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Journal ArticleDOI

Dynamic finite element method for generally laminated composite beams

01 Mar 2008-International Journal of Mechanical Sciences (Pergamon)-Vol. 50, Iss: 3, pp 466-480
TL;DR: In this paper, a dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory, where the influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformations and rotary inertia are incorporated in the formulation.
About: This article is published in International Journal of Mechanical Sciences.The article was published on 2008-03-01. It has received 72 citations till now. The article focuses on the topics: Simple shear & Finite element method.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors review most of the research done in recent years (1989-2012) on the vibration analysis of composite beams, with emphasis given to the theory being applied (thin, thick, layerwise), methods for solving equations (finite element analysis, differential transform and others) experimental methods, smart beams (piezoelectric or shape memory), complicating effects in both material and structure, and other areas that have been considered in research.

153 citations

Journal ArticleDOI
TL;DR: In this article, a general formulation for free and transient vibration analyses of composite laminated beams with arbitrary lay-ups and any boundary conditions is presented, based on a modified variational principle combined with a multi-segment partitioning technique.

67 citations


Cites methods from "Dynamic finite element method for g..."

  • ...[42] FBT...

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  • ...It should be further remarked here that many of the commonly used methods, such as the closed-form method [3,16,21,22,33,34] and the dynamic stiffness method [40–44], are mainly restricted to free vibration analysis; they soon become cumbersome when one wants to deal with the dynamic response problems of composite beams under arbitrary loading cases....

    [...]

  • ...For the cross-ply beam, the present results are compared with those FBT solutions obtained by the modified varational method [38] and the dynamic stiffness method [42], whereas for the angle-ply beam, the present solutions are compared with the corresponding values obtained by HBT[LST] [43] and HBT[R] [54]....

    [...]

  • ...They include, but are not limited to, the closed-form solution [3,16,21,22,33,34], variational method [35–39], dynamic stiffness method [40–44], transfer matrix method [45–47], differential quadrature method [48,49], meshless method [50], finite difference method [51–53], and finite element method [54–56]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a modified Fourier-Ritz approach has been adopted to analyze the free vibration of axially loaded laminated composite beams with arbitrary layup and general boundary conditions, which include classical boundaries, elastic boundaries, and their combination.
Abstract: In this paper, a modified Fourier–Ritz approach has been adopted to analyze the free vibration of axially loaded laminated composite beams with arbitrary layup and general boundary conditions, which include classical boundaries, elastic boundaries, and their combination. The influences of Poisson effect, axial deformation, couplings among extensional, bending and torsional deformations, shear deformation, and rotary inertia are incorporated in the formulation. In this present method, regardless of boundary conditions, the displacements and rotation components of the beam are invariantly expressed as a standard Fourier cosine series and several auxiliary closed-form functions. These auxiliary functions are introduced to eliminate any potential discontinuities of the original displacement function and its derivatives, throughout the whole beam including its ends, and to effectively enhance the convergence of the results. Since the displacement field is constructed to be adequately smooth in the whole soluti...

53 citations


Cites background or methods from "Dynamic finite element method for g..."

  • ...Good agreement generally exists between the values available in Jun et al.(7) and those calculated with the present method....

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  • ...The reference results were reported by Jun et al.(7) using the dynamic FEM on the basis of FSDT....

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  • ...The reference results were reported by Jun et al.7 using the dynamic FEM on the basis of FSDT....

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  • ...Good agreement generally exists between the values available in Jun et al.7 and those calculated with the present method....

    [...]

  • ...Error (%) Present Jun et al.(7) Error (%)...

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Journal ArticleDOI
TL;DR: In this article, the free vibration of carbon nanotubes reinforced composite beams is analyzed using the first-order shear deformation theory and the finite element method with various boundary conditions.
Abstract: In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.

49 citations

Journal ArticleDOI
TL;DR: Based on the nonlocal strain gradient theory, the effect of axial magnetic field on the free vibration and mechanical buckling responses of an FG graphene-reinforced sandwich deep curved nanobeam with viscoelastic core embedded in a viscocelastic medium is elucidated in this article.
Abstract: Based on the nonlocal strain gradient theory, the effect of an axial magnetic field on the free vibration and mechanical buckling responses of an FG graphene-reinforced sandwich deep curved nanobeam with viscoelastic core embedded in a viscoelastic medium is elucidated in this paper. The curved beam is also assumed to be exposed to axial external compressions. The volume fraction of the constituents of the composite face layers are presumed to be functionally graded through the thickness according to a layer-wise law. The material properties are calculated in the framework of Halpin-Tsai micromechanical scheme. Lorentz magnetic force is deduced employing electro-dynamic Maxwell's relations for a conducting body. According to a refined shear and normal deformations curved beam theory, the motion equations are introduced in the polar coordinates. Analytical solutions are obtained for the natural frequencies and critical buckling load of the viscoelastic sandwich curved nanobeams. By comparing the present results with the available data in the literature, the developed formulations are validated. Furthermore, other several numerical examples are performed to show the effects of different parameters including viscoelastic core thickness, magnetic field, structural and foundation damping factor, opening angle and graphene concentration on the frequency and buckling load of the viscoelastic sandwich curved beams.

47 citations

References
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Book
01 Jan 1978
TL;DR: This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.
Abstract: Introduction. Mathematical approximations have been used since ancient times to estimate solutions, but with the rise of digital computing the field of numerical analysis has become a discipline in its own right. Numerical analysts develop and study algorithms that provide approximate solutions to various types of numerical problems, and they analyze the accuracy, efficiency and robustness of these algorithms. As technology becomes ever more essential for the study of mathematics, learning algorithms that provide approximate solutions to mathematical problems and understanding the accuracy of such approximations becomes increasingly important. This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis.

7,315 citations

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TL;DR: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 1.0 as mentioned in this paper, including 16 pages of full-color graphics.
Abstract: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 2.0. This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users of Mathematica will need this edition. Includes 16 pages of full-color graphics.

2,894 citations

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Stephen Wolfram1
01 Apr 1991
TL;DR: This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users ofMathematica will need this edition.
Abstract: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 2.0. This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users of Mathematica will need this edition. Includes 16 pages of full-color graphics.

2,567 citations

Journal ArticleDOI
Abstract: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.

490 citations

Journal ArticleDOI
TL;DR: A review of displacement and stress based refined theories for isotropic and anisotropic laminated plates is presented in this paper, together with their merits and demerits, where exact elasticity solutions for the plate problems are cited.
Abstract: A review of displacement and stress based refined theories for isotropic and anisotropic laminated plates is presented. Various equivalent single layer and layerwise theories for laminated plates are discussed together with their merits and demerits. Exact elasticity solutions for the plate problems are cited, wherever available. Various critical issues related to plate theories are presented, based on the literature reviewed.

342 citations