INSTITUTE
OF MECHANICS AND ENGINEERING; KAZAN SCIENCE CENTER; RAS
SCIENTIFIC
SEMINAR
Problems of Continuum Mechanics
(Kazan, 2000)
D.A.Gubaidullin
Institute of Mechanics and
Engineering; Kazan Science Center; RAS
Lobachevsky
2/31, Kazan 420111
RUSSIA
e-mail: gubajdullin@sci.kcn.ru
The Scientific Seminar “Problems of Continuum
Mechanics” works on Wednesdays in the Institute of Mechanics and Engineering,
Kazan Science Center RAS. The Chairman of the Seminar is Director of the
Institute Dr. Sc. (Phys. & Math.) D.A.Gubaidullin. Problem reports and
dissertations of researchers of the Institute and scientists from other
organizations are presented and discussed at the Seminar. Main scientific
directions for presentation are:
·
non-linear
mechanics of thin-walled constructions, hydroaeroelastic and wave systems;
·
dynamics
of multiphase multicomponent media in porous structures and technological
plants;
·
non-linear
stability theory of control systems with changeable structure.
Applications to make reports at the Seminar are
considered by the Chairman.
The following reports were presented at the Seminar during the spring period of 2000.
22 March 2000
Nikiphorov A.I. On modeling suffosian in
aquifer.
A new mathematical model of release of solid particles by an aqueous flow from a porous bed is proposed. The
porous medium is modeled as two overlapping continuous media, one of which is
associated with the moving fluids and particles and another
with those fixed. Equations defining changes of the function of pore
size distribution and particle size distribution are derived. These equations
include parameters which are estimated on model presentation of the porous
medium as parallel capillary tubes. The appropriate expressions
for dynamic porosity and permeability are obtained.
22 March 2000
Soultanov R.A. On some problems of numerical simulation of nonlinear
fluid flow.
Two-phase fluid flow is considered, one of
which is a non-Newtonian fluid. It is known that for small fluid flow velocities
Darcy law (linear dependence between fluid flow velocity and pressure gradient)
is violated. Numerical simulation in these conditions encounters some problems
that are characteristic of only nonlinear fluid flow. Some approaches for their
solution are considered. Results obtained are analyzed.
22 March 2000
Gainetdinov R.R. The hydrodynamic investigation of vertical gas wells. As experimental investigations show,
the dependence of permeability on pressure is well approximated by monotonous
and convex functions. In this work a numerical algorithm is proposed for
estimating dependence of permeability on pressure in non-stationary filtration
of a gas in porous medium. The inverse problem is solved with the help of the
additional a priory information about the structure of the required solution
(monotony and convexity of the function).
5 April 2000
Gabidullina A.N, Elesin A.V, Kadyirova A.Sh, Mazurov P.A. On
identification filtration coefficient
of three-dimensional anysotropic confined aquifer. A preliminary results are given related to
constructing regularizational algorithms for identification of filtration coefficient of three-dimensional
anysotropic confined aquifer in stationary case.
19 April 2000
Malakhov V.G. An algorithm of the additional-viscosity method for
axisymmetrical deformation of shells of revolution. A variant of the
additional-viscosity method to solve the problem of large axisymmetrical deflections
and stability of elastic and elastoplastic shells of revolution has been
proposed. The canonical system of equations for unknown forces, moment and
deflection velocities has been derived. To solve the system an iteration method
in combination with the orthogonal
sweep method is employed. Results of computations are presented.
19 April 2000
Shikhranov A.N.
Nonlinear asymmetric deforming of the shallow shells of revolution with
imperfections in the form under the thermal load. Influence of asymmetric initial irregularities
in the form of the flexible elastic shallow shells of revolution under the
action of moderate heating on the character of deforming is investigated. The
problem is considered in geometrically nonlinear statement within the
medium-bend theory. Computations presented have been performed for a shallow
spherical shell under the linear distribution of the temperature over the shell
thickness.
26 April 2000
Malikov A.I. Matrix comparison systems in the
dynamic analysis and state estimation
of nonlinear continuous and discrete control systems. The modern state-of-the-art in matrix comparisons systems
method offered by E.F.Sabaev and advanced during last years in laboratory of
stability and control IME KSC RAS is considered. The results obtained are
systematized and discussed in comparison which other methods of qualitative analysis
of nonlinear systems. Connection of matrix comparison systems with square-law
Lyapunov functions and, for linear non autonomous systems, with the
evolutionary equations is established. Approaches for construction of matrix
comparison systems for adjustable systems with uncertainties and structural
changes are given. Prospects of development and application of a matrix
comparison systems method for the qualitative analysis and state estimation of
nonlinear systems in the light of using opportunities of the modern applied programs MathCad and Matlab are
considered.
26 April 2000
Zakirov U.N. Stability of orbits in the frame of Kaluza-Klein's
five-dimensional theory. Basing on the concept of the world as energy density (included in the
fifth a coordinate), space and of time, the Einstein's five-dimensional
equations are solved for the Vaidja-Kerr's metrics (for the case when the
gravitational radius depends on the fifth coordinate). Equations of deviation
with effective component dependent on the fifth coordinate are obtained. As a
result, the stability of orbits for tested particles is investigated relatively
bodies with variable energy density. In particular, the Kaplan's stable orbit,
nearest to the center, appears to depend on the fifth coordinate, unlike the
classical case.
31 May 2000
Danilaev P.G. The identification of transport processes in inhomogeneous
porous mediums. Kazan Technical University. On materials of thesis for Doctor of Sciences
Degree, specialty: 05.13.16 – Application of computer facilities, mathematical
modeling and mathematical methods in scientific researches. Reviewer DrSc
M.KH.Khairullin.
Ill-posed problems of the underground
hydrodynamics and the heat conduction are investigated. The main attention is
given to the coefficient inverse problems for parabolic type equations in
connections with their applications. Results derived from corresponding
uniqueness theorems are taken as the basic for the algorithms construction.
31 May 2000
Vishnyakova I.V. Modelling of circulation water cooling process and
reconstruction of the industrial cooling towers. Kazan Technological
University. On
materials of thesis for Candidate of Sciences Degree, specialty: 05.17.08 –
Processes and apparatuses of chemical technology. Reviewer PhD Fedyaev V.L.
Operation of the fills of the industrial
cooling towers is considered. A closed mathematical description of their
cooling water process is assumed. Results of calculation of the temperature
fields are given, the influence of the type and thickness of the fill layer on
heat efficiency of the cooling tower is estimated. The empirical dependencies
for estimation of coefficients of reverse stirring, mass transfer and wetting
of the fill walls are presented. On the basis of the presented investigations
recommendations on reconstruction of the considered cooling towers are
developed.
7 June 2000
Gainetdinov R.R. Hydrodynamic methods of investigation on the basis of
theory of ill-posed problems for gas vertical and horizontal wells. On materials of thesis for Candidate
of Sciences Degree, specialty: 01.02.05 – Mechanics of liquid, gas and plasma.
Reviewer PhD Shamsiev M.N.
Recent progress of oil and gas fields
projection theory is closely connected to the development and analysis of
mathematical models of the investigated flow processes. An important stage in
mathematical models is the solution of the inverse problem. The distinctive
feature of inverse problems connected to the research of mathematical models of
real oil and gas reservoirs is that the character of the additional information
is determined by the possibilities of field experiment.
Potential participants are kindly invited for
the presentation of their results at the Seminar. Contact address –
gubajdullin@sci.kcn.ru