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.     

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.     

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.     

Study of the effect of asymmetric arrangement of the layers on the stability of three-layer cylindrical shells in axial compression

The stability of a three-layer cylindrical shell under axial compression is examined in a three-dimensional linearized formulation. The load-bearing layers are assumed to be orthotropic, while the binder is modeled by an isotropic body. The effect of asymmetric arrangement of the layers and the mechanical characteristics of the material on the critical strains is determined.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 103–106, 1988.     

Stability of composite shells with an elastic core

The stability in axial compression of orthotropic cylindrical shells with an elastic core is investigated with allowance for the following factors: transverse shear strains in the shell material, precritical state of stress of the core, and the moments due to the surface forces exerted on the shell by the core. The numerical results obtained are compared with the results of approximate methods in which the above-mentioned factors are disregarded.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 544–547, May–June, 1976.     

Stability of orthotropic cylindrical shells under variable pressure

A method of determining the critical stresses is developed for elastic orthotropic cylindrical shells subjected to nonuniform pressure. It is assumed that the external pressure varies over the cross section and is constant along the length of the cylinder. A shell stability analysis is given for the case of a weakly varying load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1970.     

Deformation of a glass-reinforced plastic cylindrical shell encased in a thick-walled elastic cylinder

A solution is given for the axisymmetric problem of the deformation of an orthotropic glass-reinforced plastic shell of finite length encased in a soft transversely isotropic cylinder under internal pressure.Moscow Institute of Heat Engineering. Translated from Mekhanika Polimerov, No. 1, pp. 164–168, January–February, 1973.     

Dynamic stability of axisymmetrically heated glass-reinforced plastic cylindrical shells bonded to elastic cylinders

The dynamic stability of glass-reinforced plastic shells subjected to the action of a longitudinal pulsating force and an external, uniformly distributed load is examined. The shells are orthotropic, and their elastic properties are temperature-dependent and vary over the thickness of the wall. It is assumed that the elastic cylinder forms a Winkler foundation. Three boundary conditions are investigated.Moscow Institute of Chemical-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 331–337, March–April, 1972.     

Local stability of an orthotropic cylindrical shell partially filled by an elastic core and subjected to external pressure

The local stability of an infinitely long orthotropic cylindrical shell partially filled by an elastic thick-walled cylindrical core and subjected to external pressure is investigated.Scientific-Research Institute of Chemical Technology, Moscow Region. Translated from Mekhanika Polimerov, No. 3, pp. 538–542, May–June, 1971.     

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.     

Mechanical behavior of cylindrical laminated plastic shells

The static and dynamic behavior of a cylindrical glass-reinforced plastic shell with an open cross section under long-term loading and unloading has been experimentally and theoretically investigated. The experimental results are compared with the theoretical data obtained using a geometrically nonlinear theory based on the Kirchhoff hypothesis. For calculation purposes the glass-reinforced plastic is assumed to be a homogeneous orthotropic linearly elastic material.Building Research Institute, Prague. Translated from Mekhanika Polimerov, No. 1, pp. 110–115, January–February, 1976.     

Optimal designing of orthotropic cylindrical shells fastened to elastic filler

Conclusions A method has been proposed for optimally designing an orthotropic cylindrical shell rigidly fastened to an elastic and isotropic filler of finite dimensions. The design takes into account simultaneous action of pressure, body forces, and heat on the structure. The optimum design has been calculated for the case of temperature-dependent elastic properties and strength characteristics of the tape. The method allows also for limitation on the strength of the filler. The convergence of the iteration process schematically shown in Fig. 2 is quite fast. Indeed, for the given design variant, the condition of manufacturability (1) is satisfied with a sixfold margin in the third approximation (n=3) already.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 91–94, January–February, 1984.     

Solution of some dynamic problems of viscoelasticity theory by the averaging method

Damping of longitudinal vibrations of a viscoelastic bar and transverse vibrations of a freely supported orthotropic plate is investigated by the averaging method. The problem of the forced movement of a viscoelastic cylinder enclosed in a thin elastic shell under the effect of an arbitrarily time-varying internal pressure is studied.Institute of Cybernetics at the Computer Center Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 2, pp. 246–252, March–April, 1970.     

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 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.     

Vibrations of a viscoelastic cylinder with an elastic shell

The nonlinear vibrations of a viscoelastic cylinder with an elastic shell subjected to two harmonic forces are investigated using the averaging scheme described in [3, 4]. Nonresonance, resonance, and subharmonic vibrations are examined. It is shown that the presence of viscosity in the system leads to a single stationary equilibrium position for which the stability conditions are given.V. I. Lenin Tashkent State University. Translated from Mekhanika Polimerov, No. 4, pp. 691–697, July–August, 1973.     

Stability of transversally isotropic shells coupled with an elastic foundation

The stability of shells coupled with an elastic Winkler foundation is investigated. It is assumed that the shell is made of a material (glass-reinforced plastic) with low resistance to shear, as a result of which generalized theories that take transverse shear strains into account [1–4] must be used in the stability calculations. The solution obtained is compared with the corresponding solution obtained on the basis of the classical Kirchhoff-Love theory [8].Lvov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 669–673, July–August, 1969.     

Variant of the geometrically nonlinear theory of anisotropic shells with allowance for transverse shear

A very simple variant of the geometrically nonlinear theory of anisotropic shells with allowance for the high compliance of the material in transverse shear is proposed. From this theory there follow, as a special case, the equations for an isotropic shell; these differ from the relations of [2] with respect to terms of the order of the ratio of the thickness of the shell to the radii of curvature small as compared with unity. The equations obtained are used to solve the problem of the stability of orthotropic shells of revolution relative to the starting axisymmetric state of stress.Translated from Mekhanika Polimerov, No. 5, pp. 863–871, September–October, 1969.     

State of stress and strain of a rubbery cylindrical layer reinforced by an anisotropic shell

An exact solution is obtained for the nonlinear problem of elastic equilibrium of a rubbery cylinder reinforced by an anisotropic shell.L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 3, pp. 534–537, May–June, 1971.     

Stability of a transversely isotropic spherical shell coupled with an elastic foundation

The stability "in the small" of a flat spherical shell with elastic reinforcement is investigated. It is assumed that the shell is made of material (glass-reinforced plastic) with low shear resistance [7, 8], which determines the choice of calculation procedure: generalized applied shell theories of the Timoshenko and Ambartsumyan types [1, 3]. The results obtained are compared with the corresponding results of the Kirchhoff-Love theory.L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 129–131, January–February, 1970.