
Archive issue  vol.8, No.4
2.
NUMERICAL ANALYSIS OF LOADBEARING SYSTEMS
OF MULTISTORY BUILDINGS
P. ALIAWDIN
University of Zielona Góra, ul. Szafrana 2, 65516 Zielona Góra, POLAND
email: P.Aliawdin@ib.uz.zgora.pl
A. MORDICH and V. SIMBIRKIN
Belarusian Research Institute  BelNIIS, Minsk, BELARUS
email: lnk@it.org.by
The paper presents a numerical evaluation of various reinforced concrete structural systems with reference to their response to gravity and wind loads. The structural systems considered are multistory castinplace, precast and mixed precast and insitu skeletons with and without shear walls employed in current building practice. The results of static, dynamic, and stability FEanalyses of such systems are discussed. Castinplace and mixed skeletons are shown to be efficient loadbearing systems for multistory residential and office buildings.

Key words: 
structural systems; multistory buildings; prefabricated, castinplace and mixed reinforced concrete structures; static, normal modes and buckling analysis. 
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3.
APPLICATION OF THE LIE GROUP THEORY TO THE ANALYSIS OF FLOWS IN A TURBULENT BOUNDARY LAYER UTILIZING DIFFERENT TURBULENT VISCOSITY MODELS
A.A. AVRAMENKO and S.G. KOBZAR
Institute of Engineering Thermophysics, National Academy of Sciences
Kiev, UKRAINE
A.V. KUZNETSOV
Department of Mechanical and Aerospace Engineering, North Carolina State University
Campus Box 7910, Raleigh, NC 276957910, USA
email: avkuznet@eos.ncsu.edu
P.J. BOWEN
Mech. Eng. and Energy Studies Division Cardiff University Queen's Buildings
PO BOX 685 Cardiff CF 3TA Wales, UNITED KINGDOM
The properties of symmetry of turbulent boundary layer flows are studied utilizing the Lie group theory. The selfsimilar forms of the independent variables and the solution functions for the boundarylayer type flows for four models of turbulent viscosity are obtained. The developed approach of finding a selfsimilar transformation for turbulent boundarylayer problems makes it possible to obtain numerical and simplified analytical solutions for a number of important flow situations.

Key words: 
Lie groups, selfsimilar solutions, turbulent flows. 
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4.
ELASTICPLASTIC STRESS ANALYSIS OF SYMMETRIC
REINFORCED THERMOPLASTIC MATRIX LAMINATED BEAMS
UNDER A BENDING MOMENT
H. ÇALLIOGLU^{1}, S. AKSOY^{2}, M. TOPCU^{1} and Y. ARMAN^{2}
^{1}Department of Mechanical Engineering, Pamukkale University
Çamlik, Denizli, TURKEY
email: hasan.callioglu@deu.edu.tr
^{2}Department of Mechanical Engineering, Dokuz Eylül University
35100, Bornova, Izmir, TURKEY
In this study, an elasticplastic stress analysis is carried out on symmetric steel fiber reinforced high density polyethylene thermoplastic matrix laminated beams under a bending moment. The BernoulliEuler theory is used. The orientation angles are chosen as (90^{o}/0^{o})_{2}, (30^{o}/30^{o})_{2}, (45^{o}/45^{o})_{2} and (60^{o}/60^{o})_{2}. The composite material is assumed to be linearly hardening. The stress component 'sigma'_{x} is to be maximum at the upper and lower surfaces in the elasticplastic solution. The residual stress component 'sigma'_{x} is found to be highest at the upper and lower surfaces. However, when the plastic region is further expanded the residual stress component 'sigma'_{x} is found to be the highest at the elastic and plastic boundaries. The plastic flow is to be maximum at the upper and lower surfaces for the (30^{o}/30^{o})_{2} orientation. The transverse displacement is obtained to be highest at the free end for the (90^{o}/0^{o})_{2} orientation.

Key words: 
laminated beam, thermoplastic composites, elasticplastic stress analysis, residual stresses, analytical solution. 
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5.
ON THE VISCOELASTIC CORE OF A LINE VORTEX
EMBEDDED IN A STAGNATION POINT FLOW
M.E. ERDOGAN
Istanbul Teknik Üniversitesi
Makina Fakültesi, Gümüºsuyu, 80191, Istanbul, TURKEY
email: imrak@itu.edu.tr
The viscoelastic core of a line vortex embedded in a radially inward axisymmetric stagnation point flow for a Maxwell fluid and an Oldroyd B fluid is considered. Velocity, vorticity and stress distributions are calculated and compared with those of the Newtonian fluid. It is found that there are pronounced effects of viscoelastic properties on these distributions with respect to those of the Newtonian fluid.

