Comparison of the temperature stresses in a free and in a constrained cylinder

The conditions under which the radial and peripheral stresses in a free and in a constrained cylinder coincide at the ends of the cylinder when the temperature distribution is axially symmetrical are considered.P. I. Baranov Central Institute for Aircraft Engine Construction, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 163–165, January–February, 1972.     

Influence of the mechanical properties of a cylinder on the temperature stresses with allowance for the edge effect

The volume state of stress of a hollow homogeneous cylinder with temperature varying along the radius is analyzed for various values of Poisson's ratio, which in polymers may fluctuate over a wide range. The stresses in a cylinder of polymeric material, calculated with and without allowance for the temperature dependence of the modulus of elasticity for the same loading conditions, are subjected to a comparative analysis. Numerical results are obtained on the basis of a solution of the axisymmetric three-dimensional problem of thermoelasticity for an inhomogeneous cylinder using a collocation method.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1083–1086, November–December, 1969.     

Investigation of the effect of rheological factors on the magnitude of the circular zone of plasticity in a cylinder of elastoplastic material

The problem of the effect of rheological factors on the magnitude of the circular zone of plasticity in a cylinder of elastoplastic material was solved for two cases: for a cylinder of material reinforced with concentric fibers and for an isotropic cylinder under conditions of plane axisymmetric strain. The displacements and stresses arising in the investigated cylinders were obtained. In each case bilateral estimates were obtained for the time-variable unknown radii of plasticity.Dnepropetrovsk State University. Translated from Mekhanika Polimerov, No. 1, pp. 118–123, January–February, 1972.     

Deformations of a thick-valued,slowly rotating cylinder under gravitational load

An analytic method of calculating the deformations of an infinitely long thick-walled cylinder under a periodically varying gravitational load is described. The cylinder material is linearly viscoelastic. The solution employs the elasto-viscoelastic analogy. The corresponding elastic problem is solved by Muskhelishvili's method. The nonhomogeneity of the equilibrium equations is eliminated by applying the theorem of body forces with a potential function. As an example the maximum displacements of the inner channel are calculated for a cylinder of incompressible material in the cases of slow continuous rotation and periodic rotation through 180°.Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 4, pp. 727–733, July–August, 1970.     

Torsion of high-elastic cylinders reinforced with a rigid sleeve

The state of stress is analyzed for a cylinder of elastomeric material reinforced with a rigid sleeve and subjected to large torsional strains. Both compressible and incompressible materials are considered.Translated from Mekhanika Polimerov, No. 3, pp. 551–553, May–June, 1969.     

Radiation and Scattering by Complex Conformal Antennas on a Circular Cylinder

A technique for characterizing and designing complex conformal antennas flush-mounted on a singly-curved surface is presented. This approach is based on the hybrid finite element–boundary integral (FE–BI) method. A related method was proposed in the past utilizing cylindrical-shell finite element and roof-top rectangular basis functions for the boundary integral. Although that method proved very powerful for analyzing cylindrical–rectangular patch arrays flush-mounted to a circular cylinder, the requirement for uniform meshing in the aperture ultimately limited its usefulness. In this present formulation, tetrahedral elements are used to expand the volumetric electric fields while similar basis functions are used for the boundary integral. The curvature of the aperture is explicitly included via the use of the circular cylinder dyadic Green's function. After presentation of the formulation and validation using several well-understood examples, an example is presented that illustrates the capabilities of this method for modeling complex conformal antennas heretofore not examined by rigorous methods due to inherent limitations of the various published methods.     

Calculation of thermal stresses in an orthotropic cylinder

The present article describes the determination of thermal stresses in an orthotropic cylinder with an axially symmetric temperature field taking into account the change in the elasticity constants over the cylinder radius. A closed solution is given for constant elasticity coefficients.P. I. Baranov Central Institute of Aircraft-Engine Building, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 310–314, March–April, 1972.     

