Concerning the static-geometric analogy and the complex equations of Timoshenko-type shell theory

The static-geometric analogy of the classical Kirchhoff-Love shell theory, established by Gol'denveizer, is extended to the theory (Timoshenko type) in which transverse shear strains are taken into account [1, 2, 7, 8]. The construction of the complex equations of this theory is discussed.Franko L'vov State University; L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 5, pp. 942–945, September–October, 1969.     

Stability of glass-reinforced plastic plates resting on an elastic foundation

The stability of oriented glass-reinforced plastic plates resting on an elastic Winkler foundation is investigated using the theories of Timoshenko [2, 6] and Ambartsumyan [7], which permit the shear strains to be taken into account. The solution obtained is compared with the corresponding solution based on the classical Kirchhoff theory [8].L'vov Polytechnic Institute. Institute of Polymer Mechanics, AS LatSSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1082–1088, November–December, 1968.     

On the applicability of two-dimensional applied theories to problems of the stability of axially loaded cylindrical shells made of materials with low shear stiffness

The applicability of two-dimensional applied theories of the Kirchhoff-Love, Timoshenko, and Ambartsumyan types to problems of the stability of shells with low shear stiffness [1] is discussed. The critical loads given by these theories are compared with those recently obtained [6–8] by solving the problem of the stability of a cylindrical shell on the basis of general solutions [3, 4] of the three-dimensional linearized equations of the theory of elasticity [5].Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 141–143, January–February, 1970.     

Bending of long rectangular plates with low shear strength

The bending of rectangular glass-reinforced plastic plates is investigated for various edge conditions on the basis of generalized applied theories of the Timoshenko and Ambartsumyan types [4]. A series of qualitative and quantitative differences is obtained as compared with the corresponding results of the classical Kirchhoff theory [1].L'vov Polytechnic Institute; Ivano-Frankovsk Institute of Oil and Gas; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 945–950, September–October, 1969.     

Certain problems in developing a theory and design methods for anisotropic shells and plates with finite stiffness in shear. A survey

A survey is presented here of research on theory and design methods for shells and plates made of anisotropic materials, such as laminate reinforced plastics [4–13], compliant in shear. The report is based mainly on studies made at the Western Science Center, Academy of Sciences of the Ukrainian SSR during the last five years (after the previous survey [8] has been published), with the introduction of generalized Timoshenko-type theories.Branch of Mathematical Physics, Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 2, pp. 269–284, March–April, 1975.     

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.     

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.     

Action of a concentrated load on an elastic ring pressed into a circular hole in an anisotropic plate

A solution is obtained for the elastic equilibrium problem for an anisotropic plate with a circular hole into which is pressed a ring of arbitrary cross section symmetrical about the middle surface of the plate. Before deformation the outside radius of the ring differs from the radius of the hole in the plate by the amount of the permissible elastic displacements. A normal concentrated load is applied to the ring. The ring is analyzed in accordance with the theory of thin curved bars. A numerical example is given.I. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 6, pp. 1054–1059, November–December, 1973.     

Some problems of the theory and analysis of anisotropic plates and shells with low shear stiffness

Certain problems associated with the theory and analysis of plates and shells made of materials with low shear stiffness are discussed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 4, pp. 693–714, July–August, 1970.     

Effect of material properties on the stability of transversely isotropic shells with an elastic filler subjected to the action of mechanical loads and temperature

The effect of the low shear strength of the material (glass-reinforced plastic) on the stability of cylindrical shells with an elastic filler is investigated in relation to axial compression, external pressure, and heating. The equations of the thermoelastic problem of the theory of monotropic shells, constructed with allowance for the effect of tangential shearing stresses, are used in the calculations.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 903–907, September–October, 1970.     

Contact problems for beams and plates with low shear stiffness

The low shear stiffness and strength of unidirectionally reinforced plates and beams predetermines the choice of calculation model in specific problems [4]. The contact problem is considered for a glass-reinforced plastic plate resting on a Winkler foundation; the deformation properties of the plate are described by the equations of an orthotropic material; the investigation is based on generalized applied theories of the Timoshenko and Ambartsumyan types [5–8], which permit the high shear compliance of thin-walled structures to be taken into account.L'vov Polytechnic Institute; Ivan Franko Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 4, pp. 715–720, July–August, 1970.     

Effect of material properties on the bending of cantilevered plates under a concentrated load

In a continuation of a previous study [4] a solution is obtained for the problem of a transversely isotropic plate in the form of an infinite strip bent by a concentrated load applied at an arbitrary point. The solution obtained is investigated in relation to the geometric and physicomechanical properties of the plate. The results are compared with the corresponding classical Kirchhoff solution [7].Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov; Kamenets-Podol'skii General Engineering Department of Khmel'nitskii Technological Institute. Translated from Mekhanika Polimerov, No. 4, pp. 704–707, July–August, 1971.     

Resolvents of the theory of orthotropic shells with low shear stiffness in force-moments and stress functions

The problem of the theory of orthotropic layered shells with low shear stiffness is reformulated in force-moments and stress functions on the basis of new strain continuity relations constructed with allowance for transverse shears.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1970.     

Ultrasonic method of strengthening fluoroplastic 4D

A method of strengthening fluoroplastic 4D (a modification of polytetrafluoroethylene) is proposed. It is shown that ultrasonic vibration in kerosene improves the strength of the material in air and extends its life in liquid media.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 2, pp. 346–347, March–April, 1971.     

On the absence of the Ahlfors and Sullivan theorems for Kleinian groups in higher dimensions

Khabarovsk and L'vov. Translated fromSibirskii Matematicheskii Zhurnal, Vol. 32, No. 2, pp. 61–73, March–April, 1991.     

Theoretical and experimental investigation of the state of stress of a cantilevered plate with low shear stiffness

A general solution is obtained for the problem of a cantilevered, transversely isotropic plate in the form of an infinite strip with a clamped edge bent by a concentrated load applied at the free edge. The investigation relies on the equations of the generalized theory of plates [21–23] with allowance for interlaminar shears. In contrast with the Papkovich solution [1], the maximum theoretical bending moment at the clamped edge depends on the relative width of the strip and on the properties of the material. The classical result is asymptotically exact as h 0 or G_Z . The experimental results confirm the principal conclusions based on the theoretical solution.Kamenetsk-Podol'sk General Engineering Department, Khmel'nitskii Technological Institute. L'vov Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR. Translated from Mekhanika Polimerov, No. 3, pp. 476–481, May–June, 1971.     

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.     

State of stress of an anisotropic plate with a closed rod pressed into a curvilinear hole in it

A method is proposed for solving the problem of elastic equilibrium in the case of an anisotropic plate with a closed rod pressed into a curvilinear hole in it (or stretched over an anisotropic disk). This method is based on representing the boundary conditions in the form of contour integrals of an arbitrary function holomorphic within the region of that plate. The normal magnitude of the jump of the displacement vector at the contact line is given as the function of the arc. Friction at the contact line is assumed negligible. The stress-strain state of the rod (ring) is described by the equations in the theory of thin curvilinear beams.I. V. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 2, pp. 304–309, March–April, 1976.     

Meromorphic functions of completely regular growth and their logarithmic derivatives

L'vov. Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, vol. 33, No. 1, pp. 44–52, January–February, 1992.     

Characterization of convexZ-sets in linear metric spaces

L'vov State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 4, pp. 77–79, October–December, 1994.