Issue 3
JTAM, Sofia, vol. 6 Issue 3 (1975)

On the Viscosoelastic Behaviour of a Two Phase Mixture. II. Equivalent Model with Elements Connected Partly in Parallel. Linear Constitutive Theory

P.A. Marinov
Sofa, Institrte of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km


Gibbs' equation for a two phase mixture with a viscosoelastic matrix and elastic filler based on an equivalent mechanical model with elements connected partly in parallel is derived. A thermodynamic approach, including internal state variables is used. The tensor of total stress, the inelastic tensor stress and the state equat ons respectively are defined. The invariability of the model in comparison with the considered equivalent model with elements connected partly in series is shown. A linear constitutive theory is derived.

JTAM, Sofia, vol. 6 Issue 3 pp. 009-016 (1975)

On the Elastic Constants of Hetero generous Systems

K.Z. Markov1, M.M. Mihovski2, A.C. Mečkov3
1Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km
2Institute of Metal Science and Technology of Metals, Bulgarian Academy of Sciences, IV km – Sofia
3Scientific Research and Technological Institute of Metalceramics, 122 Tintjava St., Sofia

The paper is dedicated to the analysis of the system of equations obtained by Skorohod for calculat on of the elastic characteristics of heterogeneous systems. The possible approximate methods of solutian are considered in the first part and the results from numerical computer solutions are given. The second part of the paper contains the experimental proof of results obtained for powdered metallurgical materials based on iron The experiments are carried out with ultrasonic measuring equipment. Practical methods for use of the theoretical conclusions for real not fully consolidated materials are discussed.

JTAM, Sofia, vol. 6 Issue 3 pp. 017-024 (1975)
On the Theory of Double Curved Shallow Shells

A.D. Tepavičarov
Sofia, Higher Institute of Civil Engineering. Blvd. H. Smirnenski 1

It is shown that the system of mixed partial differential equations after V. Z. Vlasov for investigation of the stress and strain state of double curved shallow shells may be represented with the aid of an approximete relationship in another form. In the important practical case – a shallow shell over a rectangular base supported on ideal diaphragms, these equations are reduced to independent partial differential equations of the 4th order with constant coefficients for the stress function and the function of radial displacement respectively. Simplified solutions based on the latter equations may be obtained which are convenient for practical application.

JTAM, Sofia, vol. 6 Issue 3 pp. 025-030 (1975)
A Numerical Method for Computing the Strength of a Discus with the Plastic Deformation Taken into Account

A.I. Birger, M.F. Jakoviev, V.F. Guk
USSR, Moskow

A discus under the influence of centrifugal forces and irregular heating is considered. The formation of plastic zones is taken into account. A power relationship between the intensities of strains and stresses is assumed. A numerical method of finite differences is proposed.

JTAM, Sofia, vol. 6 Issue 3 pp. 031-038 (1975)
On the Question of Water Column Detachment during Unstable Currents in Tubes

H.I. Hristov
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km

The dynamic characteristics of unstable motion when a water column is detached are determined. The cases of an inclined and a vertical pipe-line are considered. The velocity of return during closure of the detached water column is determined.

JTAM, Sofia, vol. 6 Issue 3 pp. 039-046 (1975)
On the Oscillations of Elliptical Cylindrical Shells

M.M. Kozarov
Sofia, Higher Institute of Civil Engineering, Blvd. H. Smirnenski 1

The free oscillations of elliptical cylindrical shells according to the membrane and momental theory of shells is considered. The basic differential equations are obtained by the method of Ostrogradski – Hamilton. The Rayleigh-Ritz method is applied in the solution of the problem. Results for different types of oscillations are obtained from different forms of displacements. The frequency equations are in the form of equations of determinants.

JTAM, Sofia, vol. 6 Issue 3 pp. 047-060 (1975)
Synthesis of Initial Gear Surfaces with Arbitrary Crossed Axes

K.M. Petrov
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km

The theoretical basis of the synthesis of initial surfaces of spatial mechanisms with higher kinematic couples and arbitrarily crossed axes is given. The relationships between the geometric parameters of the primary sinuses of gears of the hypoide type and the longitudal and transversal orientation of the teeth's surfaces in the initial point of contact are derived. The qualitative characteristics are investigated for this point which allows the determination of the optimum couple of initial surfaces with concrete requirements satisfied by varying some parameters.

JTAM, Sofia, vol. 6 Issue 3 pp. 061-074 (1975)
On the Solution of the Problem of Determining Elastic Deformations of a Circular Cylinder. I

K.A. Jamboliev
Sofia, Central Laboratory of Physical and Chemical Mechanics, Bulgarian Academy of Sciences, IV km

A semireversible method for solving the elastic problem of a cylinder with a given length is proposed. The displacement functions of the cylinder are determined. They depend on a definite number of coefficients. The displacement in given points of the cylinder must be known previously for determining these coefficients. The problem is solved for mixed boundary conditions. Fourier Series of Bessel Functions are applied. The solution is valid for cylinders with known geometric and elastic characteristics regardless of the material they are made from if only displacement in several points of the cylinder must be known.

JTAM, Sofia, vol. 6 Issue 3 pp. 075-080 (1975)