On the deformation of a ribbed cylindrical shell with initial deflection under dynamic loading

Shul’ga, N. À.; Bogdanov, S. Yu.

doi:10.1007/s10778-006-0045-8

Cited by 4 publications

(1 citation statement)

References 6 publications

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“…[ the integro differential method of constructing difference schemes to find the response of conical shells with different taper angles subjected to an impulsive load. The same authors [143] proposed a numerical scheme based on the finite difference method to study the dynamic stress strain state of reinforced circular cylindrical shells subjected to different initial deflections. Vibrations of discretely ribbed, reinforced shells were also investigated by Meish and Kairov [144] based on the Timoshenko shell theory and using a finite difference scheme.…”

Section: Forced Vibrations Of Shells Subjected To Other Types Of Loadmentioning

confidence: 99%

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: Forced Vibrations Of Shells Subjected To Other Types Of Loadmentioning

confidence: 99%

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

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

214

View full text Add to dashboard Cite

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On numerical solution of dynamic problems in the theory of reinforced shells

et al. 2006

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Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed Keywords: reinforced cylindrical shell, Timoshenko model, discrete ribs, forced vibration, numerical algorithm, Richardson extrapolationThere are two basic approaches to the stress-strain analysis of reinforced shells: use of a structurally orthotropic model [1] and use of a model that allows for the discreteness of ribs [2]. During forced vibration of reinforced thin-walled shells, the presence of inhomogeneities and the wave nature of the process strongly affect the redistribution of the fields of material parameters. This situation suggests incorporating discrete ribs into the shell model, which would in turn complicate problem statements. The complexity of problem statements (boundary conditions, geometrical nonlinearity or geometrical and physical nonlinearities, the inhomogeneity of shells across the thickness, etc.) in the theory of discretely reinforced shells [4-6, 8-13, 17-21] calls for the use of numerical methods. If finite-difference methods are used, then the following two approaches are possible: shock capturing and isolation of spatial discontinuities [3]. The former approach helped to solve several problems for reinforced shells of revolution (cylindrical, spherical, and conical ones) under forced vibration. A numerical analysis shows that with such an approach the site of a rib smears over several spacings. Satisfactory solutions can be obtained from fairly fine meshes for reinforced shells under distributed loads [5,16,17,21]. In the case of boundary loads, the approach produces significant errors, which makes it impossible to accurately locate spatial discontinuities [3,8,16]. Finite-difference schemes with isolation of spatial discontinuities allow increasing the accuracy of solutions for shells reinforced with discrete ribs. Such an approach was used to solve dynamic problems for reinforced shells under distributed and boundary loads [4,6,[10][11][12][13][18][19][20]. However, even this approach provides in some cases poor convergence because of spatial discontinuities.The present paper gives a geometrically nonlinear formulation to problems for shells reinforced with discrete ribs and outlines an algorithm of numerical solution based on the Timoshenko theory of shells and rods. It is proposed to use finite-difference schemes with Richardson extrapolation [7]. We conducted computations for reinforced cylindrical shells. The numerical results allow us to judge the efficiency of our method.

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On stability of cylindrical shells of variable thickness with initial imperfections

2009

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The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution Keywords: cylindrical shell, reliability against buckling, probabilistic approach, initial imperfections Introduction. The current state of the art permits creating highly reliable structures. Thin-walled shells lose their load-carrying capacity by buckling [2-8, 10, 12-15], which characterizes their reliability. In this paper, we propose a numerical method for the stability analysis of cylindrical shells with initial imperfections [5, 6] and use the probabilistic approach developed in [1] and tested in [11] to determine the reliability against buckling of a cylindrical shell with initial imperfections and variable wall thickness under surface pressure.1. Problem Statement. The reliability of structures is known to be strongly dependent on the probabilistic characteristics of the initial imperfections. By defining the probability density of initial imperfections, we can find the probability density of the critical load as a scalar random variable. The functional dependence of the critical load on the initial imperfections permits defining the reliability against buckling as the probability that a structure will not buckle if the load is less than a certain level:

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On the deformation of a ribbed cylindrical shell with initial deflection under dynamic loading

Cited by 4 publications

References 6 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

On numerical solution of dynamic problems in the theory of reinforced shells

On stability of cylindrical shells of variable thickness with initial imperfections

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