Issue 4
JTAM, Sofia, vol. 2 Issue 4 (1971)

Vitold Novatzki (On the Occasion of His 60th Anniversary)

G. Brankov
Bulgarian Academy of Sciences, “7-i Noemvri”, st. 1


JTAM, Sofia, vol. 2 Issue 4 pp. 009-012 (1971)

Approximate Molecular Theory

G. Brankov
Bulgarian Academy of Sciences “7-i Noemvri” st., 1

Approximate molecular theory for deformable medium is presented on the basis of discrete model. The mutual translations and angular rotations of the bonds between the material points (atoms) of the crystal lattice are taken into account. The oscillations of the material points of the discrete model are also considered in the deduction of the basic equations.

JTAM, Sofia, vol. 2 Issue 4 pp. 013-018 (1971)
Finite Differences Schemes for Problems of the Elasticity Theory in Regions with Curvilinear Boundaries. Compilation of the Schemes. Preliminary Assessment

R.D. Lazarov

The variational difference schemes of coordinated ununiform net are com¬piled for two dimensional symmetric region with smooth boundary. The aim of the paper is the approximation of the basic problems of the static elasticity theory for homogeneous isotropic bodies. A preliminary assessment is drawn for the solution of the difference equation system, from which follows the convergency of The difference analogue in the integral metric to a sufficiently smooth solution of the initial problem.

JTAM, Sofia, vol. 2 Issue 4 pp. 019-030 (1971)
Relation between the Linear Integrals of One Holonomic and One Non-Holonomic Mechanic Systems

Il, Iliev
Plovdiv, Higher Institute for Science and Mathematics

A non-holonomic system in inertia motion, subjected to linear non- holonomic relations (1.1), is considered. It can be assumed that the living power determines a holonomic system in inertia motion. The condition under which the linear integral of the holonomic system is the same for the non-holonomic system, is found. The following theorem is proved: A sufficient condition for the linear integral of the holonomic system to be the same for the non- holonomic system is the vector solution of (1.3) to lie in the admissible space.

JTAM, Sofia, vol. 2 Issue 4 pp. 031-034 (1971)
On Some Properties of the function Φν (a) Cnsisting of Bessel’s Functions, Applicable for Mechanical Problems

L. Salchev, V. Popov
Sofia. Higher Institute for Mechanical Engineering, Darvenitza

It is shown that for some mechanical problems the equation (1) is readied which consists of first and second kind Bessel’s functions. The function Φν (a) which is a ratio of the Bessels’ functions of first and second kind is introduced for finding a solution of (1) at arbitrary index ν. Some properties of the function are investigated. The concept pseudoperiod Πν (a) is defined for the function. Graphs of the pseudoperiods Fν (a), by means of which solutions of equation (1) are found, are shown in Figs. 4 and 5.

JTAM, Sofia, vol. 2 Issue 4 pp. 035-042 (1971)
Velocity Profiles for Polymer Flows in Capillaries and Slits

St. Zahorski
Institute of Basic Technical Problems, Warsaw

It is of great importance for the technological processes as well as for the more advanced analysis of flows (anomalous effects, instability etc.), to know the possibly exact velocity profiles for polymer solutions and melts in pipe and channel flows. The constitutive equations of a visco-elastic fluid of third grade are proposed for description of slow laminar flows of molten polymers in slits and cylindrical capillaries. These equations are not only of more general type (an approximation for simple fluids) but also the resultant relations can be easily modified for the case of an “effective slip’’ at the walls. For further illustration the velocity profiles resulting from our theoretical considerations have been compared with the slit flow experiments of other authors. 

JTAM, Sofia, vol. 2 Issue 4 pp. 043-054 (1971)
Analysis of the Deformations in the Interior of a Pressed Glass Plastic Cylinder

K. Jamboliev
Institute of Technical Mechanics, Bulgarian Academy of Sciences, IV bl., kv. Geo Milev

The distribution of the measured deformations in the interior of a solid, circular glassplastic cylinder, reinforced non-orientedly, subjected to central pressure is considered. The diagrams of the deformations, caused from normal and tangential stresses in points of the mid-cross section of the cylinder and on the surface of distribution of the deformations, caused from normal stresses, arc obtained. Unilateral deformation of the cross section and bending of the cylinder due to the non-homogeneousness of the deformation properties of the glassplastic are established.

JTAM, Sofia, vol. 2 Issue 4 pp. 055-066 (1971)
State of Stress and Strain of an Elasto-Plastic Cylitidric Shell with Many Fulcrums

A. Mitov
Sofia, I. Rilski str. 32

A cylindric shell on many fulcrums, made of elasto-plastic material with nonlinear strainhardening, is considered. The load is accepted to be uniformly distributed internal pressure, different in the separate parts along the shell longitude. The analysis is carried out according to the theory of the small elasto-plastic deformations. D. Kolarov’s method for the softened physical equations is applied. The proposed method of solution is illustrated with a numerical example and graphs.

JTAM, Sofia, vol. 2 Issue 4 pp. 087-078 (1971)