Journal of Theoretical and Applied Mechanics

Volume 31, Number 1, 2001



P. K. Kolev, V. S. Nedev

Higher Military School of Transport,

158, Geo Milev Str., 1574 Sofia, Bulgaria




Abstract. This investigation deals with a manipulation robot with hydraulic drives of its modules. To satisfy the requirements for robot fast actions and its position accuracy, it is necessary to develop more precise dynamic model. With respect to this, the model under consideration is a system with distributed mass and elastic parameters. The differential equation of robot stationary motion for one of the system regional motions is derived. A single frequency solution is developed in asymptotic series by means of Krilov - Bogoljubov’s method. As a result, the law of motion is obtained taking into account the characteristic equation zero root.

Key words: a manipulation system, distributed mass and elastic parameters.



P. G. Kalitzova-Kurteva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Sofia,





Abstract. In the present work non-isothermal gas absorption or desorption in a horizontal liquid layer of finite depth is considered. The chemical component that absorbs or desorbs is considered to be not surface-active. The instability is induced

by temperature gradients along the gas-liquid surface, due to the thermal effect on it during the mass transfer through this surface. The linear stability analysis is applied and the corresponding eigenvalue problem is solved. The oscillatory threshold is obtained in analytical form when perturbed fluxes of mass and heat on the layer bottom are zero - “insulating” case. The behavior of the neutral stability curves is studied in dependence on the ratio between heat flux across the layer and net of heat released or absorbed in the free surface.

Key words: oscillatory Marangoni instability, heat of solution, gas absorption or desorption.


D. Stoyanov

Institute for Industrial Mathematics,

Erwin Schroedinger Str., Geb.49, D-67663 Kaiserslautern, Germany,e-mail:


Institute of Applied Mathematics and Informatics,Technical University of Sofia, 8, St. Kl. Ohridski Blvd., 1756 Sofia, Bulgaria,



O. Iliev

Institute for Industrial Mathematics,Erwin Schroedinger Str., Geb. 49, D-67663 Kaiserslautern, Germany,e-mail:


Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria,



On a Flexible Tool for Upscaling Porous Media Flow Problems

Abstract. Porous media flow modelling is characterised by two scales: micro, or pore scale, and macroscale, where one needs to investigate certain effects. Usually it is not possible to resolve the microscale at existing computers, therefore macromodels are solved. The upscaling of the model can be done within the framework of the homogenisation theory. Solving Stokes or Navier-Stokes equations in a representative porous media cell is required there as a step to calculating the permeability tensor involved in the Darcy law. A flexible tool for solving such problems with extremely complex geometry is presented here, together with some real computations.

Key words: incompressible flow, multigrid, upscaling of porous media flows, flexible solver.



S. D. Iliev

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,



Simulated “Stick-Slip” Behaviour of the Contact Line of the liquid drop on a horizontal plane

Abstract. In the present article the effect of the “stick-slip’ behaviour of the liquid droplet located on a horizontal plane contact line is discussed. More precisely the case when the contact line retains its stability under a change of the drop volume until it suddenly moves into an equilibrium state, and sharply changes its contact line is considered. The base of our study is a continuum model of three-phase fluid/liquid/solid system equilibrium that permits us to describe the contact line resistance to shift by potential barrier. We assume the system to move into an equilibrium state following a specific path. Numerically simulated stick-slip behaviour under a slow change of the drop volume with varied contact lines located on a horizontal plane is realised.

Key words: stick-slip behaviour, liquid drops, contact line.

N. D. Nikolov, J. D. Nikolova

University “Prof. Dr. Assen Zlatarov” – Bourgas,

1, Prof. Yakimov Str., 8008 Bourgas, Bulgaria,



L. P. Bojinov

Technical University – Varna,

1, Studentska Str., 9010 Varna, Bulgaria,



Ultrafiltration of lubricant emulsions

Abstract. A process of ultrafiltration at continuous withdrawal of superconcentrate from the existing concentration zone at circular cross section of the channel and steady-state flow at laminar region was carried out. Acetatecellulose tubular membranes with inside diameter of 12,5 mm were used. An increased relative productivity was established versus the case of utilization without superconcentrate receptacle.

