Non-linear Vibrations of Deep Cylindrical Shells by the<i>p</i>-Version Finite Element Method

Ribeiro, Pedro; Cochelin, Bruno; Bellizzi, Sergio

doi:10.1155/2010/291043

Cited by 13 publications

(6 citation statements)

References 21 publications

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“…[167] a shooting method in conjunction with the Newton method was utilized to solve the equations of motion and to obtain the non linear frequency response curves. Similar finite element formulations were presented by Ribeiro et al [168] to study non linear vibrations of deep cylindrical panels.…”

Section: Cylindrical and Doubly Curved Panelsmentioning

confidence: 79%

Non-linear vibrations of shells: A literature review from 2003 to 2013

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

214

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International audienceThe present literature review focuses on geometrically non linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non linear vibrations of shells subjected to normal and in plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non linear vibrations of shells and panels, including (i) fluid structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non linear normal modes and meshless methods are reviewed in depth

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Section: Cylindrical and Doubly Curved Panelsmentioning

confidence: 79%

Non-linear vibrations of shells: A literature review from 2003 to 2013

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

214

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“…Generally, the p-version FEM is superior to the traditional h-version FEM. The application of the p-version FEM in three dimensions, including in three -dimensional linear elastic fracture analysis, can be found in [ 21 , 22 , 23 , 24 , 25 , 26 , 27 ].…”

Section: P-version Finite Element Methods and Contour Integral Methods In Three Dimensionsmentioning

confidence: 99%

Direct Computation of 3-D Stress Intensity Factors of Straight and Curved Planar Cracks with the P-Version Finite Element Method and Contour Integral Method

Zhang

et al. 2021

Materials

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This paper presents direct computations of 3-D fracture parameters including stress intensity factors (SIFs) and T-stress for straight and curved planar cracks with the p-version finite element method (P-FEM) and contour integral method (CIM). No excessive singular element or enrichment function is required for the computation. To demonstrate the accuracy and efficiency of the proposed approaches, several benchmark numerical models of 3-D planar straight and curved cracks with single and mixed-mode fractures are considered and analyzed: a through thickness edge straight crack in a homogeneous material, a through thickness inclined straight crack, a penny-shaped crack embedded in a cube and a central ellipse shaped crack in a homogeneous cube. Numerical results are analyzed and compared with analytical solutions and those reported by the extended finite element method (XFEM) and the scaled boundary finite element method (SBFEM) in the available literature. Numerical experiments show the accuracy, robustness and effectiveness of the present method.

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“…This is not a large value and, according to Leissa and Narita (1984), Singh and Kumar (1996) and Qatu (2004), R ¼ 2a is the limit until which a shell can be considered to be shallow. Ribeiro et al (2010) computed the natural frequencies of a shell where R ¼ 2a using shallow shell and non-shallow shell approaches; the values provided by the two approaches were rather close. Ventsel and Krauthammer (2001) indicate more limitative values, such that @w i x, y ð Þ=@x À Á 2 is not superior to 0.05.…”

Section: Formulationmentioning

confidence: 98%

Linear modes of vibration of cylindrical shells in composite laminates reinforced by curvilinear fibres

Ribeiro

2016

Journal of Vibration and Control

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Modes of vibration of thin cylindrical shells made up of layers with curvilinear fibres (variable stiffness composite laminates (VSCL) shells) are investigated in the linear regime. A p-version finite element type formulation is developed for that purpose; in the absence of data on vibrations of cylindrical VSCL shells, the formulation is verified by comparisons with published data on laminated shells reinforced by straight fibres and on VSCL plates. Parametric studies are performed, in order to investigate how curvilinear fibre paths can influence the modes of vibration. It is found that curvilinear fibre paths can have a very large effect, larger than on plates, on the natural frequencies and natural mode shapes of vibration of cylindrical shells. Factors that strongly influence the modes of vibration of VSCL shells are found; these include the fibre orientation at boundaries and in relation to principal normal sections.

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Non-linear Vibrations of Deep Cylindrical Shells by thep-Version Finite Element Method

Cited by 13 publications

References 21 publications

Non-linear vibrations of shells: A literature review from 2003 to 2013

Non-linear vibrations of shells: A literature review from 2003 to 2013

Direct Computation of 3-D Stress Intensity Factors of Straight and Curved Planar Cracks with the P-Version Finite Element Method and Contour Integral Method

Linear modes of vibration of cylindrical shells in composite laminates reinforced by curvilinear fibres

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