Laminated beam analysis by polynomial, trigonometric, exponential and zig-zag theories

Carrera, Erasmo; Filippi, Matteo; Zappino, Enrico

doi:10.1016/j.euromechsol.2013.02.006

Cited by 111 publications

(45 citation statements)

References 44 publications

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“…Structural models included thin-walled sections, point loads and shell-like natural modes, whereas further studies have been addressed towards the analysis of open cross-sections, lateral edge enforced boundary conditions and layer-wise approaches [40]. Moreover, in [40] the displacement field across the section was modeled by means of Lagrange polynomials, whereas in [41] trigonometric, exponential and zig-zag theories have been used.…”

Section: Introductionmentioning

confidence: 99%

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

Filippi

Pagani

Petrolo

et al. 2015

Composite Structures

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Please cite this article as: Filippi, M., Pagani, A., Petrolo, M., Colonna, G., Carrera, E., Static and free vibration analysis of laminated beams by refined theory based on Chebyshev Polynomials, Composite Structures (2015), doi: http://dx.Abstract This paper presents a new class of refined beam theories for static and dynamic analysis of composite structures. These beam models are obtained by implementing higher-order expansions of Chebyshev polynomials for the three components of the displacement field over the beam cross-section. The Carrera Unified Formulation (CUF) is adopted to obtain higher-order beam models. The governing equations are written in terms of fundamental nuclei, which are independent of the choice of the expansion order and the interpolating polynomials. Static and free vibration analysis of laminated beams and thin walled boxes has been carried out. Results obtained with the novel Chebyshev Expansion (CE) model have been compared with those available in the literature. For comparison, Taylor-like Expansion (TE) and Lagrange Expansion (LE) CUF models, commercial codes, analytical and experimental data are exploited. The performances of refined beam models in terms of computational cost and accuracy in comparison to the reference solutions have been assessed. The analysis performed has pointed out the high level of accuracy reached by the refined beam models with lower computational costs than 2D and 3D Finite Elements.

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Section: Introductionmentioning

confidence: 99%

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

Filippi

Pagani

Petrolo

et al. 2015

Composite Structures

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“…In previous papers, encouraging results were obtained by using several advanced theories based on trigonometric, exponential, polynomials and miscellaneous expansions for the study of composite structures. For a thorough and clear description of the new displacement theories, the authors suggest [22,23]. An example of a displacement model which can be used is the following:…”

Section: The Carrera Unified Formulationmentioning

confidence: 99%

“…As said before, the reader can refer to [22,23] for a more detailed description of the used displacement fields.…”

Section: Nomenclature Used To Denote Various Expansionsmentioning

confidence: 99%

“…CUF was initially introduced for the development of refined plate and shell theories [20] and later extended to beam formulation [21]. CUF has been extensively used for dealing with a wide range of structural problems including, for instance, the static and dynamic analysis of composite structures [22,23,24,25], the free vibration analysis of rotors [26] and FG structures [27,28,29] and the study of the mechanical behaviour of structures with unconventional cross-sections [30,31]. In particular, with regard to the static behaviour of FG structures, the unified formulation was previously adopted by Tornabene et al [32] and Cinefra [33], which developed refined 2D theories using the Differential Quadrature Method and the Finite Element approach, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Static analyses of FGM beams by various theories and finite elements

Filippi

Carrera

Zenkour

2015

Composites Part B: Engineering

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133

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“…Only some of many papers devoted to bending, vibration and buckling of fiber reinforced composite beams-type structures are cited here [1][2][3][4][5][6][7][8][9][10]. A development of a new kinds of progressive composites such as functionally graded materials (FGM) in recent years is in a rapid increase.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear buckling behaviours of thin-walled functionally graded open section beams

Lanc

Turkalj

et al. 2016

Composite Structures

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Laminated beam analysis by polynomial, trigonometric, exponential and zig-zag theories

Cited by 111 publications

References 44 publications

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

Static analyses of FGM beams by various theories and finite elements

Nonlinear buckling behaviours of thin-walled functionally graded open section beams

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