Some Problems of Thin Circular Cylindrical Shells. I. The Equations

Buchwald, V. T.

doi:10.1002/sapm1967461237

Cited by 5 publications

(3 citation statements)

References 13 publications

(9 reference statements)

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“…For ECL, differences between the results are small, but with increase of the cylinder length the simplified stability equations lead to more and more overestimated results. This reflects a similar conclusion suggested by Buchwald (1967Buchwald ( , 1968 within the linear first-approximation theory of thin elastic shells. He found that some simplified versions of the linear shell equations for the cylinder, obtained by omitting some supposedly small terms, led to incorrect solution for long cylinders.…”

Section: Influence Of Different Approximations In the Derivation Of Tsupporting

confidence: 78%

On refined analysis of bifurcation buckling for the axially compressed circular cylinder

Opoka¹,

Pietraszkiewicz²

2009

International Journal of Solids and Structures

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a b s t r a c tWe present extensive numerical results of bifurcation buckling analysis of the axially compressed circular cylinder. The analysis is based on the modified displacement version of the non-linear theory of thin elastic shells developed by Opoka and Pietraszkiewicz [Opoka, S., Pietraszkiewicz, W., 2009. On modified displacement version of the non-linear theory of thin shells. International Journal of Solids and Structures, 46,[3103][3104][3105][3106][3107][3108][3109][3110]. To solve the buckling problem we apply the separation of variables and expansion of all fields into Fourier series in circumferential direction, with subsequent accurate calculations of eigenvalues of determinants of corresponding 8 Â 8 complicated matrices. The numerical analysis of the buckling load is performed for the cylinders with length-to-diameter ratio in the range (0.05, 60), with eight sets of incremental work-conjugate boundary conditions analogous to those used in the literature and partly summarized in the book by Yamaki [Yamaki, N., 1984. Elastic Stability of Circular Cylindrical Shells. Elsevier, Amsterdam], and additionally with six sets of boundary conditions not discussed in the literature yet. The results allow us to formulate several important conclusions, such as: (a) omission in the non-linear BVP small terms of the order of error introduced by the error of constitutive equations leads to overestimated buckling loads for long cylinders with clamped boundaries; (b) for some relaxed boundary conditions the buckling load decreases for short cylinders with decrease of the cylinder length; (c) the results for additional six sets of boundary conditions reveal existence of several new cases, in which by relaxing geometric boundary conditions the buckling load falls down to about one half of the classical value in a wide range of the cylinder length-to-diameter ratios.

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Section: Influence Of Different Approximations In the Derivation Of Tsupporting

confidence: 78%

On refined analysis of bifurcation buckling for the axially compressed circular cylinder

Opoka¹,

Pietraszkiewicz²

2009

International Journal of Solids and Structures

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“…-trigonometric series in combination with Fourier integral used by Darevskii [32,35,36], Grigolyuk and Tolkachev [30], Dem'yanovich [37], Kowalski and Perederii [53], Kozhekhmetov [54], Buchwald [118], Ting, Yuan [140];…”

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confidence: 99%

Fundamental-solution methods in stress-concentration problems for thin elastic shells

Шевченко

2007

Int Appl Mech

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This paper deals with fundamental-solution methods applied to stress-concentration problems for thin elastic shells. Publications concerned with the relevant division of the theory of plates and shells are reviewed. The theories behind the methods are described, and specific results for static and dynamic concentrated loads are presented. The capabilities of the methods are illustrated by fracture problems for orthotropic shells with notches and holes under mechanical loading and for isotropic shells with notches under thermal loading Introduction. The intensive use of thin-walled shells of different configurations in various branches of modern mechanical engineering (aeronautical engineering and space technology, chemical engineering, shipbuilding, etc.) raises new challenges associated with the theoretical strength analysis of shells with stress concentrators. This involves problems of stress concentration in shells in the presence of local mechanical and thermal fields, holes, notches, elastic or rigid punches, ribs, etc. There are solutions only to special cases of such problems for mainly spherical and cylindrical shells.Extending the research to shells with various elastic properties and geometries requires a mathematical apparatus that would allow us to quickly solve complicated boundary-value problems for shells. It is efficient to reduce such problems to integral or integro-differential equations. This approach involves construction of fundamental solutions to the equations of shell theory-solutions corresponding to single concentrated forces.Thus, developing methods to construct fundamental solutions for shells with arbitrary geometries and elastic properties and using these solutions to solve stress-concentration problems for shells under local mechanical and thermal loads are a crucial task of double interest. First, this is a mathematical apparatus for deriving boundary integral equations for mixed problems of shell theory. Second, this is a model for strength analysis of shells under concentrated (or distributed over small sites) mechanical and thermal loads.The present paper describes methods for stress-strain analysis of shells under various mechanical and thermal local loads (concentrated forces, moments, temperature, thermal sources, loads distributed over small areas, etc.). The results to be discussed have been obtained using a modern mathematical apparatus based on the theory of distributions, Fourier transforms, and the theory of fundamental solutions and special functions. 1. Review of Fundamental-Solution Methods. A great many domestic and foreign studies are concerned with the development of methods to construct fundamental solutions to the equations of the theory of thin elastic shells. Problem formulations, solution techniques, and some specific solutions can be found in publications by Ambartsumyan [3], Vlasov [16], Vorovich [18], Gatimov [19], Gol'denveizer [23-25], Grigolyuk and Tolkachev [30], Darevskii [32-36], Grigorenko [31], Zhigalko [47], Mossakovskii and Hudramovych [62], Novo...

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“…">I n t r o d u c t i o nThe worst error in the result of most of the well known shell theories usually arises when the deformation is associated with a low waves number [l, 21. This is largely due to the fact that no part of the shell can any longer be regarded as a shallow shell [2]. Examining the accuracy of a shell theory causes formidable difficulties even for the linear case.…”

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confidence: 99%

A Note on the Accuracy of the Nonlinear Shell Equations in the Post Buckling Range

Naschie

Hosni

1977

Z Angew Math Mech

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Some Problems of Thin Circular Cylindrical Shells. I. The Equations

Cited by 5 publications

References 13 publications

On refined analysis of bifurcation buckling for the axially compressed circular cylinder

On refined analysis of bifurcation buckling for the axially compressed circular cylinder

Fundamental-solution methods in stress-concentration problems for thin elastic shells

A Note on the Accuracy of the Nonlinear Shell Equations in the Post Buckling Range

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