On the problem of axial tension of a circular inhomogeneous transversally isotropic shell

We consider the problem of axial tension of a circular inhomogeneous cylindrical shell by longitudinal forces. The determination of the stress-strain state of the shell is performed on the basis of a refined theory. The possibility of losing local stability under axial tension is discussed.     

Investigation of frequencies of natural vibrations of a transversally isotropic cylindrical panel with a circular hole

We consider the problem of natural vibrations of a hingedly supported transversally isotropic cylindrical panel with a circular hole. The deformation of the shell is described by modified equations of the Timoshenko theory of shells. The numerical solution of the problem is constructed by the indirect method of boundary integral equations based on the sequential representation of Green functions.     

The stressed state of a transversally isotropic medium with a spheroidal inclusion under nonideal mechanical contact

We study the problem of the stressed state of a transversally isotropic medium containing a foreign inclusion in the form of a prolate spheroid under an arbitrary homogeneous stress field at infinity. On the “medium-inclusion” interface there is slipping without flaking. The stressed state is constructed in the medium and in the inclusion using the exterior and interior problems for a prolate spheroid on the basis of potential functions. The solution of the problem is reduced to studying infinite systems of linear algebraic equations. The results of numerical studies are shown as graphs that describe the stress distribution in both the transversally isotropic medium and in the inclusion under various boundary conditions. Four figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 15–26.     

The stress-strain state of an orthotropic shell with a circular hole

We study the stress-strain state of an orthotropic shell with a circular hole. The regularities of the straiin distribution as a function of the anisotropy parameters in a spherical shell are exhibited. One table, 1 figure. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 154–158.     

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.     

Limit equilibrium of a closed transversally isotropic cylindrical shell with a nonthrough longitudinal crack

In the context of an analog of the Leonov-Panasyuk-Dagdeil model we consider the problem of limit equilibrium of a nonshallow transversally isotropic cylindrical shell weakened by a nonthrough surface longitudinal crack. Based on the equations that take account of the initial stresses, we reduce the problem to a system of two singular integral equations with unknown limits of integration. We carry out a numerical analysis of the dependence of the opening of the edges of the crack on the load and the geometric and physico-mechanical parameters of the shell. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 31–36.     

The stressed state of a transversally isotropic body with inner elliptic crack. A linearly varying pressure on the surface of the crack

An exact solution to the problem of the distribution of stresses in a transversally isotropic elastic body with inner elliptic crack is given. An assumption that the linearly varying pressure acts on the surface of the crack is made. The intensity coefficients of stresses at the vertex of the crack are found. Bibliography: 5 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 79, 1995, pp. 117–124. Original     

Stress distribution in the vicinity of a circular hole in an orthotropic spherical shell with finite shear rigidity

The authors consider the problem of stress concentration in the vicinity of a circular hole in an orthotropic spherical shell with finite shear rigidity. The case in which the hole edges are reinforced by a thin elastic ring and some associated special cases are investigated.     

On the thermal stress state of transversally isotropic solids of revolution of finite dimensions

By solving the stationary thermoelastic problem for a transversally isotropic hyperboloid of revolution we conduct an analytic study of the thermal stress state of a finite solid of revolution with a meridional section of complicated shape and propose a way to solve the problem of the reliability of information obtained using the numerical methods developed and algorithms implemented on a computer. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 7–15.     

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.     

Thermoelastic strain of a transversally isotropic cone

The exact solution to the problem of statical thermoelasticity for a transversally isotropic cone in the case where the characteristic equation has multiple roots, the surface of the cone is free of the action of external forces, and the temperature on the boundary can be represented in one variable by the Mellin integral and in a second variable, by a trigonometric series, is presented. Bibliography: 6 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 23–32.     

Stress concentration in a spherical shell with two neighboring circular holes

We have solved analytically the problem of the stressed state in an isotropic shallow spherical shell with two circular holes. The cases of the close location of holes of both equal and unequal radii in the shell under the action of internal pressure have been investigated numerically. We have detected a considerable increase in stresses on the bulkhead between the holes at their approach.     

Elastoplastic equilibrium of an isotropic strip with a circular hole under pure bending

The range of variation of external forces over which the plastic region in a bent strip develops from initiation to complete envelopment of a circular aperture is determined. A perturbation method is used to construct a solution for these interactions. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhnika, No. 30, pp. 105–111, 1999.     

Solution of the equations of a transversally isotropic cylindrical shell taking account of deformations caused by physico-chemical processes

Using the operator method we reduce the system of resolvent differential equations for a transvers ally isotropic cylindrical shell that takes account of the deformations caused by physicochemical processes to a single equation of tenth order. We construct the Green's function of this equation for the case of an infinite shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 80–84.     

Stress state of an isotropic shell with an elastic inclusion

Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 76–80, 1990.