
Archive issue  vol.9, No.2
3.
DYNAMIC TEARING OF THIN STEEL SHEET
M. ABERKANE and G. PLUVINAGE
Laboratoire de Fiabilité Mécanique, Université de Metz
57045 Metz cedex 01, FRANCE
email: aberkane@lfm.sciences.univmetz.fr
email: pluvina@lfm.sciences.univmetz.fr
A. OUIBRAHIM
Laboratoire d'Energétique Mécanique et Matériaux
Université de Boumerdes 35000, ALGERIA
email: ouibra@wissal.dz
This paper presents an energy analysis during dynamic tearing tests of thin steel sheet. A Charpy test device and an original experimental method are employed. The dynamic fracture toughness at initiation R_{0,dyn} and the dynamic tearing modulus T_{dyn} are obtained. For comparison, static trousers tearing tests are conducted, on the same material, in order to study the influence loading rate (V) on the essential work of fracture 'Gamma'_{e} (calculated from Mai and Cotterell (1984)). We have shown that by varying the loading rate from 1mm/min to 300 mm/min, the essential work of fracture 'Gamma'_{e} decreases slowly with the logarithm of the loading rate V. A significant drop in the dynamic fracture toughness compared to static one is observed, while making a comparison between R_{0,dyn} and 'Gamma'_{e} (1mm/min) due to the increase in the yield stress with loading rate.

Key words:  ductile tearing, trousers test, essential work of fracture, Charpy test device, petalling. 
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4.
MATHEMATICAL MODELLING OF WEB SEPARATION AND DYNAMICS ON A WEB ADHESION AND DRYING SIMULATOR
F. AHRENS and T. PATTERSON
Institute of Paper Science and Technology of the Georgia Institute of Technology
500 10th St., N.W., Atlanta, GA 30318, USA
F. BLOOM
Department of Mathematical Sciences
Northern Illinois University, DeKalb, IL 60115, USA
email: bloom@math.niu.edu
A mathematical model is presented of web peeling and transfer in a short open draw of the type present in many modern paper machines. Analysis of the model is shown to lead to results from which the work of adhesion may be computed; these results are compared with experimental data obtained from a Web Adhesion and Drying Simulator.

Key words:  work of adhesion, work of separation, web peel, web transfer, cohesion, web picking. 
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5.
FREE CONVECTION FROM A VERTICAL CYLINDER EMBEDDED IN A POROUS MEDIUM FILLED WITH COLD WATER
A.J. CHAMKHA
Production Engineering Department
The Public Authority for Applied Education and Training
Shuweikh, 70654, KUWAIT
C. BERCEA and I. POP
Faculty of Mathematics, University of Cluj
R3400 Cluj, CP 253, ROMANIA
A free convection boundary layer flow along a heated vertical cylinder embedded in a porous medium saturated with pure or saline water at low temperatures, up to 20^{o}C, is considered. The boundary layer analysis is formulated in terms of Darcy's law and a new density equation of state, which is of very high accuracy and of simple form, is postulated. Numerical solutions are presented and the flow field characteristics are analysed in detail for both cases of downward and upward flows. A very good agreement between the present results and those reported for particular situations was found.

Key words:  free convection, vertical cylinder, porous medium, pure or saline water at low temperatures. 
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6.
MODELING OF HEAT CHANGE RULES IN PLATE BEARINGS
E. FELDSZTEIN, M. JENEK and R. MARUDA
Mechanical Faculty, University of Zielona Góra
ul. Szafrana 4, 65246 Zielona Góra, POLAND
email: E.Feldsztein@ibmp.uz.zgora.pl
In the paper an algorithm of temperature calculation in plate bearings during their work is described. The results of temperature's level calculation in bearings for different conditions of their work using the proposed model and FEM model are given as well as the results of an experimental check on heat bearing work conditions. The differences between results of calculation and experiment are insignificant.

Key words:  temperature calculation, plate bearing, FEM. 
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7.
HALL EFFECTS ON MHD PLASMA COUETTE FLOW IN A ROTATING ENVIRONMENT
S.K. GHOSH
Department of Mathematics, Narajole Raj College
P.O.: Narajole, Dist.  Midnapore (West), West Bengal, INDIA
email: g_swapan@rediffmail.com
I. POP
Faculty of Mathematics, University of Cluj
R  3400 Cluj, CP 253, ROMANIA
email: popi@math.ubbcluj.ro
The Magnetohydrodynamic (MHD) plasma Couette flow in a rotating frame of reference subject to the Hall current is studied. This problem is confined to a startup process, which deals with an impulsive start of the moving plate as well as an accelerated start of the moving plate. The solution is obtained by employing the Laplace inversion method. An asymptotic behavior of the solution is analysed for small as well as large time T to gain the physical insight into the flow pattern. As a consequence of the physical situation of interest the fully ionized neutral plasma interacts with the frictional layer when it starts in motion. The dimensionless velocity profiles are depicted graphically and the shear stresses are presented in tables.

