### April 26, 2011

V.A. Kocheryzkin (SPbSU)

Simulating viscous fluid flow using SPH method.

Smoothed Particle Hydrodynamics (SPH) Method for solving
unsteady hydrodynamic problems is investigated.

Three models with different boundary conditions were considered:

1. Poiseuille Flow. A comparison of velocity profile
for analytical solution and numerical results was presented.

2. Classical Dam Break problem (free surface flow).
A comparison with experimental data was done.

3. Fluid flow between deformable plates.
Qualitative flow patterns were obtained.

Also different method modifications were described.
Multithreaded implementation using Nvidia CUDA were discussed.

**
Kocheryzkin Vladimir Alexeevich ** –
PhD student of the
Department of Hydroelasticity,
St. Petersburg State University. Scientific Supervisor - Prof.
B.A. Ershov.

### April 12, 2011

T.V. Zinovieva (SPSPU)

Modeling of offshore pipeline laying by means of
the S-method.

Contact analysis of a pipeline bending
in laying on a rigid seabed is carried out.
The pipeline is modeled by a semi-infinite elastic beam.
Length of its sagging part is not known and is defined in
the result of calculations.

A formula for hydrostatic loading of a rod
is derived in the paper; it is shown that in some
cases simplified accounting of the loading by reduction
of the rod’s weight for the weight of the liquid superseded
leads to significant errors.

The analysis of pipeline stress-strain state
is considered. Analytical expressions and numerical
results are received by asymptotic method and finite
difference method. The form of sagging part is defined
and internal forces, moments, and stresses are shown
depending on the angle of pipeline fixing and the
distance from the seabed. The seabed reaction is found
for two rod models: the classical and Timoshenko ones.

**
Tatiana V. Zinovieva ** –
Ph.D., Associate Professor of the Department of
Computer Technologies in Engineering at St.Petersburg
State Polytechnical University, author of 17 papers in
mechanics of solids.

### March 29, 2011

M.L. Boyarskaya (SPbSU)

Frequencies and modes of a cylindrical shell
rotating on the rolls.

An infinite cylindrical shell
supported by totally rigid cylindrical rolls is considered as
a simpliest model of a shell of centrifugal
ore-dressing concentrator.
The dependence of natural frequencies on
angular velocity of rotation and formulae for modes
of nonrotating shell with arbitrary number of
fixing rolls are obtained.
To estimate the accuracy of the model the
frequencies of a hinged shell of finite length were found
for some particular cases.

**
Boyarskaya Maria Leonidovna ** –
1st year master student of the
Department of Theoretical and Applied Mechanics of
St. Petersburg State University.
Supervisor - Prof. Filippov S.B.

### March 1, 2011

I.V. Viktorov (SPbSU)

Stability of shells of revolution reinforced by fibers.

Local forms of the buckling of the momentless axisymmetric stress
condition of the fine elastic shells of revolution are considered. It
is assumed that the shell is reinforced by two systems of fibres
inclined at angles t and -t to the generatrix. The forms of the loss
of stability of isotropic and orthotropic shells are regarded and the
comparison of these forms is conducted. The optimum reinforcement by
fibers is considered.

**
Ivan V. Viktorov ** –
graduated from St. Petersburg State University in 2002. He is
an author of 7 papers. Supervisor – Prof. P. E. Tovstik.

### February 15, 2011

L. A. Aleksandrova (SPbSUCA)

Mathematical modeling of ground smooth contour base
hydraulic structure with constant flow rate.

We consider the simulation of groundwater
flowing contours recessed rectangular weir, whose corners
are rounded to the curves of constant values of filtration rate,
when the permeable base is underlain by a curved impermeable,
which includes a horizontal Plots, characterized by a constant
flow velocity. The results of numerical calculations and gives
the hydrodynamic analysis of the impact of the basic physical
parameters of the model on the shape
and size of the underground contour of the dam.

**
Lyudmila A. Aleksandrova ** –
PhD student of the Department of
Applied Mathematics, St. Petersburg State University of
Civil Aviation. Supervisor – Prof. E.N. Bereslavsky.

### November 30, 2010

A. M. Ermakov (SPbSU)

Evaluation of the Mechanical Parameters of Multilayered
Nanotubes by means of
Nonclassical Theories of Anisotropic Shells.

The investigation of mechanical behavior of multilayered
nanotubes is the actual and important problem.
Particularly the definition of nanotubes stiffness has been
studied by means of scanning probe microscopy.
The stiffness is defined as a ratio the value of local
load (applied to a tube) to the value of the displacement.
The nanotubes made of natural chrysotile asbestos with
different materials for fillings are analyzed. The experiments
show that the stiffness

of a tube depends on the materials for filling.
The tubes with water are softer than the tubes without filling
materials and the tubes filled mercury are more rigid than
tubes without filling materials. It was previously shown
that the classical theory of beam bending could not explain
the experimental results, but the experimental results
well agree with the Timoshenko-Reisner theory (at least
qualitatively), when interlaminar shear modulus of elasticity
changes for different filling materials. When additional
factors such as lamination of structure and cylindrical
anisotropy are taken into account the theory of
Rodionova-Titaev-Chernyh (RTC) permits to obtain much
more reliable results. In this work the authors also
applied one more nonclassical shell theory, namely the
shell theory of Paliy-Spiro (PS) developed for
medium-thickness shells and considered radial pressure.
The comparison of nonclassical shell theories (RTC and PS)
with experimental data and finite elements method calculations
are presented in the report.