Motion of a non-Newtonian liquid in the annular channel of an insulation-coating tool

The axisymmetric flow of a non-Newtonian liquid with an exponential rheological law between two coaxial cylinders is considered for the case when the outer cylinder is fixed and the inner cylinder moves freely together with the liquid. At the outer cylinder the liquid moves either with or without slip. The individual theoretical conclusions are confirmed by the experimental results.Mekhanika Polimerov, Vol. 3, No. 1, pp. 151–155, 1967     

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.     

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.     

The dynamic problem of a cylinder with a slowly changing internal boundary

The problem of a hollow, viscoelastic cylinder confined in a shell is considered, and it is shown that the internal diameter changes. The fluctuations arising on applying a variable, internal pressure are analyzed.Institute of Flectronic Engineering, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1059–1065, November–December, 1972.     

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.     

Boundary-value problems for Helmholtz equations in an angular domain. I

The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out which enables one to reduce these boundary-value problems to integral equations on a one-dimensional contour — the boundary of the cross-section of this cylinder. The theorems on existence and uniqueness of solutions to the boundary-value problems and the corresponding integral equations are proved. For this case, a principle of limit absorption is established. Effective algorithms for calculating the kernels of the integral operators are constructed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 403–418, March, 1993.     

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.     

Temperature stresses in an inhomogeneous cylinder of finite length

An analytic method of determining the temperature stresses in circular cylinders is described. In the solution of the problem, based on a collocation method, together with the finite length of the cylinder its arbitrary inhomogeneity is also taken into account. In a particular case this may be caused by the effect of temperature on the mechanical constants of the material, which is especially typical of polymers at negative temperatures. The results of a calculation of the stresses in a hollow cylinder of finite length with a variable modulus of elasticity are presented as an example.Dzherzhinskii Military Engineering Academy. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 710–715, July–August, 1968.     

Vibrational mixing of granular solids in a horizontal circular cylinder

The hydrodynamic model of an incompressible viscous fluid described by the Navier-Stokes equations is applied to examine the dynamics of motion of a granular substance in a vibrating horizontal circular cylinder. The numerical results are represented by flowline maps for a fixed time moment. The maximum mixing of granular particles is observed in a zone directly adjacent to the wall of the vibrating cylinder and the particle velocities diminish in the direction toward the cylinder axis, which produces almost stagnant zones.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 75–79, 1986.     

Thermoelastic stresses in a nonuniform orthotropic cylinder

The stress distribution in a cylinder with cooling nonuniform with respect to the circumferential coordinate is investigated. The nonuniformity of the mechanical properties of the material in this direction is taken into account. Numerical results obtained at values of the parameters characteristic of wound glass-reinforced products are discussed.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 3, pp. 560–563, May–June, 1975.     

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.     

Stability with the axial compression of an axisymmetrically heated orthotropic cylindrical shell fastened to an elastic cylinder which is pliable with respect to shear

The article gives a solution to the problem of stability with the axial compression of an axisymmetrically heated orthotropic cylindrical shell fastened to an elastic thin-walled cylinder through an intermediate layer. It is assumed that the parameters of the elasticity of the orthotropic shell depend on the temperature, and vary over the thickness of the wall. The intermediate layer is assumed to be isotropic and absolutely rigid in a radial direction, but pliable with respect to axial shear. The thin-walled cylinder is considered to be elastic, isotropic, and unheated.Scientific-Research Institute for Chemical Engineering, Moscow Region. Translated from Mekhanika Polimerov, No. 3, pp. 546–550, May–June, 1970.     

Slip of a rigid cylinder along a viscoelastic foundation in the presence of friction

The problem of the slip of a rigid infinitely long cylinder along a viscoelastic foundation in the presence of friction forces dependent on the slip rate is solved in a linear quasistatic arrangement. The effect of the rheological characteristics of the foundation material and other factors on the point displacement of the surface in front of the moving cylinder is studied. Rather good agreement is obtained between theoretical and experimental data.Institute of Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mekhanika Polimerov, No. 6, pp. 1058–1064, November–December, 1974.