medicine, structural and chemical industry [9]. Researchers have been proposed a variety of plate theories to interpret the behavior of plates earlier. It is helpful to discuss some developments in plate theory a...

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“…Un cumul de connaissances et de théories des stratifiées d'ordre élevé ont été développées dans cet axe [1][2][3].…”

Section: Introductionunclassified

Buckling analysis of laminated composites plates on an elastic foundation using a new higher order theory

Benselama

Meiche

Bedia

2014

MATEC Web of Conferences

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buckling analysis of symmetric and antisymmetric laminated composites plates on an elastic foundation is examined by a new hyperbolic displacement model. The present theory with four variables is developed with formulation based on a new model which in plane displacements varies as a hyperbolic function across the plate thickness, so account for parabolic distribution of transverse shear stresses and satisfies boundary conditions. In this study, the elastic foundation is modeled as two Parameter Pasternak type foundation and Winkler type if the second parameter is zero. Governing equations are derived from the principle of virtual displacements. These plates' equations are solved analytically for the buckling by Navier's technique. Their buckling loads are found by solving the equation of stability .Some numerical results from the present study are presented in graphical and tabular form to comparison with other models published.Résumé: L'analyse du flambement des plaques stratifiées en matériaux composites, symétriques et antisymétriques simplement appuyées reposant sur une fondation élastique, est examinée par un nouveau modèle de déplacement hyperbolique. La nouvelle théorie à quatre variables est développée en tenant compte de la distribution parabolique des contraintes de cisaillement transversal. Dans cette étude, la fondation élastique est de type Pasternak de deux paramètres, et de type Winkler si le deuxième paramètre de fondation est nul. Les solutions analytiques sont obtenues en utilisant la solution de Navier, les charges critiques du flambement sont calculées en résolvant l'équation de stabilité. Les résultats numériques obtenus par l'analyse actuelle du flambement des plaques stratifiées sont comparés à ceux trouvés dans la littérature.

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Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory

Cited by 331 publications

References 42 publications

Vibration and buckling of composite beams using refined shear deformation theory

Vibration and buckling of composite beams using refined shear deformation theory

Static Bending Behavior of FG-CNT Reinforced Composite Plates Using Higher Order Shear Deformation Theory

Buckling analysis of laminated composites plates on an elastic foundation using a new higher order theory

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