Issue 4
JTAM, Sofia, vol. 14 Issue 4 (1983)

Kinematic Theory of Infinitesimally Close Locations of a Solid Body with a Single Fixed Point. Part I

S. Buchvarov
High. Inst. Mech. Electr. Eng., Durvenitsa


The paper sets forth the following problem: for a specified motion of a solid body with a single fixed point find such a body point, which three, four and five infinitesimally close locations lie on a single circle. Solution is performed for three infinitesimally close locations, by using a method, similar to that, introduced by Kotelnikov.

JTAM, Sofia, vol. 14 Issue 4 pp. 011-022 (1983)

Localization of G-Oerlikon Gear Tooth Contact

E. Nadara, P. Gruszczinski

The paper has been presented at the 4th National Congress of Theoretical and Applied Mechanics, Varna 1981.

JTAM, Sofia, vol. 14 Issue 4 pp. 023-026 (1983)
On the Linear Stabilization in a Finite-Dimensional Configuration Space

A. Cheremeskiy
Inst. Mech. Biomech., Bulg. Acad. Sci., B1. 8, Geo Milev

As is known, when stating a stabilization problem the separation of controlling and controlled variables does not prove to be a simple procedure. Let a quality quadratic functional, involving a non-singular quadratic form for both controlling variables and those standing for the description of the object conduct in the configuration space, be introduced. The paper then proves that stability conditions and the steady solution synthesis do not depend on the separation employed. Moreover, the study produces analysis of the problem of constructing both a measure and a system estimating controlling and controlled variables, with further applyication to stabilization synthesis and to surveilance of objects under “enemy`s” control.

JTAM, Sofia, vol. 14 Issue 4 pp. 027-034 (1983)
On the Solution of the General Problem of the Theory of Elasticity by Using the Enlarged Fragment Method and a Convergent Iteration

Hr. Ganev, Kr. Georgiev, Ch. Dimitrov
Inst. Water Probl., Bulg. Acad. Sci., BI. 4, Geo Milev

The enlarged fragment method (EFM) is proved to be logical development and both a variant and a mathematical generalization of the finite element method (FEM). The region under consideration is not to be discreticized into separate fictitious elements, but is to be approximated by a single fragment bounded by a closed polygon. The EPM stands for a discretization method, for the sought function of displacements – vector field and v(x, y) is approximated by means of a finite number of interpolation functions (i.e. Green's function, the influence function) of degree n, and for the whole region including the boundary, continuity of order n is provided. If Lagrange's principle of virtual displacement is applied, there occurs a possibility to obtain higher accuracy of the sought static or dynamic solution, by using a much less number of variable parameters. A convergent iteration is proposed, whereas an approximate but sufficiently accurate solution is used.

JTAM, Sofia, vol. 14 Issue 4 pp. 035-044 (1983)
On the Viscoelastic Behaviour of Particulate Composites

K. Markov
Faculty of Mathematics and Mechanics, University of Sofia, P. O. Box 373, 1090 Sofia

Some methods for analyzing the overall viscoelastic behaviour of particulate composite materials are outlined. It is first proposed to employ the so-called defects of the elastic moduli in order to get an idea about the influence of the filler upon the overall viscoelasticity. A simple approximate method for evaluation of the creep and/or relaxation curves for the composite is next proposed. The method, when applied to polymer concrete, led to a good agreement with the experiments.

JTAM, Sofia, vol. 14 Issue 4 pp. 045-053 (1983), [Full Article]

A Transversely Isotropic Plate Indented by a Flat Annular Rigid Stamp Over lying an Elastic Foundation

M. Lal
School for Studies in Mathematics, Jiwaji Univ., Gwalior, India

The present paper attempts to solve the problem of a transversely isotropic plate indented by a flat annular rigid stamp, overlying on an elastic foundation. In this problem the normal displacement is specified inside an annular area a ⩽ r ⩽ b, the normal stress is zero in the region 0 ⩽ r ⩽ a, r > b and shearing stress is zero on the upper surface z = –h of the elastic layer. The continuity of the normal and shearing stresses is assumed at the interface (z = 0) between the elastic layer and the elastic foundation, having different elastic constants. The problem will be reduced to the solution of an infinite set of simultaneous equations. Radial distributions of stress, displacement and total compressive load are illustrated graphically.

