Stress concentration around a circular hole in a transversely isotropic spherical shell

Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 99–106, December 2004.     

Problem on small motions of ideal rotating relaxing fluid

We study an evolution problem on small motions of the ideal rotating relaxing fluid in bounded domains. We begin from the problem posing. Then we reduce the problem to a second-order integrodifferential equation in a Hilbert space. Using this equation, we prove a strong unique solvability problem for the corresponding initial-boundary value problem.     

The mutual influence of the boundaries of a hole and the faces of a cylindrical shell under distention

We consider the problem of distention of a thin circular cylindrical shell of finite length weakened by a circular slit. On the basis of the complex equations of the theory of cylindrical shells we construct a solution that makes it possible to take account of the influence of the boundaries of the hole and the faces. Using the method of boundary collocations and taking account of the conditions for single-valuedness of the displacements, we reduce the problem to a system of linear algebraic equations. We study numerically the behavior of the membrane stresses as the boundaries of the hole and the faces are moved closer together. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 45–48.     

Small Motions of a Partially Dissipative Hydrodynamic System

A new problem is discussed: small motions of the hydrodynamic system {viscous fluid + set of ideal fluids}. The conditions are determined for the existence of a strong solution of the initial/boundary-value problem corresponding to small motions of the investigated hydrodynamic system, subject to the condition that the system is statically stable in the linear approximation.     

On the Interaction of Closely Spaced Circular Openings in a Transversely Isotropic Shallow Cylindrical Shell

A transversally isotropic shallow cylindrical shell with two different circular openings under axial tension is examined. The centers of the openings are aligned along a generatrix. Stresses are evaluated by finding an approximate analytical solution to differential equations of a two-dimensional shell theory that takes transverse shears into account. The results are compared with those obtained by the finite-element method     

On stabilization of solutions to incomplete second-order integrodifferential equations

We consider abstract incomplete linear second-order integrodifferential equations in a Hilbert space. Operator coefficients of the equations are unbounded selfadjoint nonnegative operators. These equations arise naturally in viscoelasticity and hydroelasticity. We prove a theorem on asymptotic stability of strong solutions of the equations.     

The operator approach to Il’yushin’s models of viscoelastic media under the isothermal processes of deformation

Three Il’yushin’s models of viscoelastic media are considered. The theorems of strong unique solvability of the corresponding initial boundary-value problems are proved. All models are uniformly reduced to the Cauchy problems for differential first-order equations in some Hilbert space under some restrictions on physical parameters. Using these equations, we pose the problems of a spectrum of various viscoelastic media.