Vibration of thin shells of revolution based on a mixed finite element formulation

Altman, Wolf; Neto, Eliseu Lucena

doi:10.1016/0045-7949(86)90221-x

Cited by 11 publications

(2 citation statements)

References 8 publications

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“…In addition to the analytic method [1], alternative methods have been proposed including the ÿnite di erence [2], transfer matrix [3] and ÿnite element methods [4][5][6][7]. Among these various methods, the ÿnite element method is recognized as the most powerful analysis tool.…”

Section: Introductionmentioning

confidence: 99%

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

Kim

2001

Numerical Meth Engineering

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In this study, we present free vibration analysis of shells of revolution using the hybrid-mixed ÿnite element. The present hybrid-mixed element, which is based on the modiÿed Hellinger-Reissner variational principle, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical di culties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out by the Guyan reduction. Several numerical examples show that the present element with cubic displacement interpolation functions and consistent quadratic stress functions is highly accurate for the free vibration analysis of shells of revolution, especially for higher vibration modes.

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Section: Introductionmentioning

confidence: 99%

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

Kim

2001

Numerical Meth Engineering

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“…A clamped hemispherical dome with radius a and uniform thickness t (a/t = 100), see Figure 3, is considered [51,52]. The values of the non-dimensional frequency parameter λ = aω (j) (ρ/E) 1/2 are reported in Table 2, for the first six modes and for different values of the harmonic number j.…”

Section: Clamped Hemispherical Shell In Free Vibrationmentioning

confidence: 99%

NURBS-Based Collocation Methods for the Structural Analysis of Shells of Revolution

Bellis

Artioli

2016

Metals

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Abstract:In this work we present a collocation method for the structural analysis of shells of revolution based on Non-Uniform Rational B-Spline (NURBS) interpolation. The method is based on the strong formulation of the equilibrium equations according to Reissner-Mindlin theory, with Fourier series expansion of dependent variables, which makes the problem 1D. Several numerical tests validate convergence, accuracy, and robustness of the proposed methodology, and its feasibility as a tool for the analysis and design of complex shell structures.

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Free Vibration Analysis of Kirchhoff Plates Resting on Elastic Foundation by Mixed Finite Element Formulation Based on Gâteaux Differential

Omurtag¹,

Özütok²,

Aköz³

et al. 1997

Int. J. Numer. Meth. Engng.

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SUMMARYThe main objective of the present work is to give the systematic way for derivation of Kirchhoff plate-elastic foundation interaction by mixed-type formulation using the GaL teaux differential instead of well-known variational principles of Hellinger-Reissner and Hu-Washizu. Foundation is a Pasternak foundation, and as a special case if shear layer is neglected, it converges to ¼inkler foundation in the formulation. Uniform variation of the thickness of the plate is also included into the mixed finite element formulation of the plate element PLTVE4 which is an isoparametric C class conforming element discretization. In the dynamic analysis, the problem reduces to solution of the standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and at each node transverse displacement two bending and one torsional moment is the basic unknowns. Proper geometric and dynamic boundary conditions corresponding to the plate and the foundation is given by the functional. Performance of the element for bending and free vibration analysis is verified with a good accuracy on the numerical examples and analytical solutions present in the literature.

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Vibration of thin shells of revolution based on a mixed finite element formulation

Cited by 11 publications

References 8 publications

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

NURBS-Based Collocation Methods for the Structural Analysis of Shells of Revolution

Free Vibration Analysis of Kirchhoff Plates Resting on Elastic Foundation by Mixed Finite Element Formulation Based on Gâteaux Differential

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