Issue 2
JTAM, Sofia, vol. 7 Issue 2 (1976)

Application of Muskhelishvili's Method to the Solution of a Class of Problems Involving the Bending of a Thin Plate Containing a Fissure

I.M. Mihovski
Sofia, Sofia University, Faculty of Mathematics and Mechanics, A. Ivanov St., 5


Muskhelishvili's method has been successfully used in solving a broad range of plane linear-elastic problems for an infinite plane with section. This method reduces the original problem to Riemann-Hilbert's problem of elastic potentials. Using the analogy existing between these two problems and the problem of pure bending of thin linear-elastic plates containing fissures, a diagram has been proposed in the article which, taking account of the specifi city of the problem of pure bending of plates, makes it possible, as in the case of the above method, to reduce the original problem to the solution of Riemann-Hilbert's problem for complex potentials. By way of illustration of the diagram proposed, the author has presented the solution of the problem for pure bending of an infinite plate containing a fissure.

JTAM, Sofia, vol. 7 Issue 2 pp. 009-014 (1976)

On the Linearization and Solution of Non-Linear Differential Equations Describing the Movement of Compressible Fluids in Pipelines

G.K. Nikolov

The article proposes linearization in the solution of the nonlinear differential equations describing the movement of compressible fluids in pipelines. Concrete illustrating calculations have been carried out by computer.

JTAM, Sofia, vol. 7 Issue 2 pp. 015-019 (1976)
Application of the Method of Conformal Representation in Calculating Tunnel Linings

S. Hristov, K. Popova
Sofia, Institute of Mathematics and Mechanics

The displacements and stresses in a tunnel lining have been determined by the method of conformal representation. The material of the lining is assumed to be linearly elastic. The problem is reduced to the solution of a first basic boundary problem of the elasticity theory. The solution is performed numerically by a computer. A numerical example is also given

JTAM, Sofia, vol. 7 Issue 2 pp. 020-026 (1976)
Free Convection Effects on MHD Stokes Problem for a Vertical Plate

V.M. Soundalgekar, S.K. Gupta, R.N. Aranake
Cardiff, Great Britain, Department of Mechanical Engineering, UWIST

An exact analysis of MGD Stokes problem (also Rayleigh's problem) for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started vertical plate, under the action of transversely applied magnetic field, is carried out. The heat due to viscous dissipation and the indused magnetic field are assumed to be negligible. The effects of the externally heating or cooling of the plate by the free convection currents are studied. It is observed that reverse flow occurs when the plate is heated by the free convection currents.

JTAM, Sofia, vol. 7 Issue 2 pp. 027-033 (1976), [Full Article]

Torsional Buckling of a Cylindrical Shell with Elliptic Cross Section

P.T. Kolev
Sofia, Higher Institute of Construction Engineering, 1, Smirnensky St.

The torsional buckling of a thin-wall isotropical cylindrical shell with elliptic cross section under uniformly distributed tangential stresses on the edges is considered in the paper. Using Reisner's variational principle, a formula is obtained for critical tangential stress by torsion. It has been established that the cylindrical shell with elliptic cross section under torsion is "stiffer" with respect to the circular cylindrical shell circumscribed around the ellipse.

JTAM, Sofia, vol. 7 Issue 2 pp. 034-040 (1976)
Change in the Form of Equilibrium of Polymeric Cylindrical Shells under Longitudinal Pressure

A.E. Alexandrov, A.A. Nikishin, V.I. Lukyanovich

The authors present the basic methodological, experimental and theoretical principles used in the solution of the problem of determining the time of loss of stability at the creep of closed viscous-elastic shells, charged with longitudinal pressure load uniformly distributed along the annular boundary outline. The pre-critical stressed state is taken as instantaneous and is described by non-linear correlations. The problem is solved through a numerical method on a BESM-4 computer. The results from the calculations compare satisfactorily with those experimentally obtained.

JTAM, Sofia, vol. 7 Issue 2 pp. 041-049 (1976)
Solution of the Equations of the Unidirectional Smoothly Varying Irregular Thrust Motion, Due Account Being Taken of the Elastic Properties of the Liquid and of the Boundary

I. Ivanov, M. Sotirov
Sofia, Institute of Mathematics and Mechanics with Computer Centre, Bulgarian Academy of Sciences

On the basis of the method of characteristics, a numerical method has been worked out for solving the equations of the uniform smoothly varying irregular thrust movement, due account being taken of the elastic properties of the liquid and of the rigid boundary, at the corresponding initial and boundary conditions of the concrete practical problems. By using the programme worked out, it has been possible to determine the interval of the pitch at which a stable solution is obtained.

JTAM, Sofia, vol. 7 Issue 2 pp. 050-062 (1976)
Waves in an Unlimited Thermoviscoelastic Medium with Temperature-Rate Dependence

Ts.P. Ivanov
Sofia, Institute of Mathematics and Mechanics with Computer Centre, Bulgarian Academy of Sciences

The propagation of harmonic waves in an unlimited thermoviscoelastic medium with temperature-rate dependence is discussed in the article. The effect is examined of a plane source of heat applied in a plane perpendicular to the propagation of the waves and varying in time according to a harmonic principle. Assymptotic formulae have been obtained for the phase velocity and for the attenuation factor at large and small values of the reduced frequency. Further examined is the influence of the mechanical and thermal properties of the medium on the ratio of the amplitudes of displacement and temperature and on the phase displacement between them.

JTAM, Sofia, vol. 7 Issue 2 pp. 063-073 (1976)
Theoretical and Experimental Investigation of the Stability of a Polymer Bar with Linearly Increasing Compression

K. Popov1, G. Mandachev1, E. Bonchev2, P. Lazarov3, G. Venkov4
1Higher Institute of Chemical Technology at Durvenitsa
2Centre of Mathematics and Mechanics at the Higher Institute of Mechanical and Electrical Engineering
3Higher Institute of Mechanical and Electrical Engineering at Durvenitsa
4Higher Institute of Chemical Engineering at Durvenitsa

This is a study into the problem of the stability of a polymer rod of constant cross section, hingedly secured at either end and loaded with linearly growing pressure force. A comparison has been drawn between the theoretical and the experimental results, which reveals a satisfactory degree of coincidence.

JTAM, Sofia, vol. 7 Issue 2 pp. 074-077 (1976)