Journal of Theoretical and Applied Mechanics

Volume 39, Number 4, 2009

 

Contents

 

N. Petrov

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: petrov333@gmail.com

 

A. Szekeres

 

Department of Applied Mechanics, Budapest University of Technology and Economics,

Muegyetem 1-3, Budapest H1111, Hungary,

e-mail: szekeres@mm.bme.hu

 

NON-CLASSICAL THERMOELASTICITY

 

Abstract. The aim of the present study is to offer new, non-classical theory of thermoelasticity, which is able to solve the paradox of the infinite speed of propagation of the thermal perturbation, resulting from the application of Fourier law for the heat conduction. In this article we offer an extension of Clausius–Duhem inequality, which consists in replacement of the momentary dependence between the entropy and energy fluxes and their sources with dependences of memory type. As a result we found the restrictions, following from the validity of the second law of thermodynamics, on the constitutive equations and obtained hyperbolic differential equation for the caloric balance.

 

Key words: extended, non-classical, thermoelasticity, Clausius - Duhem, memory, paradox, infinite speed, heat conduction.

 

Nikolay K. Vitanov

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: vitanov@imbm.bas.bg

 

Bounds for heat transport for convection in rotating fluid layer

 

Abstract. We apply the Howard-Busse method of the optimum theory of turbulence and investigate numerically the effect of strong rotation on the upper bound on the convective heat transport in a horizontal fluid layer of infinite Prandtl number Pr. We discuss the case of single wavenumber fields and detect formation of nonlinear structures similar to the nonlinear vortex discussed by Bassom and Chang [1]. When R and Ta are large enough there is a reshaping of the horizontal structure of the optimum fields.

 

Key words: convective heat transfer, rotating fluid, turbulence, optimum theory of turbulence.

 

L. I. Turchak

 

Dorodnicyn Computing Centre, Russian Academy of Sciences,

40, Vavilov St., Moscow 119333, Russia,

e-mail: turchak@ccas.ru

 

Modelling of wake vortex evolution

 

Abstract. The objective is the detailed study of generation and evolution of wake vortices past aircraft by means of mathematical modelling methods and revelation of impact of different conditions on intensity, evolution and lifetime of wake vortices. Currently, the presence of wake vortices past different objects limits the airspace capacity and flight safety level for aircraft of different purposes. However, wake vortex nature and evolution have not been studied in full measure. A mathematical model simulating the process of near wake generation past bodies of different shapes, as well as the wake evolution after rolling-up into wake vortices (far wake) will be developed. The processes are suggested to be modelled by means of the Method of Discrete Vortices. Far wake evolution is determined by its complex interaction with the atmosphere and ground boundary layer. The main factors that are supposed to take into account are: wind and ambient turbulence 3D-distributions, temperature stratification of the atmosphere, wind shear, as well as some others which effects will be manifested as considerable during the investigation. The ground boundary layer effects on wake vortex evolution are substantial at low flight altitudes and are determined through the boundary layer separation. The separation leads to changes in the wake vortex altitude and intensity.

 

Key words: wake vortices, Method of Discrete Vortices, flight safety.

 

L. I. Turchak, V. P. Shidlovskii

 

Dorodnicyn Computing Centre, Russian Academy of Sciences,

40, Vavilov Sr., Moscow 119333, Russia,

e-mail: turchak@ccas.ru

 

NUMERICAL ANALYSIS OF GAS LUBRICATION PROBLEMS

 

Abstract. The Navier-Stokes equations for compressible and heat-conducting fluid are taken as an initial set of control equations for the study of the problems of gas lubrication. After the presentation of these equations in dimensionless form it becomes evident that the only a priori small parameter for the study of gas lubrication problem is the ratio h*/L (gamma), where h* is the characteristical thickness of the lubrication layer, and L is the characteristical size of the bearing.

After elementary transformations it is found that the equations, describing the problems of interest, are formally coinciding with the boundary layer equations for a gas, though the boundary problems are now quite different from the aerodynamical ones.

All the properties listed above pertain to a general case of unsteady three-dimensional problems, but considered here is the simplest version of a two-dimensional steady problem.

The survey of the method of a numerical analysis of the gas lubrication problem on the basis of a formulation depicted embraces the method of small parameter, the spectral method and the method of integral relations. The generalization of these methods on the unsteady and 3D cases is connected only with the increased volume of computations, but does not evoke any difficulties of principal character.

 

Key words: gas lubrication, numerical analysis, Navier-Stokes equations.

 

E. Manoach

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: e.manoach@imbm.bas.bg

 

damage detections IN nonlinear vibrating thermally loaded structures

 

Abstract. In this work, geometrically nonlinear vibrations of fully clamped beams and plates subjected to thermal changes are used to study the sensitivity of some vibration response parameters to the presence of damage and elevated temperature. The geometrically nonlinear version of the Mindlin plate theory and Timoshenko beam theory are used to model the structure behaviour. Damage is represented as a thickness reduction in a small area of the structure. The structures are subjected to harmonic loading leading to large amplitude vibrations and temperature changes. The main results are focussed on establishing the influence of damage on the vibration response of the heated and the unheated structures and the change in the time-history diagrams and the Poincaré maps caused by damage and elevated temperature. The damage detection criterion formulated earlier for non-heated plates, based on analyzing the points in the Poincaré sections of the damaged and healthy plate, is modified and tested for the case of plates and beams additionally subjected to elevated temperatures. The importance of taking into account the actual temperature in the process of damage detection is shown.