Key words: 
viscoelastic fluid, core radius, vortex flow, Maxwell fluid, Oldroyd fluid. 
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6.
WATER WAVE SCATTERING BY TWO THIN SYMMETRIC
INCLINED PLATES SUBMERGED IN FINITE DEPTH WATER
R. GAYEN (née CHOWDHURY) and B.N. MANDAL
Physics and Applied Mathematics Unit, Indian Statistical Institute
203, B.T. Road, Kolkata  700 108, INDIA
email: biren@isical.ac.in
Water wave scattering by two thin symmetric plates submerged in water of uniform finite depth is investigated here assuming the linear theory. The problem is formulated in terms of two hypersingular integral equations involving the discontinuities in the symmetric and antisymmetric potential functions describing the motion in the fluid, across one of the plates. These are solved approximately by an expansioncumcollocation method in which the unknown discontinuities across a plate are approximated by a finite series involving Chebyshev polynomials of the second kind. The reflection and transmission coefficients are then obtained numerically. The numerical results for the reflection coefficient are depicted graphically against the wave number for different configurations of the plates. It is observed that if the depth of submergence of the mid points of the plates below the free surface is of the order of onetenth of the depth of the water bottom, then the deep water results effectively hold good. Also known results for two thin vertical plates, a single vertical plate are recovered as special cases.

Key words: 
water wave scattering, linear theory, inclined plates, hypersingular integral equations, reflection coefficient. 
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7.
BOUNDARY INTEGRAL METHOD FOR AN OSCILLATORY STOKES FLOW PAST A SOLID PARTICLE
M. KOHR
Faculty of Mathematics and Computers Science
BabeºBolyai University, M. Kogãlniceanu 1
3400 ClujNapoca, ROMANIA
email: mkohr@math.ubbcluj.ro
I. POP
Faculty of Mathematics
University of Cluj
R3400 Cluj, CP 253, ROMANIA
In this paper, we present a boundary integral method in order to determine the oscillatory Stokes flow due to translational or rotational oscillations of a solid particle in an unbounded viscous incompressible fluid. As an application of this method, we study both cases of smalland highfrequency oscillations. Finally, we give some numerical results in the case of transverse oscillations of a prolate spheroid.

Key words: 
boundary integral method, oscillatory Stokes flow, oscillatory singlelayer potential. 
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8.
MOVING LOAD RESPONSE AT THERMAL CONDUCTING FLUID
AND MICROPOLAR SOLID INTERFACE
R. KUMAR
Department of Mathematics, Kurukshetra University
Kurukshetra, Haryana, INDIA
email: rajneesh_kuk@rediffmail.com
P. AILAWALIA
Department of Mathematics, S.S.I.E.T, Derabassi
Distt. Patiala, Punjab, INDIA
email: praveen_2117@rediffmail.com
The steady state response of a micropolar elastic solid with an overlying semiinfinite thermal conducting fluid subjected at the plane interface to a moving point load is determined. The analytic expressions of displacement components, force stress, couple stress and temperature distribution are obtained in the physical domain for LordShulman (LS), GreenLindsay (GL), coupled theory (CT) and GreenNaghdi (GN) theories of thermoelasticity by the use of Fourier transform technique and are shown graphically for magnesium crystal like material. The integral transform has been inverted by using a numerical technique.

Key words: 
steady state, micropolar elastic solid, couple stress, thermoelasticity, Fourier transform. 
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9.
ELASTODYNAMICS OF TIME HARMONIC SOURCES
IN A THERMALLY CONDUCING CUBIC CRYSTAL
R. KUMAR and L. RANI
Department of Mathematics, Kurukshetra University
Kurukshetra 136119, Haryana, INDIA
email: rajneesh_kuk@rediffmail.com
The disturbance due to a time harmonic mechanical, horizontal or vertical and thermal source in a homogeneous, thermally conducting cubic crystal, elastic halfplane is investigated by applying the Fourier transform. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystallike material are illustrated to compare the results for different theories of generalized thermoelasticity for insulated boundary and temperature gradient boundary.

Key words: 
generalized thermoelasticity, cubic crystal, relaxation time, Fourier transform. 
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10.
A GENERALIZED FE FORMULATION FOR BUCKLING ANALYSIS OF SOLID OR BUILTUP COLUMNS WITH NONPRISMATIC SECTION
G.Q. LI
Department of Building and Structural Engineering, Tongji University
1239 Siping Road, Shanghai, 200092, P.R. CHINA
email: gqli@mail.tongji.edu.cn
J.J. LI
National Maglev Transportation Engineering R&D Center
2520 Longyang Road, Shanghai, 201204, P.R. CHINA
In this paper, a generalized FE formulation for buckling analysis of nonprismatic columns with various crosssections is established by using the Chebyshev polynomial approach to the governing differential equation. The proposed formulation includes the effects of shear deformation and is therefore applicable to solid or builtup columns. The change of the sectional properties along the length direction, such as the area and inertia moment, need not be fitted with approximate expressions and can be defined exactly and freely with userdefined functions in programming. Buckling of the three structures, respectively for a tapered mast column with a circular hollow section, a webtapered Isectional column and a tapered lattice column, is studied numerically and compared with the results of previous studies. The effects of shear deformation on the buckling loads of those tapered columns are specified.