JTAM, Sofia, vol. 14 Issue 4 pp. 054-063 (1983), [Full Article]

Transient Thermocapillary Flow in a Thin Viscous Liquid Layer. I. Small Reynolds Number Case

J. Kojuharova, Sl. Slavchev
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8, Geo Milev

A thermocapillary viscous flow in a thin layer under the action of the surface-tension driving force is studied. The surface tension gradient is due to a nonsteady and nonuniform heating or cooling of the fluid free surface. The axisymmetric dynamic and thermal problems in the case of small Reynolds numbers are analytically solved for small and great time values. The flow and temperature patterns and the layer thickness are illustrated as well. The influence of the gravitational force on the flow development is determined in comparison with a thermocapillary flow at reduced gravitation.

JTAM, Sofia, vol. 14 Issue 4 pp. 064-073 (1983)
Determination of the Gas-Surface Interaction Parameters by Using Experimental Data on Gas Motion in Channels

V. Akinshin, B. Porodnov, V. Seleznev, Y. Markelov, A. Fljagin

JTAM, Sofia, vol. 14 Issue 4 pp. 074-089 (1983)
Estimation of the Resistance to Fracture of Nitrided Steel by Means of the Steel Mechanical Characteristics

Hr. Kortenski, K. Minchev, St. Vodenicharov
NPO "Technologiya na metalite", 43 Chapaev Str., Sofia

The resistance-to-fracture estimation, involving low-strength steel and using criteria of the linear fracture mechanics, grows difficult due to the availability of preliminary plastic deformation. To obey the body dimension demands, i.e. a, b, c ⩽2.5(Ka/Rc)2, it is necessary to test specimens of considerable size. This results however into the employment of powerful devices, great metal losses and difficulties, barring the specimen manufacture. Obstacles can be surmounted by using relations between resistance to fracture and material mechanical characteristics στ, εв, ψ, ρ, easily provided by standard experiments. Two material correlative dependences are involved in the paper. To determine the resistance to fracture, tests of notched cylindrical specimens with fatigue cracks are performed and criteria of the linear fracture mechanics are employed.

JTAM, Sofia, vol. 14 Issue 4 pp. 090-092 (1983)
Postcritical Deformation of Thin Elastic Orthotropic Shells of Linear History. Part II

Y. Ivanova
Inst. Mech. Biomech., Bulg. Acad. Sci., BI. 8, Geo Milev

In this second part postcritical deformations are investigated by means of an A variational principle, valid for linearly viscous shells. However, restrictions imposed in part I, do not hold. Henceforth, integral equations are solved numerically, both for the determination of the normal suspension and the value of the lower critical pressure. Results are presented graphically, for various values of creep parameters in axial and radial direction. A tendency to both explicit increase of the normal suspension and decrease of critical pressure is revealed for an increase of the creep critical time. Results, obtained in part I, have been confirmed.

JTAM, Sofia, vol. 14 Issue 4 pp. 093-098 (1983)
Axsymmetric Problem Involving Separation of an Elastic Material from a Hard Spherical Inclusion and under Entire Cohesion in the Contact Region. Part II

V. Valeva
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8, Geo Milev

The axisymmetric problem is solved for an infinite material with a hard spherical inclusion, involving special loading and a matrix separation. The system of singular integral equations thus obtained is solved by using quadrature formulas, which take into account the oscillating behaviour of the solution in the vicinity of the separation boundary.

JTAM, Sofia, vol. 14 Issue 4 pp. 099- (1983)