**
Ermakov Andrey Mihailovich ** – PhD student, Department
of Theoretical and Applied Mechanics SPSU.
Supervisor – Prof. S.M. Bauer.

### November 16, 2010

N. V. Zakharenkova (SPbSUCA)

Modeling of filtration flows from channels with evaporation
on the free surface

**
Natalia V. Zakharenkova ** – a graduate of the Department of
Applied Mathematics, St. Petersburg State University of
Civil Aviation. Supervisor – Prof. E.N. Bereslavsky.

### November 2, 2010

Karamshina L.A. (SPbSU)

Models of sandwich shells in ophtalmology.

**
Lyudmila A. Karamshina ** – PhD student,
Department of Theoretical and Applied Mechanics SPSU.

### October 19, 2010

Efimov I.V. (SPbSU)

Anisotropic materials fluidity contour construction technique.

The report is devoted to actual problem of processing experimental
researches. The purpose of the research is to construct
the fluidity contours for the various constructional materials
with difficult rheology. The problem, thay is a classical problem
of regression analysis, is reduced to evaluation of the
contour factors providing minimum to
the objective function.
Three fluidity contour construction methods for experimental data are
considered: i) manual selection, ii) the method of coordinate descent,
iii) the method of the fastest descent.
On their basis the technique permitting to obtain the result
with the least error is proposed. The computer code realizing the
proposed technique is developed.

**
Ivan V. Efimov ** – PhD student, Department of Theoretical and Applied Mechanics SPSU.

### October 5, 2010

M.G. Zhuchkova (SPbGMTU)
and D.P. Kouzov (SPbGMTU, IPME RAS)

Flexural-gravity wave scattering by point
obstacles in an elastic plate floating on water.

The paper deals with periodic wave phenomena in a thin elastic plate
floating on the surface of an incompressible fluid. The plate covers
its entire surface and performs flexural vibrations that accompany
gravity waves in the fluid. Free vibrations of the plate are violated
along an infinitely-long straight line (or several straight lines
having arbitrary spacing between them). We study the transmission
and reflection of flexural-gravity waves which are orthogonally
incident from infinity upon the so-called “point linear” obstacles
in the plate. Exact analytical expressions are found for the wave
field in the fluid and flexural field in the plate. The transmission
and reflection coefficients of the incident waves are determined.
Analytical wave fields’ expressions are also obtained for two
approximate models of water depth: infinite and shallow water.
First we consider the general problem with arbitrary types of the
plate’s obstacles. After that to illustrate the general solution
three following types of the obstacles are used. They are rigid
supports (clamps), movable supports and infinitely thin cracks.
By obtained explicit formulae we numerically calculate the
transmission and reflection coefficients, the plate’s deflection
and the internal forces (shearing forces and bending moments)
appeared in the plate’s supports. Numerical results obtained are
compared to determine the validity ranges of the approximate models
of water depth (infinite and shallow water).

**
Marina Gennad’evna Zhuchkova ** – senior lecturer in higher
mathematics of the Department of applied mathematics and
mathematical modeling of St Petersburg Marine Technical
University (SMTU). She graduated from SMTU with M.Sc. degree
(with honors) in applied mathematics (from the Department of
applied mathematics and mathematical modeling). During 2000-2003
years she was a postgraduate student in mechanics of deformable
solids. The list of her publications contains 6 papers.
Research interest is mathematical physics. Research supervisor
is Professor D.P. Kouzov.

**
Daniil Petrovich Kouzov ** – doctor of sciences in physics and
mathematics (acoustics), professor of the Department of applied
mathematics and mathematical modeling of St Petersburg Marine
Technical University (SMTU), leading researcher in Institute of
Problems in Mechanical Engineering (RAS), professor of Soros.
Main research interest is mathematical acoustics. He developed
boundary-contact problems of acoustics (BCPA). He studied structural
fields in separated elastic structures, frictional vibrations of
elastic bodies and others problems of mathematical acoustics.
He is an author more then 130 papers. He is the head of the
regular St Petersburg Workshop on Theoretical and Computational
Acoustics of the Russian Academy of sciences.

### September 21, 2010

D.N. Gavrilov (math-mech, SPSU)

On the generalized Gauss principle in the problem of the
console vibration damping.

**
Gavrilov Dmitry Nikolaevich** – PhD student,
Department of Theoretical and Applied Mechanics SPSU.

### 7 October, 2010

S.I. Peregudin and S.E. Kholodova(AM-CP, SPSU)

On dynamics of the rotating layer of the ideal incompressible
electroconductive fluid.