Issue 4
JTAM, Sofia, vol. 6 Issue 4 (1975)

Influence of the Couple Stresses on the Limit State of an Infinite Medium with Circular Opening

N.Y. Bogdanova-Bontcheva, N.B. Medarova
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Bl. 8, kv. Geo Milev


A numerical solution has been given to the boundary problem of an infinite medium with circular opening. The material is assumed to be rigid-plastic, with couple stresses, cohesion and internal friction. The examination covers three kinds of loading along the outline of the opening, with three values of the material parameter, taking account of the influence of the couple stresses. The distribution of the stresses has been obtained and an analysis has been carried out of the influence of the couple stresses and of the different boundary conditions.

JTAM, Sofia, vol. 6 Issue 4 pp. 009-018 (1975)

Investigation of Statistically Indenterminable Girders upon Non-Linear Physical Law

T. Ganev
Sofia, Higher Institute of Civil Engineering, 1, Hristo Smirnensky Blvd.

The author discusses a method of investigating physically non-linear girders by means of which, with a comparatively simple algorithm, it is possible to obtain an approximate solution. By discretization of the full energy of the system a system of non-linear algebraic equations is obtained whose solution enables us to determine the displacement of the section forces in a particular number of points from the structure.

JTAM, Sofia, vol. 6 Issue 4 pp. 019-028 (1975)
A New Treatment to the Finite-Element Method and a Method of Large Fragments

H.G. Ganev
Sofia, Institute of Water Problems, Bulgarian Academy of Sciences, Bl. 4, kv. Geo Milev

A new treatment has been presented to the finite-element method which uses the full cubic polynomial and the respective triangular element with ten nodal points. Furthermore, it is not necessary to introduce the artificial so-called equivalent external concentrated forces at the nodal points of the triangular elements. This idea has been generalized also for expressing the state of strain and stress of an arbitrary polygonal element which has been expanded in the limit case to the entire elastic region under consideration. The respective polynomial will then be not of the third degree, but of a higher one, corresponding to the number of the sides of the polygonal boundary. The method of large fragments proposed in the article has been worked out for the more general two-dimensional problem of the shell from which it is possible through a limit transition to obtain the particular problems of the plate and plain state of strain and stress.

JTAM, Sofia, vol. 6 Issue 4 pp. 029-038 (1975), [Full Article]

Reduced Coefficient of Friction of a Crane-Type Pulley-Block System

A.V. Andreev
Sofia, Technical School of Mechanical and Electrical Engineering and Metallurgy

This is an examination of the oscillations of a crane-type pulley-block system as a system with two degrees of freedom. It provides physical and geometrical interpretation of the adduced generalized friction coefficient which is characteristic of the damped oscillations in the system.

JTAM, Sofia, vol. 6 Issue 4 pp. 039-048 (1975)
Boundary-Layer Growth on a Circular Cylinder

S.G. Slavchev
Sofia, Institute of Mathematics and Mechanics with Computer Centre, Bulgarian Academy of Sciences, Bl. 8, kv. Geo Milev

The author examines the boundary-layer growth on a circular cylinder started from rest in a viscous incompressible fluid with velocity depending on the time as a power function. The Navier-Stokes equations are solved by the method of matched asymptotic expansions. The second approximation to the flow velocity and the skin friction is calculated. The distance covered by the cylinder before separation of the boundary layer has been found. The solution is uniformly valid in the whole flow field and takes into account such second-order effects as a curvature of a body surface and inteaction between the boundary layer and the outer flow.

JTAM, Sofia, vol. 6 Issue 4 pp. 049-055 (1975), [Full Article]

Solution of the Problem of Non-Steady Motion in Pipes by Integration with Indefinite Coefficients

H.I. Hristov
Sofia, Institute of Mathematics and Mechanics with Computer Centre, Bulgarian Academy of Sciences, BI. 8, kv. Geo Milev

The method proposed of solving the problem of non-steady motion in pipes is generally related to the solution of linear particular differential equations of the hyperbolic type and can be applied to other problems in investigating transitional patterns in currents in ordinary and branched pipes.

JTAM, Sofia, vol. 6 Issue 4 pp. 057-066 (1975)
On the Solution of the Problem of Determining the Elastic Strains of a Compact Circular Cylinder. II

K.A. Yamboliev
Sofia, Central Laboratory of Physical-Chemical Mechanics, Bulgarian Academy of Sciences. Bl. 4, kv. Geo Milev

Numerical solution of the problem of determining the stressed and strained state of a finite cylinder of a particular length is found. A semi-inverse method, subject of earlier publication is used for the solution of the problem. The method has been applied to a cylinder of concrete for which the strains at a certain number of points had been determined experimentally in advance. The calculations were carried out on a computer, and the final expressions for the displacements and strains were obtained. The article also gives the expressions for the tangential stresses and strains in the contact zones of the cylinder, as caused by the existing friction.

JTAM, Sofia, vol. 6 Issue 4 pp. 067-074 (1975)
Forced Longitudinal Single-Frequency Oscillations of Systems of n Material Points, Involving Accounting for the Energy Dissipation

S.N. Buchvarov, Ts.N. Paraskov
Sofia, Higher Institute of Mechanical and Electrical Engineering, kv. Durvenitsa

A study has been made into the influence of energy dissipation on the oscillation of material systems of n material points with dissipative connections and equal masses. The case of forced oscillations without resonance has been examined. The dissipation of energy is accounted for according to Davidenkov's hypothesis. The authors have established the principle of motion, the amplitude, and the phase displacement in a first approximation, applying the method of Krilov-Bogolyubov.

JTAM, Sofia, vol. 6 Issue 4 pp. 075-082 (1975)