Effect of an elastic core on the dynamic stability of an orthotropic cylindrical shell

A method of determining the regions of dynamic instability of an orthotropic cylindrical shell "bonded" to an elastic cylinder is proposed. An expression for the core reaction is obtained from the coupling conditions for the forces normal to the lateral surface and the radial displacements of the shell and the core at the contact surface. When the reaction is substituted in the system of equations of motion of the shell, the part corresponding to the free vibrations of the cylinder is discarded. The system of equations of motion of the shell is reduced to an equation of Mathieu type, from which transcendental equations for determining the boundaries of the regions of dynamic instability are obtained. These regions are analyzed for various modes of loss of stability and different values of the core modulus of elasticity.     

Effect of transverse shear on the stability of an orthotropic cylindrical shell with an elastic core in axial compression

The effect of transverse shear on the stability of a composite shell in axial compression has been investigated. The core is treated as an isotropic elastic cylinder bonded to the inner surface of the shell. The effect of the tangential shearing forces between the shell and the core is taken into account.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 267–273, March–April, 1973.     

Dynamic stability of an elastic orthotropic cylindrical shell with allowance for transverse shears

The resolvents for the dynamic stability of an elastic orthotropic cylindrical shell are obtained in accordance with the Ambartsumyan and Timoshenko-type refined theories. The regions of instability given by the classical and refined theories are compared. The dependence of the refinements on the shell parameters, the shear moduli of the material, and the buckling modes are investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–320, March–April, 1973.     

Long-time stability of orthotropic cylindrical shells under external pressure

The problem is solved using a refined theory of shells that takes shear strains into account. The shell deformations are described by means of the relations for an orthotropic material, it being assumed that creep strains develop only as a result of shear forces. The geometrically linear problem is considered. For the sake of comparison, the long-time critical load is calculated on a Minsk-22 computer using the Kirchhoff-Love and refined models. It is shown that when shears are taken into account, in certain cases the critical load may be reduced by 30%.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 315–320, March-April, 1969.     

Torsional stability of a glass-reinforced plastic cylindrical shell with an elastic core

The problem of the stability of a glass-reinforced plastic cylindrical shell with an elastic core subjected to twisting moments applied to the edges of the shell is considered. As in various other studies [4–6], the glass-reinforced plastic is treated as an elastically orthotropic material. The core is treated as an isotropic elastic cylinder, whose outer surface is bonded to the shell. Expressions for the critical stresses are obtained for an infinitely long shell and a shell of finite length.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1082–1086, November–December, 1970.     

Linear-heredity analysis of orthotropic cylindrical shells with initial deflection subjected to external pressure

The bending of a cylindrical shell with initial deflection under the long-time action of external hydrostatic pressure is investigated on the basis of the theory of linear heredity. The material of the shell is assumed to be orthotropic. The problem is solved in the geometrically linear formulation.Translated from Mekhanika Polimerov, No. 4, pp. 680–686, July–August, 1969.     

Parametric vibrations of an orthotropic cylindrical shell with an elastic core. 2. Some numerical results

It is shown that the operator of the problem belongs to the class of oscillation operators. The first five regions of dynamic instability of an elastic orthotropic cylindrical shell with an elastic isotropic core are determined in the first approximation. The effect of the core and transverse shear in the shell on the width and location of these regions of dynamic instability of the system is determined. The effect of transverse shear on the natural frequencies of the empty shell is established.     

Dynamic stability of cylindrical orthotropic shells with an elastic core under a longitudinal periodic load

The dynamic instability of a cylindrical orthotropic shell with an elastic core subjected to a longitudinal periodic load is considered. Equations are obtained for determining the regions of dynamic instability for different core models.     

Static and dynamic beam forms of the loss of stability of a long orthotropic cylindrical shell under external pressure

A cylindrical shell with end sections which are closed and supported by hinges, in accordance with the concepts of the rod theory, is considered to be under the action of an omnidirectional external pressure which remains normal to the lateral surface during the deformation process. It is shown that, for such shells, the previously constructed consistent equations of the momentless theory, reduced using the Timoshenko shear model to the one-dimensional equations of the rod theory, describe three forms of loss of stability: (1) static loss of stability, which occures through a bending mode from the action of the total end axial compression force since, under the clamping conditions considered, its non-conservative part cannot perform work on deflections of the axial line; (2) also a static loss of stability but one which occurs through a purely shear mode with the conversion of a cylinder with normal sections into a cylinder with parallel sloping sections and a corresponding critical load which is independent of the length of the shell; (3) dynamic loss of stability which occurs through a bending-shear form and can only be revealed by a dynamic method using an improved shear model.     

