Linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

In this paper we present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region Ω onto a disk with circular slits. The method is based on some uniquely solvable boundary integral equations with classical adjoint and generalized Neumann kernels. These boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. Some numerical examples are presented to illustrate the efficiency of the presented method.     

An optimal compressed circular cylindrical shell

The stability is considered for a shell of optimum weight. An isotropic shell is found to be suitable, and the bifurcation in the undeformed state can occur via an axially symmetric or other form. This explains the sensitivity of an isotropic shell to perturbation.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 944–947, September–October, 1973.     

Symmetric deformation of a circular cylindrical shell of variable wall thickness

Zusammenfassung Es werden für die Differentialgleichung der Biegung einer zylindrischen Schale mit kreisförmigem Querschnitt und veränderlicher Wandstärke Lösungen in Form bekannter Funktionen angegeben.

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Supported by the Office of Naval Research under contract with the Massachusetts Institute of Technology.     

Approximation of a circular cylindrical shell by Clough-Johnson flat plate finite elements

Summary In this paper, we study the approximation of a right circular cylindrical shell by a nonconforming method using Clough-Johnson flat plate finite elements. Compatibility conditions which have to be satisfied by the degrees of freedom at every node of the triangulation are given. Then, we prove that convergence is insured for shallow shells when using particular families of triangulations which are practically easy to implement. Finally, we propose a new approximation method by flat plate finite elements which assures the convergence for any kind of circular cylindrical shell.     

Bending of a cantilevered glass-reinforced plastic cylindrical shell weakened by a circular opening

The stress concentration is investigated in the neighborhood of a circular opening in a cantilevered glass-reinforced plastic cylindrical shell with a concentrated load at the free end. The problem is solved by the Bubnov method using a Ural-2 computer. The theoretical results have been checked experimentally on glass-reinforced plastic shells.All-Union Correspondence Polytechnic Institute, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 152–157, January–February, 1970.     

Elastic buckling of an axially compressed open circular cylindrical shell

The paper is devoted to stability problem of an axially compressed open elastic circular cylindrical shell. Two curvilinear edges of the open cylindrical shell are simply supported while two straight edges are free. Two load cases of the shell are assumed. The first load case ‐ was the invariable axially normal force intensity, and the second load case ‐ the linearly varying axially normal force intensity. Critical loads of the shell for both load cases are determined. These critical loads are compared with a classical load for closed circular cylindrical shell. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges

The problem of the existence of natural oscillations of a thin elastic orthotropic circular closed cylindrical shell with free and hinge-mounted ends and of an open cylindrical shell with free and hinge-mounted edges, when the two boundary generatrices are hinge-mounted is investigated. Dispersion equations and asymptotic formulae for finding the natural frequencies of possible vibration modes are obtained using the system of equations corresponding to the classical theory of orthotropic cylindrical shells. A mechanism is proposed by means of which the vibrations can be separated into possible types. Approximate values of the dimensionless characteristic of the natural frequency and the attenuation characteristic of the corresponding vibration modes are obtained using the examples of closed and open orthotropic cylindrical shells of different lengths.     

The stressed state of a cylindrical shell with a circular neck loaded by internal pressure

We study the stressed state of a thin cylindrical shell with a circular neck loaded by a constant internal pressure. We start from the equations obtained using Reissner's variational principle applying expansions of the components of the stress tensor and the displacement vector with respect to the coordinates along the normal to the base surface of the shell. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Stability of shear-compliant cylindrical shells connected with an elastic foundation in a geometrically nonlinear formulation

The effect of transverse shear strains on the stability "in the large" of a cylindrical transversal-isotropic shell with an elastic filler under the effect of axial compression is investigated. The length of the cylindrical shell is assumed to be greater than the diameter. The approximate solution is obtained by the Bubnov-Galerkin method. Such a problem for an isotropic shell was considered earlier in [2, 4] on the basis of the equations of the classical Kirchhoff-Love theory.L'vov Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR. Ternopol Branch, L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 113–117, January–February, 1972.     