Key words:  Hall current, Coriolis force, viscous layer, neutral plasma, Rayleigh layer. 
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8.
THE STEADYSTATE RESPONSE ANALYSIS OF FLEXIBLECOUPLINGROTOR SYSTEMS
ShengChung HSIEH and AnChen LEE
Department of Mechanical Engineering, National Chiao Tung University
1001 Ta Hsueh Road, Hsinchu 30049, TAIWAN, R.O.C.
email: aclee@cc.nctu.edu.tw
JuhnHorng CHEN
Department of Mechanical Engineering
Chung Hua University
TAIWAN, R.O.C.
In this paper, a modeling procedure is presented to deal with the steadystate analysis of rotor systems with rubber cushiontype flexible couplings. The rubber cushiontype flexible coupling was modeled by an equivalent spring and the effect of misalignment was investigated. Moreover, we introduce the flexible coupling model in combination with the FEM model of rotating shafts to develop a complete formulation of a couplingrotor system. Finally, to illustrate the effects of the coupling misalignments on the dynamic behavior of the system, numerical examples of this couplingrotor system are presented.

Key words:  rubber cushion, flexible coupling, misalignment, rotor. 
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9.
EFFECTS OF CHEMICAL REACTION, HEAT AND MASS TRANSFER ON NONLINEAR BOUNDARY LAYER FLOW WITH HEAT SOURCE, THERMAL DIFFUSION IN THE PRESENCE OF SUCTION
R. KANDASAMY
Department of Mathematics
Institute of Road and Transport Technology
Erode  638 316, INDIA
email: kandan_kkk@yahoo.com
The problem concerns a nonlinear laminar boundary layer, chemical reaction, heat and mass transfer flow of an incompressible and viscous fluid past a continuously moving infinite vertical porous plate in the presence of suction under the influence of heat source and thermal diffusion. The similarity transformation has been utilized to convert the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then the numerical solution to the problem is given using the Gill method. The analysis of this results obtained shows that the flow field is influenced appreciably by the presence of suction at the surface, chemical reaction and magnetic effects.

Key words:  chemical reaction, heat and mass transfer, thermal diffusion, incompressible fluid and heat source. 
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10.
CALCULATION OF GEOMETRIC PROPERTIES OF OPEN CROSS SECTIONS OF THINWALLED BEAMS
M. MAÆKIEWICZ
Institute of Applied Mechanics, Poznañ University of Technology
ul. Piotrowo 3, 60965 Poznañ, POLAND
The work is devoted to an arbitrary open crosssection of a thinwalled beam. The shape of the crosssection is described with parametric curves, whereas the thickness is given as one parameter function.

Key words: 
open crosssection, thinwalled beam, warping function, Bézier cubic curve, geometric continuity. 
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11.
ELASTIC BENDING OF AN ISOTROPIC POROUS BEAM
K. MAGNUCKI^{ab} and P. STASIEWICZ^{a}
^{a} Institute of Applied Mechanics, Poznañ University of Technology
ul. Piotrowo 3, 60965 Poznañ, POLAND
^{b} Institute of Rail Vehicles "TABOR"
ul. Warszawska 181, 61055 Poznañ, POLAND
email: Krzysztof.Magnucki@put.poznan.pl
The subject of this paper is an isotropic porous beam with a rectangular cross section. Mechanical properties of the isotropic porous material vary across the depth of the beam. A nonlinear hypothesis of deformation of a plane cross section of this beam is described. The system of differential equations and boundary conditions of the problem is derived on the basis of the principle of minimum potential energy. A numerical analysis for simply supported beams under uniformly distributed load is made. A comparative analysis with the use of FEM and the COSMOS/M system is presented.

Key words: 
porous beams, cellular material, shear deformation, displacement. 
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12.
A NEW HIGHPRECISION TRIANGULAR PLATE ELEMENT
M.C. MANNA
Bengal Engineering College (Deemed University)
P.O.  Botanic Garden, Howrah  711 103, West Bengal, INDIA
email: mcmbecdu@lycos.com
This paper deals with the development of a new triangular finite element for bending analysis of isotropic rectangular plates by an explicit stiffness matrix. The first order shear deformation theory (FOSDT) is used to include the effect of transverse shear deformation. The element has eighteen nodes on the sides and six internal nodes. The geometry of the element is expressed by three linear shape functions of area coordinates. The formulation is displacement type and the use of area coordinates makes the shape functions for field variables to be expressed explicitly. No numerical integration is required to get the element stiffness matrix. The element has fiftyone degrees of freedom, which can be reduced to thirtynine degrees of freedom by a standard static condensation of the degrees of freedom associated with the internal nodes. An interesting feature of the element is that it is not prone to shear locking. Numerical examples are presented to show the accuracy and convergence characteristics of the element.