Key words: ultrafiltration, concentration polarization, laminar flow, tubular membranes, superconcentrate.



G. Marinova, A. Baltov

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,



A. Zlatarski

Industrial Furnaces, Rudmetallurgproject J.S.Co.,

205, Al. Stamboliyski Str., 1309 Sofia, Bulgaria

Effect of Model Selection on the Thermal Conduction Process under Harmonic Temperature Actions

Abstract. We aim to clarify what is the influence of the thermal relaxation time in the Maxwell-Cataneo model on the bodies under harmonic temperature action. This could help to identify the model for the process under consideration in the case of given experimental data.

Key words: thermal conductivity, harmonic temperature field, thermal relaxation model.


A. Zolochevsky

Fukui University, Department of Mechanical Engineering,

9-1, Bunkyo 3-chome, Fukui, 910-8507, Japan,



S. N. Sklepus

Institute for Problems of Machinery,

Department of Applied Mathematics and Computational Methods,

Ukrainian Academy of Sciences,

2/10, Pozharsky Str., Kharkov-46, 61046, Ukraine,



J. Betten

Technical University Aachen,

Department of Mathematical Models in Materials Science,

55, Templergraben Str., Aachen, D-52062, Germany,



New Model of Unilateral Creep Damage

Abstract. New constitutive equation of creep and damage growth equation for materials with parallel microcracks are derived here. These equations describe different behaviour of materials in tension and compression, unilateral damage as well as damage induced anisotropy. The equivalent stress in the creep potential contains the stress intensity and two joint invariants of the stress tensor and of the unit vector associated with parallel microcracks. Data of uniaxial tension, uniaxial compression and pure torsion tests were used to determine material parameters in the proposed model. Creep constitutive equation and damage evolution equation introduced are evaluated on the basis of experimental data on creep behaviour of AK4-1T aluminium alloy. Comparison of the theoretical results with the experimental data indicates that the proposed model gives good predictions of the creep rupture times under multiaxial loading.

Key words: unilateral creep damage, damage induced anisotropy, creep potential, microcracks, basic experiments.


V. Kavardjikov, P. Dineva, St. Karastanev

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,




Abstract. A hybrid theoretical–experimental method of solving two-dimensional time-harmonic elasto-dynamic problem of a finite cracked body using Laser Diffraction and Boundary Integral Equation Method (BIEM) is proposed.

Displacement BIEM fails at solution of the crack problems and the hyper-singular traction BIEM is used. Traction BIEM suffers because the size of the singular near-tip field is unknown, a priori, and the numerical solution is accurate only at an optimum size of the special crack-tip boundary elements modelling this field.

The proposed hybrid method shows that the experimental data for crack opening displacements can help in evaluation of the singular near-tip field and can increase the accuracy of the numerical method. As an illustrative example a study of the dynamical behaviour of a centre-cracked rectangular plate under uniform dynamic load is presented.

Key words: crack opening displacement, BIEM accuracy, crack-tip boundary elements, laser light diffraction.



I. Paskaleva, M. Kouteva

Central Laboratory for Seismic Mechanics and Earthquake Engineering (CLSMEE),

Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 3, 1113 Sofia, Bulgaria,




Abstract. This study is provoked in connection with the safety construction of pipelines for high pressure in northeastern Bulgaria. Data bank containing geological, seismomechanical and geodetical information is created specially for the purposses of this analysis. The maximum values of the surface strains are determined on the base of registered maximum velocities during earthquakes recorded in this part of the country. A comparison between the recorded strains and the geodetical observations done immediatly after strong ground motions occur is carried out. The results are used for mapping the surface strains, which are very important for the seismic safety design of different lifelines, special structures, sensitive to ground deformations (pipelines, bridges, underground excavations etc.).

Key words: ground motion, maximum velocity, accelerogram, strain.