Key words: plates, beams, damage detection, Poincaré maps, thermal loads.

 

A. Benhamena, G. Mesmacque, A. Amrouche, N. Benseddiq

 

Laboratoire de Mécanique de Lille, Université de Lille 1,

UMR CNRS 8107, Villeneuve dAscq 59650, France,

e-mails: ali_benhamena@yahoo.fr, gerard.mesmacque@univ-lille1.fr,

abdelwaheb.amrouche@univ-lille1.fr, noureddine.benseddiq@univ-lille1.fr

 

A. Aid

 

Laboratoire LPQ3M BP 763, Université de Mascara, Algerie,

e-mail: aid_abdelkrim@yahoo.com

 

M. Benguediab

 

Department of Mechanical Engineering, University of Sidi Bel Abbes,

BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000, Algeria,

e-mail: benguediab_m@yahoo.fr

 

Elastic and Elastic–plastic J-integral solution for semi-elliptical surface crack in piping system

 

Abstract. The integrity assessment of defects in Pressurized Water Reactor (PWR) vessel involves detailed fracture assessment of pipes and elbows considering through wall cracks. The evaluation of the J-integral plays a central role in the integrity assessment of this structure. In this study, a three-dimensional finite element method was used to analyse the fracture behaviour of piping systems (pipe and elbow) by computing the J-integral along the crack front. The obtained results show that the geometrical configuration (pipe and elbow) and the crack size influence on direction of crack growth for semi-elliptical crack. The effects of the size, locations, orientations and the forms of crack on the evolution of J-integral are analyzed. The corner angle of elbow has a very important effect on the direction of crack growth.

 

Key words: pipe, elbow, Pressurized Water Reactor (PWR), surface crack, fracture mechanics, J-integral, limit load, Finite Element Method (FEM).

 

S. Cherneva, R. Iankov

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mails: sabina_cherneva@yahoo.com, iankovr@yahoo.com

 

D. Stoychev

 

Institute of Physical Chemistry, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 11, 1113 Sofia, Bulgaria,

e-mail: stoychev@ipchp.ipc.bas.bg

 

Determination of mechanical properties of electrochemically deposited thin gold films

 

Abstract. In the present work the mechanical properties of thin gold film with given thickness were investigated. The film was deposited electrochemically over brass substratum with given thickness and mechanical properties. It was realized micro indentation experiment of the film and as a result of this the experimental load-displacement curve was obtained. After that the process of micro indentation was modelled numerically by means of finite element method and numerical load-displacement curve was obtained. Subsequently experimental and numerical load-displacement curves were compared. Results, which were obtained through numerical simulations, give good agreement with the experimental results. Therefore the proposed method can be successfully applied for identification of material parameters of the accepted model.

 

Key words: thin films, mechanical properties, microindentation, finite-element analysis.

 

Y. Stoynov

 

Faculty of Applied Mathematics and Informatics,

Technical University of Sofia,

8, St. Kl. Ohridski St., 1756 Sofia, Bulgaria,

 

T. Rangelov

 

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

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

e-mail: rangelov@math.bas.bg

 

Time-harmonic crack problems in magnetoelectroelastic plane by biem

 

Abstract. Time-harmonic dynamic behaviour of a cracked magneto-electroelastic plane under an anti-plane electrical and magnetic load is studied. A fundamental solution for the coupled system of governing equations in the frequency domain is derived in a closed form using the Radom transform. Boundary Integral Equation Method (BIEM) is applied to evaluate the dependence of the Generalized Stress Intensity Factors (GSIF) on the frequency, on the material characteristics and on the direction of the incident time-harmonic wave. Software based on the BIEM is created using Mathematica and FORTRAN. The computational tool is validated by a solution of a benchmark example for an impermeable crack in an infinite magnetoelectroelastic plane subjected to an incident SH-wave. Simulation studies show the sensitivity of the dynamic generalized stress concentration field to the type of the magnetoelectroelastic material, to the characteristics of the applied generalized dynamic load and to the coupled character of the magnetoelectroelastic continua.

 

Key words: magnetoelectroelastic plane, time-harmonic behaviour, anti-plane crack, BIEM, GSIF computation.

 

P. Dineva

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: petia@imbm.bas.bg

 

T. Rangelov

 

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

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

e-mail: rangelov@math.bas.bg

 

Time-harmonic behaviour of a cracked inhomogeneous piezoelectric solid by biem

 

Abstract. The Boundary Integral Equation (BIE) solution of the dynamic problem for a cracked finite inhomogeneous solid subjected to in-plane mechanical and/or in-plane electrical loads is presented. As numerical example a center cracked rectangular GaN piezoelectric plane with quadratic varying inhomogeneity is investigated.

 

Key words: functionally graded piezoelectric solids, GaN material, in-plane cracks, BIEM, SIF computation.