Dynamic stability of a viscoelastic orthotropic cylindrical shell

A method based on the use of Laplace transforms has been developed for reducing the system of equations of motion of a viscoelastic orthotropic cylindrical shell to a single integro-differential equation. The effect of the viscous components on the regions of dynamic instability is investigated (creep due to the action of the shear stresses is taken into account).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 714–721, July–August, 1973.     

Behavior of glass-reinforced plastic cylindrical shells subjected to an external pressure pulse

The transient process of deformation of a cylindrical glass-reinforced plastic shell loaded with an axisymmetric external pressure pulse has been experimentally investigated. It is shown that as the amplitude of the load is monotonically increased (duration fixed), the axisymmetric motion of the shell is characterized first by linear and then nonlinear flexural oscillations.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 327–330, March–April, 1972.     

A WKB analysis of the buckling condition for a cylindrical shell of arbitrary thickness subjected to an external pressure

We consider the plane-strain buckling of a cylindrical shellof arbitrary thickness which is made of a Varga material andis subjected to an external hydrostatic pressure on its outersurface. The WKB method is used to solve the eigenvalue problemthat results from the linear bifurcation analysis. We show thatthe circular cross-section buckles into a non-circular shapeat a value of µ₁ which depends on A₁/A₂ and a mode number,where A₁ and A₂ are the undeformed inner and outer radii, andµ₁ is the ratio of the deformed inner radius to A₁. Inthe large mode number limit, we find that the dependence ofµ₁ on A₁/A₂ has a boundary layer structure: it is constantover almost the entire region of 0 < A₁/A₂ < 1 and decreasessharply from this constant value to unity as A₁/A₂ tends tounity. Our asymptotic results for A₁ – 1 = O(1) and A₁– 1 = O(1/n) are shown to agree with the numerical resultsobtained by using the compound matrix method.     

Concerning the critical load for an orthotropic cylindrical shell with a viscoelastic core

The problem of determining the critical load for a cylindrical shell with a viscoelastic core is considered. An expression for the critical load under quasistationary loading is obtained on the basis of a generalization of the Winkler hypothesis.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1049–1053, November–December, 1973.     

Dual problem of optimizing an orthotropic cylindrical shell

The problem of optimizing the weight of an orthotropic cylindrical shell is examined, using the duality theory of geometrical programing.     

Axisymmetric vibrations of an orthotropic non-uniform cylindrical shell

The axisymmetric vibrations of a circular cylindrical shell of constant thickness, orthotropic along the principal geometrical directions and non-uniform along the generatrices, are considered. It is shown, using a particular problem as an example, that the non-uniform physical-mechanical characteristics of the shell material may lead to qualitatively new results in problems of shell dynamics.     

The numerical analysis of an orthotropic cylindrical shell

This paper is devoted to an orthotropic cylindricall simply supported shell subjected to external pressure. This analysis is focused on determining geometrical shape of shell. Main subject of investigation is to maximize the stability of the shell. Mathematical model of double layer shell was implemented. Numerical solution was obtained for particular class of shells by using the finite element code ABAQUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plastic buckling of cylindrical shells subjected to external fluid pressure

Summary The problem considered here is that of a thin-walled circular cylindrical shell whose external surface is submitted to uniform fluid pressure. The condition under which bifurcation will occur in the shell beyond the elastic limit is examined and the true tangent modulus formula for the plastic buckling is established. Numerical results are presented for the critical pressure, covering both elastic and plastic ranges of buckling.

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Zusammenfassung Einige Betrachtungen über das Verzweigungsproblem einer dünnen Kreiszylinderschale mit homogen verteiltem Aussendruck führen zu einem exakten Ausdruck für die kritische Last im elastisch-plastischen Bereich. Verschiedene numerische Resultate für die kritische Last im elastischen sowie im plastischen Bereich werden angegeben.

     

Parametric oscillations of an orthotropic cylindrical shell with an elastic filler I. Formulation of the problem

A linear model of a Timoshenko-type shell with an elastic filler is proposed for solving the problem of the parametric oscillations of the system. A class of operators is derived, which act in a Hilbert space, for which the problem of the determination of a spectrum of eigen-values permits an iterative scheme of solution. Thus, the method for solving problems of parametric oscillations of structures proposed by Bolotin is confirmed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 470–478, May–June, 1974.     

Axially symmetrical deformation of an orthotropic layered cylindrical shell

An orthotropic layered cylindrical sheet subject to axially symmetrical loading is considered. A solution free from the hypothesis of the straight normal is presented; the material of the shell is regarded as incompressible in the radial direction. An attempt is made to allow for the real character of the rigid fixing at the edge of the shell. The stressed state in the neighborhood of the edge is analyzed.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 5, pp. 816–823, September–October, 1972.