Issue 3
JTAM, Sofia, vol. 8 Issue 3 (1977)

On the Diffusion Boundary Layer of the Flow Past a Fixed Sphere in a Slowly Rotating Viscous Fluid

Z. Zaprianov, Iv. Zheleva
Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Sofia


This is an investigation of the mass transfer in a slowly rotating fluid motion with a constant velocity U past a stationary sphere. We suppose that Peclet number is large and the reaction rate tends to infinity. The classical boundary layer approximation of the convective diffusion equation is applied. It is found that the total mass flux of matter increases for small Rossby numbers with increasing the Taylor number T and decreases with increasing T for large Rossby numbers E. The local flux of matter depends upon the rotating more strongly before the middle of the sphere than behind it.

JTAM, Sofia, vol. 8 Issue 3 pp. 011-015 (1977), [Full Article]

Analysis of Compressible Jet Flow Stability with Fluid-Fluid System Concerned

Iv. Pentchev, St. Radev
Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Sofia

A laminar jet flow stability analysis is given. An approximate transitory solution of the boundary layer equation, describing the jet form and its velocity profile, is used. The influence of fluid viscosity and jet velocity profile over the jet unbroken part and the drop size is investigated.

JTAM, Sofia, vol. 8 Issue 3 pp. 016-022 (1977), [Full Article]

Shock Thermomechanical Wave Propagation in Infinite Medium

A. Baltov, K. Vassilev
Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Sofia

A longitudinal and transversal shock wave propagation in infinite medium is analysed. The above medium is thermomechanically coupled while the temperature propagation has a finite velocity. The deformable medium demonstrates elastic, visco-elastic or visco-plastic behaviour. Conditions of different order are found. They must be satisfied on the shock wavefronts. Equations of evolution of jumps on the wavefronts in the process of wavefront propagation are derived.

JTAM, Sofia, vol. 8 Issue 3 pp. 023-026 (1977), [Full Article]

A Postbuckling Deformation Analysis for Thin Anisotropic Shells, 4

V. Babenko1, J. Ivanova2
1Harkov, USSR, Institute of Physics and Technics for Low Temperatures, Academy of Sciences of the Ukrainian SSR
2Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Sofia

In this paper is analysed the postbuckling behaviour of elastic anisotropic shells. The shells concerned protrude with pressure applied. The article is a sequel of part 3. The shell edge fixing effect is taken into account. Particularised formulae are proposed, as well as graffic results for two types of orthotropy. The results are compared to those of L. M. Afanasieva (she deals with spherical sloping orthotropic shells).

JTAM, Sofia, vol. 8 Issue 3 pp. 027-033 (1977)
Analysis of Overconstrained Spatial Mechanisms

F. Litvin1, R. Jamalov1, K. Petrov2
1Leningrad, USSR, Leningrad Institute of Precision Mechanics and Optics
2Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Sofia, Bulgaria

It is well-known that link movability of overlimited lever mechanisms is realised by associating the construction parameters. The paper proposed an associative method, based on: a) conditional breaking of the kinematic chain; b) the theorem of implicit function system existence.

JTAM, Sofia, vol. 8 Issue 3 pp. 034-042 (1977), [Full Article]

Unsteady Hydrodynamical Stability of a Cylindrical Composite Shell in Acoustic Medium

M. Kozarov
Higher Institute of Civil Engineering, Sofia, Bulgaria

A cylindrical composite shell, sunk in water, is concerned. It has an infinite length and is loaded by harmonically changing distributed pressure. Shell hydrodynamical stability is analysed.

JTAM, Sofia, vol. 8 Issue 3 pp. 043-051 (1977)
A Circular Arc Crack in a Plate Subjected to Bending

I. Mihovsky
Sofia University, Department of Mathematics and Mechanics

The problem of pure bending of an elastic thin plate, containing a crack in the form of a circular arc is considered in the paper. The Kirchhoff plate bending theory is used. The initial problem is reduced to Rieman – Hilbert problems for the complex “elastic potentials", which are solved. The stress intensity factors are determined for certain types of loading. The reduction of the problem to the case of a straight line crack is considered.

JTAM, Sofia, vol. 8 Issue 3 pp. 052-058 (1977)
A Geometry Way to Localising the Interpolation Parameters of a Finite Element

St. Grigorov
Institute of Water Problems, Bulgarian Academy of Sciences, Sofia, Bulgaria

If the method of finite elements in solving mechanical problems is concerned, one often expresses approximately the parameters wanted by means of algebraic polynomials. The values of the functions approximated or those of their derivatives, in a definite number of points, represent the interpolation parameters. Those parameters define the coefficients before the polynomial basic functions. The point position, as well as the parameter position is not arbitrary. In some cases its definition is extremely difficult. The paper proposes a geometry way of point locating and parameter definition. By means of the method proposed one can obtain a one-valued interpolation. Parallel to that, some conditions, related to solving problems by using the method of finite elements, could be satisfied.

JTAM, Sofia, vol. 8 Issue 3 pp. 059-065 (1977)
Thermodynamical Model of Diffusion with Memory with Deformable Medium Concerned

N. Petrov, R. Rangelova
Central Laboratory of Biomechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

The main point in this paper is a fluid diffusion modelling in a porous matrix. It is said that: (i) there is an interaction between the deformation plain and the fluid concentration area; (ii) a part of the fluid reacts with the matrix. The constitutive equations are derived by means of nonequilibrium thermodynamics. A relation between diffusional flow and fluid concentration gradient is demonstrated. All that thecry is illustrated by a boundary problem, which models the process of thin plate drying out.

JTAM, Sofia, vol. 8 Issue 3 pp. 066-072 (1977)
Second Transfer Functions of Spatial Kinematic Chains

K. Markov, M. Konstantinov
Higher institute of Mechanical and Electrical Engineering, Sofia, Bulgaria

In this paper it is shown how to find the second transfer functions of spatial kinematic chains by the help of algebraic operations for a given displacement, metrical parameters and acceleration of the input link of the mechanism. In this sense the kinematic definability of mechanisms is shown. A numerical example of a spatial crank and connecting-rod assembly is considered.

JTAM, Sofia, vol. 8 Issue 3 pp. 073-078 (1977)
Discrete Cellular Array

A. Ugel, S. Zlateva
Technical University of Drezden, Drezden, DDR

Schemes, consisting of great number of equal functional cells, are known in literature as cell schemes. This paper deals with cellular array which is a summary of those schemes. Some mathematical transformations are given beforehand.

JTAM, Sofia, vol. 8 Issue 3 pp. 079-088 (1977)
On a Strain-Gradient Elastic Model of a Composite Material

K. Markov
Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, Sofia, Bulgaria

In the paper a theory of a composite material is considered, in which the interactions of the phases are introduced phenomenologically by using a strain-gradient elastic model. In the second part a system for determining the elastic moduli of the composite is proposed. The size effect is observed, that means a decreasing of the elastic moduli when the inclusion sizes increase. The particular case of a porous body is also detailed.

JTAM, Sofia, vol. 8 Issue 3 pp. 089- (1977)