The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside

In this paper we investigate two systems consisting of a spherical shell rolling without slipping on a plane and a moving rigid body fixed inside the shell by means of two different mechanisms. In the former case the rigid body is attached to the center of the ball on a spherical hinge. We show an isomorphism between the equations of motion for the inner body with those for the ball moving on a smooth plane. In the latter case the rigid body is fixed by means of a nonholonomic hinge. Equations of motion for this system have been obtained and new integrable cases found. A special feature of the set of tensor invariants of this system is that it leads to the Euler — Jacobi — Lie theorem, which is a new integration mechanism in nonholonomic mechanics. We also consider the problem of free motion of a bundle of two bodies connected by means of a nonholonomic hinge. For this system, integrable cases and various tensor invariants are found.     

The response of a plastic cylindrical shell to axial impact

Zusammenfassung Es wird eine Theorie des plastischen Knichens zylindrischer Schalen unter axialer Stossbelastung aufgestellt und eine Formel angegeben für die Stossgeschwindigkeiten, weilche in einer gegebenen Schale kleine Biegewellen erzeugen. Ferner wird eine einfache Berechnungsmethode für die Eigenfunktionen der Biegeschwingungen angegeben. Die Übereinstimmung der Theorie mit Versuchsergebnissen ist gut.     

Bifurcation theory applied to buckling states of a cylindrical shell

Veins, bronchii, and many other vessels in the human body are flexible enough to be capable of collapse if submitted to suitable applied external and internal loads. One way to describe this phenomenon is to consider an inextensible elastic and infinite tube, with a circular cross section in the reference configuration, subjected to a uniform external pressure. In this paper, we establish that the nonlinear equilibrium equation for this model has nontrivial solutions which appear for critical values of the pressure. To this end, the tools we use are the Liapunov-Schmidt decomposition and the bifurcation theorem for simple multiplicity. We conclude with the bifurcation diagram, showing the dependence between the cross-sectional area and the pressure.     

Parametric oscillations of a viscoelastic cylindrical shell

The formulation of the problem of parametric oscillations of viscoelastic shells is given. It was shown that this problem is reduced to the study of the equations, investigated in [4, 5].Moscow Institute of Geodesy, Aerophotography, and Cartography Engineers. Translated from Mekhanika Polimerov, No. 3, pp. 479–483, May–June, 1974.     

Dynamic stability of a porous cylindrical shell

This paper is devoted to a closed cylindrical shell made of a porous-cellular material. The mechanical properties vary continuously on the thickness of a shell. The mechanical model of porosity is as described as presented by Magnucki, Stasiewicz. A shell is simply supported on edges. On the ground of assumed displacement functions the deformation of shell is defined. The displacement field of any cross section and linear geometrical and physical relationships are assumed in cylindrical coordinate system. The components of deformation and stress state were found. Using the Hamilton's principle the system of differential equations of dynamic stability is obtained. The forms of unknown functions are assumed and the system of a differential equations is reduced to a simple ordinary equation of dynamic stability of shell (Mathieu's equation). The derived equation are used for solving a problem of dynamic stability of porous-cellular shell with intensity of load directed in generators of shell. The critical loads are derived for a family of porous shells. The unstable space of family porous shells is found. The influence a coefficient of porosity on the stability regions in Figures is presented. The results obtained for porous shell are compared to a homogeneous isotropic cylindrical shell. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber

The nonlinear interaction of a laminar flow and a sprung rigid circular cylinder results in vortex-induced vibration (VIV) of the cylinder. Passive suppression of the VIV by attaching an internal nonlinear vibration absorber that acts, in essence, as a nonlinear energy sink (NES) to the cylinder has been observed in finite-element computations involving thousands of degrees of freedom (DOF). A single-DOF self-excited oscillator is developed to approximate the limit-cycle oscillation (LCO) of the cylinder undergoing VIV. This self-excited oscillator models the interaction of the flow and the cylinder. Then, a two-DOF reduced-order model for the system with the internal NES is constructed by coupling the single-DOF NES to the single-DOF self-excited oscillator. Hence, the complicated high-dimensional system of flow-cylinder-NES involving thousands of DOF is reduced to a two-DOF model. The two targeted energy transfer mechanisms responsible for passive VIV suppression that are observed in the finite-element computations are fully reproduced using the two-DOF reduced-order model. This reduction of the dynamics to an easily tractable low-dimensional reduced-order model facilitates the approximate analysis of the underlying dynamics. Moreover, the underlying assumptions of the order reduction, and the parameter ranges of validity of the reduced-order model are formulated and systematically studied.