Issue 2

JTAM, Sofia, vol. 4 Issue 2 (1973)

The 60th Anniversary of the Birth of G. Brankov – Corresponding Member of the Bulgarian Academy of Sciences, Professor Doctor of Technical Sciences

Editorial Board

JTAM, Sofia, vol. 4 Issue 2 pp. 009-010 (1973)

Physical-Mechanical Constructive Modelling of Wavewise Flat Roof Shells

G. Brankov, T. Markov, B. Dimitrov, Sp. Pamoukchiev, D. Panichkov
Bulgarian Academy of Sciences, “7 Noemvri" st., 1. Sofia

There are given the results from some experimental investigations carried out for establishing the actual stress strain state and the manner and form of the loss of stability as well as the process of fracture of wavewise flat shells subjected to uniformly distributed continuous loadings with regards to the working out of new methods for their calculation.

JTAM, Sofia, vol. 4 Issue 2 pp. 011-020 (1973)

On the Theory of Visco-Plasticity at Large Deformations

D. Kolarov, A. Baltov
Institute of Mechanicis and Mathematics, Bulgarian Acaemy of Sciences, Geo Milev distr., Sofia

The behaviour of deformable bodies at large visco-plastic deformations is analyzed by means of thermodynamical structural method. The first group of constitutive equations for visco-plastic bodies at large deformations is variationally deduced. The general character of the evolution equations for such bodies is also investigated.

JTAM, Sofia, vol. 4 Issue 2 pp. 021-030 (1973)

Investigation on an Elastic Cable As an Element of Spatial Suspension Construction

A. Popov
Higher Institute of Civil Engineering, blvd. “Hr. Smirnenski" 1, Sofia

At generally accepted basic premises, the behaviour of a flexible elastic cable subjected to variations in loading, temperature and distance between the supports, the prestressing and other factors is investigated as a result of the variation in the stress strain state of the suspended construction as a whole. The deduced basic equation (31) reflects the dependence between the variations of all physical and geometrical magnitudes. On its basis two partial problems are examined: the effect of the variation of the distance between the supports and the temperature and the variation of the initial loading. Except analytically, the results are presented also graphically and can be used both for solution of concrete problems and for assessment of the accuracy of some simplificating premises of theory of the suspended constructions.

JTAM, Sofia, vol. 4 Issue 2 pp. 031-048 (1973)

Stability at Creeping of One Surface Hyperbolic Shell with Axial Loading

M. Kozarov, P. Kolev
Higher Institute of Civil Engineering, blvd.

Results are given from the investigation of the stability at creeping of a freely supported thin isotropic one surface hyperbolic shell for which the external loading is accepted axially uniform along the shell edges. The problem is solved by means of the variational theorem of Sanders – McComb – Schlechte accounting the geometric and physical non-linearity as well as the initial imperfection of the intermediate surface of the shell. By means of Hoff's criterion the critical time is determined. The obtained system of nonlinear equations is linearized and solved numerically and the results are graphically presented.

JTAM, Sofia, vol. 4 Issue 2 pp. 049-060 (1973)

Qualitative Analysis of the Rate Sensivitity of Some Metals Subjected to Deformations

J. Klepachko1, D. Dimitrov2
1Institute of Basic Technical Problems, “Shwjentokshinska" st. 21, Warsaw
2Institute of Mathematics and Technical Mechanics, "Chapaev" st. 53, Sofia

On the basis of carried out qualitative analysis concrete forms of the functions, describing in the constitutive equations for aluminium and technically pure iron the rate effect of the plastic deformation, are proposed. For the purpose copious experimental material from other papers is used and numerous graphs are given.

JTAM, Sofia, vol. 4 Issue 2 pp. 061-072 (1973)

Statical Investigation on Slabs with Complex Contour

V. Droumev
Higher Institute of Civil Engineering, blvd. “Hr. Smirnenski

A slab the contour of which is formed from segments parallel to the axes x and y and which can be fixed in one or more points, is considered. The stress state is searched as a sum from the basic state, satisfying the statical conditions, and the correction selfstress state which on its hand in determined from the conditions for compatibility of the deformations. The complex derivative ψ(x,y) = ∂2 τ/∂x∂y is introduced as unknown magnitude. The solution is analogous to the method of forces in mechanics. A numerical example is given.

JTAM, Sofia, vol. 4 Issue 2 pp. 073-088 (1973)

On the Statical Investigation of Slope Spherical Shells on Rectangular Basis

A. Tepavicharov
Higher Institute of Civil Engineering, blvd. 'Hr. Smirnenski" 1, Sofia

The boundary conditions for which the V. S. Vlasov's differential equation for determination of the function of radial translation, coinciding with the equation of a plate on elastic basis is concrete, are shown. The deduced differential equation for determination of the function of stresses for a shell supported on ideal diaphragms also coincides with the equation of a plate on elastic basis. The right hand side of this equation is a membrane solution of the same shell. Differential equations analogous to the M. Mishonov's ones are obtained in the general case. A general closed approximate solution of V. S. Vlasov's differential equation is obtained after the method of Bubnov – Galyorkin. The shell solutions for some concrete loadings and boundary conditions are given in a table.

JTAM, Sofia, vol. 4 Issue 2 pp. 089-098 (1973)

One Monofrequency Oscillations with External Disturbances in Third Rank Resonance

B. Cheshankov
Center of Applied Mathematics, Sofia

One monofrequency resonance oscillations of mechanical systems with internal symmetry, subjected to external harmonic disturbances, are investigated. The problem is brought to examining the canonical systems describing the resonance phenomena. The cases when β ≈ 1, β ≈ 3, β ≈ 1⁄3, for which the canonical systems are (2.11), (6.1), (6.3) respectively, are considered. The canonical systems are investigated in a phase plane. The typical images of the phase trajectories are constructed.

JTAM, Sofia, vol. 4 Issue 2 pp. 099-112 (1973)

Difference Schemes for Rroblems from the Elasticity Theory in Regions with Curvilinear Boundaries. II. Assessment of the Convergency Rate. Nomerical Examples

R. Lazarov
Institute of Mathematics and Mechanics, Geo Milev dist., Sofia

Differential schemes of finite differences for two-dimensional symmetric regions with curvilinear boundaries, approximating the basic statical problems of the elasticity theory for a homogeneous isotropic body are compiled and investigated in the paper. Assessment is made of the convergency rate of the schemes in an energetic norm. Numerical example solved by means of BESM-6 computer is given.

JTAM, Sofia, vol. 4 Issue 2 pp. 113-124 (1973)

On the Necessary and Sufficient Conditions for Stability of Stationary Motions of Satellite-Gyrostat

B. Bonev, L. Lilov
Institute of Mechanics and Mathematics, Geo Milev distr., Sofia

The multitude of positions of relative equilibrium in orbital co-ordinate system is determined in Eulerian angles for a satellite with rotors (gyrostat) the mass centre of which describes a circular orbit in central Newton field of forces. The necessary conditions for stability of all positions of relative equilibrium are found. It is shown that the obtained necessary conditions are simultaneously sufficient conditions for stability, provided that the rotors rotate with angular speed sufficiently great in absolute magnitudes.

JTAM, Sofia, vol. 4 Issue 2 pp. 125-132 (1973)