Key words: 
solid column, builtup column, nonprismatic section, shear deformation, FE analysis, buckling load. 
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11.
LASER DRIVEN ABLATIVE SURFACE INSTABILITY
IN INERTIAL FUSION ENERGY
N. RUDRAIAH, P. SRIDHARAN and T. DESAI
National Research Institute for Applied Mathematics (NRIAM)
No.492/G, 7th Cross, 7th Block (West), Jayanagar, Bangalore  560 082, INDIA
email: nrudraiah@hotmail.com
and
UGC  Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics
Central College Campus, Bangalore University, Bangalore  560 001, INDIA
In recent years there has been a considerable theoretical and experimental interest in a laser driven ablative surface in inertial fusion energy (IFE). The existing studies of nonuniformities will not prevent the surface instabilities which originate at the ablation surface due to acceleration of high density plasma by low density plasma, known as the RayleighTaylor instability (RTI). The present work is aimed at controlling the growth rate of RTI in a laser irradiated porous target (that is a hollow target filled with a porous material) at moderate intensities. This RTI has been studied using the moment method. The dispersion relation is obtained in terms of Bond number B connected with the surface tension and the modified Reynolds number R. This dispersion relation is computed for different values of B, R and several particular cases for long and short wave length perturbation and the results are depicted graphically. It is shown that the permeability of the porous region scaled with the Reynolds number decreases considerably the growth rate of RTI compared to that of a hollow shell.

Key words: 
laser, ablative surface, instability, IFE. 
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12.
LINEAR AND NONLINEAR ANALYSES OF CONVECTION IN A RIVLINERICKSEN FLUIDSATURATED POROUS MEDIUM
P.G. SIDDHESHWAR and C.V. SRI KRISHNA
Department of Mathematics, Bangalore University
Central College Campus, Bangalore  560 001, INDIA
email: pgsiddheshwar@hotmail.com
cvsrikrishna@hotmail.com
Linear and nonlinear analyses of convection in a secondorder Boussinesquian fluidsaturated porous medium are made. The RivlinEricksen constitutive equation is considered to effect a viscoelastic correction to the Brinkman momentum equation together with a singlephase heat transport equation. The linear and nonlinear analyses are respectively based on the normal mode technique and the truncated representation of Fourier series. The linear theory reveals that the critical eigenvalue is independent of viscoelastic effects and the principle of exchange of stabilities holds. The nonlinear study of cellular convection leads to an autonomous system of differential equations which is solved numerically. The finite amplitude disturbances are found to be independent of transient conditions and viscoelasticity is shown to stabilize the system. The Nusselt number is calculated for different values of the parameters arising in the problem. The possibility of chaotic motion and its similarity to the problem of magnetoconvection are discussed.

Key words: 
RivlinEricksen fluid, nonNewtonian, viscoelastic, porous media, nonlinear, chaos, heat transfer. 
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13.
STABILITY OF SUPERPOSED COUPLESTRESS FLUIDS
IN THE PRESENCE OF SUSPENDED PARTICLES IN POROUS MEDIUM
SUNIL
Department of Applied Sciences
National Institute of Technology
Hamirpur (H.P.)  177 005, INDIA
R.C. SHARMA
Department of Mathematics
Himachal Pradesh University
Summer Hill, Shimla  171 005, INDIA
RAJENDER SINGH CHANDEL
Department of Mathematics
Government Degree College
Palampur (H.P.)  176 061, INDIA
The stability of two superposed couplestress fluids of uniform densities, permeated with suspended particles, in a porous medium is considered. A stability analysis is carried out and for mathematical simplicity we consider two highly viscous fluids of equal kinematic viscosities and equal couplestress kinematic viscosities. The system is found to be stable for a potentially stable configuration under certain condition whereas a potentially unstable configuration remains unstable for the couplestress fluid permeated with suspended particles in a porous medium. The growth rates of perturbation are found to be both increasing (for some wave numbers) and decreasing (for other wave numbers) with the increase in medium permeability.

Key words: 
couplestress fluid, suspended particles, porous medium, stability of superposed fluids. 
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14.
NONLINEAR DYNAMIC BEHAVIORS OF HIGH SPEED ROTOR SUPPORTED BY ROLLING ELEMENT BEARINGS
S.P. HARSHA and R. PRAKASH
Mechanical Engineering Group, Birla Institute of Technology and Science
Pilani333031, INDIA
email: suraj@bitspilani.ac.in
K. SANDEEP
Asian Institute of Medicine, Science and Technology, 08000 Sungai Petani, MALAYSIA
The paper presents a model for investigating structural vibrations in rolling element bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of nonlinearity such as the Hertzian contact force, surface waviness and internal radial clearance transition resulting from no contact to contact state between rolling elements and the races. The contacts between the rollers and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and resulting force. The nonlinear stiffness is obtained by using the equations for the Hertzian elastic contact deformation theory. As the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease computer time for system analysis. The effects of various defects of a rotor bearing system in which the rolling element bearings show the periodic, quasiperiodic and chaotic behavior are analyzed. Poincare maps and Fourier spectra are used to elucidate and to illustrate the diversity of the system behavior. It is shown that due to defects such as surface waviness and internal radial clearance the system exhibits an undesirable jump phenomenon with quasiperiodic, subharmonic and chaotic motions.

Key words: 
nonlinear dynamic response, chaotic vibration, Poincare map, Newmarkb, rolling bearings, Ball passage frequency. 
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