Mechanics

2004, No. 4

A.G. Zhigalin

AN ASYMPTOTIC METHOD FOR SOLVING PROBLEMS OF DYNAMIC ELASTICITY

In the paper the asymptotic method for solving dynamic problems from the elasticity theory is given. A sample problem for a flat cylindrical shell is considered. The proposed method in comparison with other numerical procedures allows to reduce the time of computation especially for a dynamic problems for thin shells.

E.A. Karackulin, A.V. Rusetskaya

EFFECT OF VAPOUR CAVITATION ON UNSTABLE FLOW PARAMETERS IN A PIPE

Dependencies of parameters changing on unstable cavitating flow during hydroimpact in a pipe, obtained under consideration of variability on coordinates and acoustic velocity time are presented. They can be used in designing devices and systems to estimate the application necessity (practicability) of calculation method of cavitating liquid changing flow in a pipe. Such an operation requires much efforts and significant time of computations. System of equations for variables computed on coordinates and acoustic velocity time in a pipe with paraliquid mixture and acoustic velocity changing along the pipe for different levels of cavitation are presented.

A.V. Manzhirov, M.N. Mikhin

METHODS OF THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE IN GROWING SOLIDS MECHANICS

The theory of plain and torsion problems of growing solids mechanics is developed. Arising classical and non-classical initial boundary-value problems of solid mechanics are considered. Methods for solving problems of growing solids mechanics are proposed. These methods are based on the I) reduction of non-classical problems of accretion of viscoelastic aging solids to the problems of elasticity with a parameter, II) utilizing the theory of analytic functions for solving the latter problems, and III) reconstruction of true characteristics of stress-strain state by the aid of obtained decoding formulas. The results of this work can be used for solving a number of important applied problems of growing solids mechanics.

Y.N. Radayev, V.A. Gudkov

ON SYMMETRY GROUPS OF THE AXIALLY-SYMMETRIC EQUATIONS OF THE MATHEMATICAL PLASTICITY

Group analysis of the system of partial differential equations of axially-symmetric plastic equilibrium is given. The Tresca yielding criterion s employed. It is presumed that stress state corresponds to an edge of the Tresca prism thus allowing to consider only the static equations. The static equilibrium equations are represented in the stress principal lines co-ordinate net (isostatic net). Their symmetry groups are obtained. Then the group invariant solutions of the system are determined. It is shown that by the standard group analysis all known from earlier discussions axially-symmetric solutions can be obtained. It is proved that the self-similar solution based on the representation of the self-similar variable as product of powers of isostatic co-ordinates appears as the group invariant solution of the system.