Contact interaction between prestressed laminated shells of revolution and a flat foundation

A nonclassical model of shells that accounts for transverse shears and reduction is used to develop a method for solving the contact problem for inhomogeneous anisotropic shells of revolution subject to a field of mechanical and thermal loads. The prestresses are described by parametric terms in the linearized geometrically nonlinear equations of the second-order theory of flexible shells. The influence of the prestressed state of shells interacting with a flat surface on the contact area and the distribution of contact pressure is analyzed. Some computational features of the technique are discussed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 67–77, October 2006.     

Contact holographic interferometer for studying the deformation of small-curvature shells of revolution

The strains of a curvilinear surface are determined using holographic interferometry. Equations are derived to interpret the interference fringes for a shell of revolution. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 176–182, May–June, 2006.     

Postbuckling analysis of elastic shells of revolution considering mode switching and interaction

The postbuckling response of shells is known to exhibit complex phenomena including mode switching and interaction, particularly in the advanced postbuckling range. The existing literature contains many initial postbuckling analyses as well as advanced postbuckling analyses for a single buckling mode, but little work is available on the advanced postbuckling analysis of shells of revolution considering mode switching and interaction. In this paper, a numerical method for the advanced postbuckling analysis of thin shells of revolution subject to torsionless axisymmetric loads is presented, in which such mode switching and interaction are properly captured. Numerical results obtained using the present method for several typical problems not only demonstrate the capability of the method, but also lead to significant observations concerning the postbuckling behavior of thin shells of revolution. In particular, the results show that strong interaction between different harmonic modes may exist and the transition of deformation mode from one to another is gradual. Consequently, the conventional approach of finding the postbuckling path of a shell as the lower festoon curve of postbuckling paths of individual harmonic modes is not valid and is at best a convenient approximation.     

Stability of composite shells of revolution

An approach to solving the buckling problem for shells made of a composite material with one plane of elastic symmetry is presented. The approach employs complex Fourier series. The prebuckling stress-strain state is assumed to be geometrically nonlinear. The stability of a cylindrical shell under axial compression and uniform side pressure is analyzed using the Runge-Kutta method with discrete orthogonalization. The numerical results are compared with analytical solutions __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 109–124, March 2008.     

Torsional rigidity of shells of revolution

In this paper, the general equations of equilibrium for axisymmetrical deformation including the torsional deformation of revolutional shells are derived. It is shown that the shearing stress distribution due to torsion is independent of other stress components including those of membrane stress and bending stress. In this paper, the torsional deformation is considered to be represented by membrane action only, and also by the combined action of bending membrane deformation. It is shown that the main contribution of torsional rigidity is that related to membrane action.     

Laterally loaded elastic shells of revolution

Summary An alternate form of the Chernin type equations for laterally loaded shells of revolution is obtained. Except for terms of order of the inherent error in shell theory, the final two coupled second order ordinary differential equations are remarkably similar to the Reissner-Meissner type equations for problems involving axi-symmetric stress distributions. Unlike all previous versions, our two equations can be further reduced (just as in the case of axi-symmetric stress distributions) to a single second order equation for a complex stress function without any additional approximation for uniform cylindrical, spherical, conical and toroidal shells. The side force and tilting moment problem for a shell frustum is shown to be the static geometric analogue of the problem of asymmetric bending and twisting of a ring shell sector. An efficient method for the evaluation of the overall influence coefficients is discussed. The stress state of a complete uniform spherical shell subject to concentrated side force and tilting moment at the two poles is analyzed.

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Übersicht Es wird eine neue Form der Cherninschen Gleichung für rotationssymmetrische, seitlich belastete Schalen abgeleitet. Abgesehen von Gliedern, deren Größenordnung dem allgemeinen Fehler der Schalentheorie entspricht, haben die zwei gekoppelten gewöhnlichen Differentialgleichungen zweiter Ordnung eine merkwürdige Ähnlichkeit zu den von Reissner und Meissner abgeleiteten Gleichungen für Probleme mit axialsymmetrischem Spannungszustand. Zum Unterschied zu früheren Fassungen der Cherninschen Gleichungen können die jetzigen zu einer einzigen Gleichung zweiter Ordnung auf eine komplexe Spannungsfunktion zusammengefaßt werden, wie dies im Falle rotationssymmetrischer Spannung auch möglich ist. Dabei sind keine zusätzlichen Näherungen für gleichförmige Zylinder-, Kugel-, Kegel- und Ringflächenschalen notwendig. Es zeigt sich, daß das Problem der Beanspruchung einer Stumpfschale durch Seitenkraft und Momente statisch und geometrisch analog ist zum Problem der Beanspruchung eines Ringschalensektors durch unsymmetrische Biegung und Drillung. Es wird ein Verfahren zur Bestimmung der Einflußkoeffizienten angegeben. Außerdem wird der Spannungszustand in einer gleichförmigen vollständigen Kugelschale analysiert, die durch eine einzelne Seitenkraft und Momente an den zwei Polen beansprucht wird.

     

Axisymmetric deformation of poroelastic shells of revolution

A linear theory is developed for axisymmetric deformation of thin poroelastic shells of revolution. With fluid solid coupling included through Biot's consolidation theory, results are presented for cylindrical shells with an oscillating internal pressure and various surface boundary conditions on the fluid. First, the effects of fluid flow and shell inertia on the stretching behavior are studied through a separation of variables solution. Then, the bending behavior near a clamped edge is examined through an asymptotic solution of a matrix form of the governing equations. The results show that the asymptotic solution is accurate in the low frequency range, when the loading time is large compared to the consolidation time. In addition, for the examples studied, the fluid flow influences the membrane more than the bending behavior, but damping due to flow resistance is limited near resonance.     

Stability of shallow anisotropic shells of revolution

The paper outlines a method of analyzing layered anisotropic shells of revolution for stability using complex Fourier series. This simplifies the derivation of the basic equations compared with complete trigonometric Fourier series. Anisotropic shells in the form of a torus segment are analyzed for stability. This method allows optimizing the structure of the material and the geometry of the shell     

Introduction of shells of revolution in liquid

Moscow. Translated from Prikladnaya Mekhanika, Vol. 24, No. 12, pp. 39–44, December, 1988.     

Torsional-mode transients in variable-thickness shells of revolution

For thin shells of revolution the existence of torsional-vibration modes, uncoupled from bending and extensional modes, has been established[1]. Here a linear second-order differential equation for the uncoupled torsional stress mode is obtained and its solution for impact loading of shells is sought. The mode-superposition method which utilizes the natural modes of vibration predicted by elementary theory, is, in general, not satisfactory for sharp impact loading as many modes are often required for convergence. Hence we employ two novel techniques for solving the impact problems. Firstly a formal asymptotic procedure, based on extensions to geometrical optics, is employed to generate asymptotic wavefront expansions. Rigorous justifications for this formal technique are provided in an appendix. Secondly a transform technique whereby solutions are sought in terms of Bessel functions is discussed and applied to particular impact loading problems. The Bessel function solutions found here can be used to determine the natural frequencies of the shells. Shells both finite and infinite in extent are discussed and reflections at a stress-free end are examined.