Journal of Theoretical and Applied Mechanics

Volume 36, Number 3, 2006




P. Dobreva, M. Kartalev


Institute of Mechanics, Bulgarian Academy of Sciences,

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



N. Shevyrev, G. Zastenker


Space Research Institute, Russian Academy of Sciences,

84/32, Profsousnaya, 117811 Moscow, Russia,



A. Koval

Faculty of Mathematics and Physics, Charles University,

2, V. Holesovickach, 18000 Prague 8, Czech Republic,



Interpretation of satellite magnetosheath plasma measurements using a magnetosheath-magnetosphere numerical model


Abstract. We consider a specific implementation of a numerical magnetosheath model, where the preliminary computation of the angle between solar wind flow and Sun-Earth direction at the spacecraft trajectory points is utilized for better implementation of the angular diagram of the device. The goal is better determination of the relation between the “real” and “measured” parameters. The parameter under consideration is ion flux, measured by VDP instrument on board Interball-1 satellite. A new numerical three dimensional model of the system magnetosphere – magnetosheath, lately developed in the Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, is utilized in this study. This is a self-consistent solution of the magnetosheath problem (here in gasdynamic approach) and a hybrid numerical/data based magnetosphere model. The geometries and the positions of the bow shock wave and the magnetopause are obtained as a part of the solution. The model provides in particular a 3D distribution of plasma parameters in the magnetosheath under certain parameters of the solar wind flow. One of the advantages is the capability of the model to simulate the influence of the specific 3D geometry of the magnetopause on the magnetosheath flow. The comparison of the model predictions and the measured parameters may discover magnetosheath flow disturbances which are not of the solar wind origin. We consider and discuss data obtained along the trajectory of a real Interball-1 magnetosheath crossing. The present study is a continuation of the preliminary consideration, published earlier.


Key words: model, magnetosheath, magnetosphere, gas dynamic satellite.


R. Raghavendra Rao


Department of Mathematics,

Eritrea Institute of Technology and Teachers Education,

Mai-Nefhi, Eritrea, (North East Africa),





Abstract. A generalized form of Reynolds equation for two symmetrical surfaces is derived by considering slip at the bearing surfaces. This equation is applied to study the effects of velocity-slip for the lubrication of Journal bearings using Reynolds boundary conditions. Expressions of pressure, load capacity and coefficient of friction are obtained and were numerically analized for various parameters. It is found that the point of cavitations moves away from the centre due to the slip and moves towards the centre due to high viscous layer at the periphery. The load capacity decreases due to slip which is unfavourable for lubrication.


Key words: Reynolds equation, velocity-slip, viscosity, journal bearing, Reynolds boundary conditions, point of cavitations, load capacity, coefficient of friction.


Valeriy Lokhov, Yuriy Nyashin, Valentine Kiryukhin


Department of Theoretical Mechanics,

29, Komsomolskii prospect, 614000, Perm, Russia,



Franz Ziegler


Department of Civil Engineering,

Vienna University of Technology,

8/E2063, Wiedner-Hauptstrasse, A-1040, Vienna, Austria,





Abstract: Many problems in continuum mechanics rely on the concept of eigenstrain. The authors proved the theorem on decomposition of eigenstrain (when imposed in an elastic body) into two parts, namely into its stress-free and deformation-free constituents. Individual determination of these constituents is crucial to keep the control of deformation and of stress by eigenstrain independent. General conditions for eigenstrain to be stress-free are derived. The generalized statement of the appropriate boundary value problem with eigenstrain is applied that becomes important for discrete and discretized systems. The relation between the criterion for such stress-free eigenstrain and Duhamel’s analogy is established.


Key words: eigenstrain decomposition, generalized solution, optimal shape control, elastic body.


J. Ivanova, G. Nikolova


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Interphase model for a multilayer structures in heat conduction problems. Non-perfect contact


Abstract. In the present paper the thermal behaviour of the interphase layer, disposed between two bodies in the case of non-perfect contact on the interfaces is analyzed by Biot’s variational principle. The main aim is to find the local partial differential equations for interphase layer for two types of distribution of the temperature - linear and quadratic. The comparisons of the temperatures in the interphase layer are done for effective thermal and elastic characteristics of a layer, composed by and . The non-perfect contact conditions for temperatures are assumed along the interfaces. The application example for elastic isotropic interphase layer with finite length is performed. One part of the interfaces allows the perfect contact condition. On the rest part of the interface length a non-perfect contact for temperatures thought Kapitza thermal resistance  is assumed.

The layer is assumed elastic on the first part while on the rest part the thermal stress reaches its yield limit. The critical length of the perfect contact condition is analytically found.

The results are illustrated in figures and discussed.


Key words: heat conduction, interphases layer, FGMs, non-perfect contact, thermal stresses.


Angel S. Mladensky, Victor I. Rizov


University of Architecture, Civil Engineering and Geodesy,

1, Chr. Smirnensky Blvd, 1046 Sofia, Bulgaria,





Abstract. In the present study a crack problem under mixed Mode I/II/III loading conditions in a rectangular composite beam is considered in the terms of the total strain energy release rate. The beam structure is made of two unidirectional composite materials. The crack is situated between them and propagates longitudinally to the beam axis. An analytical solution of the problem for determination of the strain energy release rate is obtained. For this purpose the values of the crack front internal forces are used. The solution is based on the linear elastic fracture mechanics. The correctness of the formula derived is checked by comparison with a known linear elastic beam theory solution. An extensive investigation of the influence of some material, geometrical and load parameters on the strain energy release rate is also carried-out.


Key words: fracture mechanics, strain energy release rate, unidirectional fiber reinforced composite materials, internal forces.


G. B. Stoychev, P. I. Matov


Technical University of Sofia,

8, Kl. Ohridski Blvd, 1000, Sofia, Bulgaria,



Finite element modelling of semi-compensated overhead contact line system


Abstract. A finite element model of semi-compensated overhead contact line system is under consideration in this paper. Numerical results are obtained and analyzed. A university-licensed version of finite element code ANSYS is used to perform the numerical experiments. Results for the deflection of the overhead contact line and the tensile force in the catenary wire are given for some typical values of the temperature conditions. On the other hand, a laboratory model of semi-compensated overhead contact line system is investigated. The numerical and experimental data are compared with analytically obtained results for the same temperature conditions. There is a good agreement between computed results and experimental data from the laboratory model. In the cases of loaded and unloaded support droppers some advantages of the finite element modelling are established.


Key words: electric railways, semi-compensated overhead contact line system, finite element analyses, experimental investigations.


M. Kirilova, S. Stoytchev, D. Pashkouleva, V. Kavardzhikov,


Institute of Mechanics, Bulgarian Academy of Sciences, 

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





Abstract. The structural, physical and mechanical properties of three commercially available in Bulgaria hernia meshes were compared. Uniaxial tensile tests on flat specimens in two orthogonal directions were performed by using testing device FU1000/E. The experimental data were represented as load- stretch ratio relationships. It was shown that all investigated meshes revealed orthotropic mechanical properties except one, which possessed isotropic properties. A criterion was proposed for design and selection of optimal synthetic hernia mesh. The comparison between different brands of meshes was done on the basis of the proposed criterion. The surgical mesh Surgimesh1 was chosen as the most appropriate for surgical implantation.


Key words: hernia meshes, fascia, tensile strength, elasticity.