Key words: 
explicit stiffness matrix, FOSDT, static condensation, shear locking, convergence characteristic. 
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13.
Dedicated to Dr. Jack Halow
A THEORETICAL STUDY OF HEAT TRANSFER TO FLOWING GRANULAR MATERIALS
M. MASSOUDI
U.S. Department of Energy, National Energy Technology Laboratory
P.O. Box 10940, Pittsburgh, PA 15236, USA
email: Massoudi@netl.doe.gov
N.K. ANAND
Department of Mechanical Engineering, Texas A&M University
College Station, Texas 77843, USA
The mechanics of flowing granular materials such as coal, sand, agricultural products, fertilizers, dry chemicals, metal ores, etc., and their flow characteristics have received considerable attention in recent years. In a number of instances these materials are also heated prior to processing or cooled after processing. In this paper, the governing equations for the flow of granular materials, taking into account the heat transfer mechanism are derived using a continuum model proposed by Rajagopal and Massoudi (1990). For a fully developed flow down a heated inclined plane, the governing equations reduce to a system of nonlinear ordinary differential equations for the case where the material properties are assumed to be constants. The boundary value problem is solved numerically and the results are presented for the volume fraction, velocity, and temperature profiles.

Key words: 
granular materials, convective heat transfer, inclined fully developed flow, continuum mechanics. 
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14.
BLASIUS FLOW OF VISCOELASTIC FLUIDS: A NUMERICAL APPROACH
K. SADEGHY and M. SHARIFI
Faculty of Engineering, Department of Mechanical Engineering
University of Tehran
P.O. Box: 113654563, Tehran, IRAN
email: sadeghy@chamran.ut.ac.ir
The effects of a fluid elasticity on the characteristics of a boundary layer in a Blasius flow are investigated for a secondgrade fluid, and also for a Maxwell fluid. Boundary layer approximations are used to simplify the equations of motion which are finally reduced to a single ODE using the concept of similarity solution. For the secondgrade fluid, it is found that the number of boundary conditions should be augmented to match the order of the governing equation. A combination of finite difference and shooting methods are used to solve the governing equations. Results are presented for velocity profiles, boundary layer thickness, and skin friction coefficient in terms of the local Deborah number. An overshoot in velocity profiles is predicted for a secondgrade fluid but not for a Maxwell fluid. The boundary layer is predicted to become thinner for the secondgrade fluid but thicker for the Maxwell fluid, the higher the Deborah number. By an increase in the level of fluid elasticity, a drop in wall skin friction is predicted for the secondorder fluid but not for the Maxwell fluid.

Key words: 
Blasius flow, secondgrade fluid, Maxwell fluid, finite difference, shooting method. 
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15.
RHEOLOGICAL MODELS OF HUMAN BLOOD AS A NONNEWTONIAN FLUID
J. WOJNAROWSKI
Silesian Technical University
Email: Wojnarowski@rmt4.kmt.polsl.gliwice.pl
K. MIROTA
University of BielskoBiala
Email: kmirota@ath.bielsko.pl
One of the most important problems of model hemodynamics is the descriptions of the rheological properties of the flowing blood. In this work, two basic classes of a hemorheology models have been analysed. The first one considers human blood as a nonNewtonian and timeindependent fluid. However, the dynamical formation of its timedependent collective structure leads to a viscoelastic and tixotropic blood response. In consequence, this study presents a second class of hemorheology model, considering blood as a fluid thinning and thickening with time.

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16. Brief note
CHEMICAL REACTION ON MOVING INFINITE VERTICAL PLATE WITH VARIABLE TEMPERATURE
R. MUTHUCUMARASWAMY
Department of Information Technology, Sri Venkateswara College of Engineering
Pennalur, Sriperumbudur 602 105, INDIA
email: msamy@svce.ac.in
S. VENKATESH and P. SANTHOSH
Department of Chemical Engineering
Sri Venkateswara College of Engineering, Pennalur
Sriperumbudur 602 105, INDIA
An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of variable temperature and mass diffusion is presented here, taking into account the homogeneous chemical reaction of firstorder. The dimensionless governing equations are solved using the Laplacetransform technique and the solutions are valid only at a lower time level. The velocity, temperature and concentration profiles are shown in graphs. It is observed that due to the presence of a first order chemical reaction, the velocity as well as concentration decreases with of the increasing of the chemical reaction parameter.

Key words: 
vertical plate, heat and mass transfer, chemical reaction, exact. 
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