Issue 4

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

Non-Linear Electroelasticity. Part I. Kinematics and Balance Equations

G. Brankov, N. Petrov
Bulgarian Academy of Sciences, 1, Sedmi Noemvri Street, Sofia; IMM – BAN, kv. Geo Milev, bI. 8, Sofia

This is an examination into a dielectric body composed of two interacting ionic continuums. The basic equations worked out, which are averaged along the two continuums, indicate that the state of the medium is determined by the strain gradients, the temperature, the polarization, and the polarization, gradients. In the particular case of a body made up of particles with a dipole moment of a constant size, it is possible to model its mechanical properties by means of the basic equations of the micropolar theory.

JTAM, Sofia, vol. 4 Issue 4 pp. 009-017 (1973), [Full Article]

Variational Problems of the Theory of Viscous-Plasticity at Great Strains

P. Pezyna1, A. Baltov2
1IPPT – PAN, 21 Swetokszyska Street, Warsaw, Poland
2IMM – BAN, kv. Geo Milev, bl. 8, Sofia

Demonstration is offered for variational theorems for elastic/viscous-elastic bodies under great strains. The instance of static loading is examined. The initial-boundary problem is formulated in terms of velocities of strains and displacements.

JTAM, Sofia, vol. 4 Issue 4 pp. 019-028 (1973)

Critical Loading of an Elastic Circular Arc of Variable Cross-Section

M. Oğuztiöreli1, D. Mangeron2, V. Poterasu2
1Alberta University, Edmonton 7, Alberta, Canada
2Polytechnical Institute, Rumania

The authors have worked out the basic equations for determining the critical force for an elastic circular arc of variable cross-section, which lead to a relatively simple and easily applicable algorithm.

JTAM, Sofia, vol. 4 Issue 4 pp. 029-036 (1973)

Stability of Inclined Orthotropic Shells of Variable Thickness Upon Taking Account of the Transverse Angular Strains

M. Kolchakov
ISK, 6 Lenin Square, Sofia

An examination is made into the stability of inclined orthotropic shells on a rectangular base, for given geometrical non-linearity, under the effect of radial loading. Use is made of a specified theory of shells which allows for taking account of the transverse angular strains and of the transverse skidding stresses. The critical loads have been obtained depending on the geometrical and physical parameters of the shell. It was established that the difference between the results obtained with the classical and with the re-specified theory depends on the ratio between the thickness and the dimensions in ground plan of the shell, on the ratio between the modules of skidding in ground plan and in a transverse direction, as well as on the parameters of the variable thickness.

JTAM, Sofia, vol. 4 Issue 4 pp. 037-052 (1973)

Torsion of Prismatical Bars Made of Micropolar Material

Cz. Usidus
IPPT – PAN, Swetokszyska Street, Warsaw, Poland

The paper examines the torsion of prismatic bars under the assumption that the material of the bar is governed by the equations of the non-symmetrical theory of elasticity. The solution has been obtained by means of the Saint-Venant function and by a supplementary function of the stresses. The differential equations for this function and their corresponding boundary conditions have been worked out. The case involving a bar of circular cross-section is examined in detail, with due reference to the influence of the momentum stresses on increasing the torque.

JTAM, Sofia, vol. 4 Issue 4 pp. 053-061 (1973), [Full Article]

Loci of the Additional Kinematic Elements upon the Relative Movement of a Solid Body

S. Buchvarov, Z. Cherneva-Popova
VVMI – Durvenitsa, Sofia

Worked out in the paper are certain loci of the additional kinematic elements upon the relative movement of a solid body, which are characterized by definite metric properties. A trihedron is introduced at an arbitrary point of the body and is oriented in a definite manner in relation to the relative angular velocity of the body. In this trihedron the kinematic element is resolved into three components, and the subsequent stage is to find loci for which one of these components is equal to zero.

JTAM, Sofia, vol. 4 Issue 4 pp. 063-072 (1973)

Certain Sufficient Conditions for Applicability of the Hamilton-Jacobi Theorem for a Non-Holonomic Scleronomous System

I. Iliev
47, Asen Halachev Street, Plovdiv

Sumbatov's work [1] deals with the cases in which the trajectories of the non-holonomic system are part of the trajectories of a holoromic system with kinetic energy coinciding with the kinetic energy of the non-holonomic system released from the bonds and a suitably selected force function. Hence the conclusion that the Hamilton-Jacobi theorem is applicable to the non-holonomic system. A sufficient condition for applicability of the Hamilton-Jacobi theorem to a non-holonomic scleronomous system is presented in the article.

JTAM, Sofia, vol. 4 Issue 4 pp. 073-078 (1973)

Normal Circular Elastic Waves in an Infinitely Long Thick-Walled Cylinder Filled with Ideal Liquid

G. Gergiev1, E. Lazarov2
1VMGI, Sofia
2VMEI – Durvenitsa, Sofia

A study is made into the spreading of normal circular waves in an elastic cylinder filled with ideal liquid. The characteristic equation for the oscillation is worked out and its general integrals are given. Calculations are made for the dispersion curves of the phase velocities and the radial displacements of the external surface of the cylinder are determined.

JTAM, Sofia, vol. 4 Issue 4 pp. 079-088 (1973)

Dynamics of a Regulator for Ensuring Uniformity in Bringing Down Loads Suspended on a Rope

H. Popov
30, S. Vrachansky Street B., Varna

There exists information in pertinent literature about regulators ensuring uniformity in the lowering of loads suspended on a rope, as is the case with the Buas Sard regulator. The article presents for examination a regulator of a rather simple design for the same use though operating on another principle. The author has also worked out and studied the system of non-linear differential equations of the movement in the mechanical system. It is demonstrated that the system allows for a stable stationary regime.

JTAM, Sofia, vol. 4 Issue 4 pp. 089-094 (1973)

Studies into Post-Ultimal Strains of Thin Anisotropic Shells

V. Babenko, Y. Ivanova
IMM – BAN, kv. Geo Milev, bl. 8, Sofia

The paper contains a study of post-ultimate strains of inclined anisotropic shells or rather determinations of the lower critical loads of thin shells upon various manners of loading. It has been assumed that the relative strains appearing in the anisotropic shells are small, that the shell is sufficiently thin, and that it is linearly elastic. The geometric method of A. V. Pogorelov has been used in solving this problem. An analogue has been obtained of his variational principle A for anisotropic shells. The authors have examined the post-critical equilibrium states of strictly convex anisotropic shells under the effect of concentrated force and external pressure. Orthotropic shells have been studied in greater detail.

JTAM, Sofia, vol. 4 Issue 4 pp. 095-106 (1973)

Scientific Activities – Second National Congress on Theoretical and Applied Mechanics, Varna, October 8-14, 1973

JTAM, Sofia, vol. 4 Issue 4 pp. 107-108 (1973)