The hydrodynamic effect of capillary rise of fluid.

A mathematical model of groundwater outflow
from the channel at capillarity of soil and water evaporation
is investigated within the frame of stationary filtration.
Appeared mixed boundary value problem is solved with
the use of POB method of Polubarinova-Kochina, as well
as that of conformal mapping of specific domains, met in
hydro- and aerodynamics.

The forced oscillations of two console
rods system.

The solution of the problem on
the forced oscillations of system of two identical
console rods joined by a hinge was deduced on the basis of
Timoshenko's theory. The first rod has the given forced
oscillations of the left end with amplitude А, and
the second rod (connected to the first by a hinge)
is rigidly jammed on the right end. Development of
the constructed exact solutions on a case when between
rods the spring with coefficient of a flexibility d
is reduced. Numerical calculations on the basis of solutions
of the showed problems which results are illustrated in tables
and on graphs and also compared to the results
received on the basis of the theory of Bernulli-Euler.

The effect of gravity on wave
processes in an ideal gas.

The effect of gravity on wave
processes in an ideal gas using an elementary barotropic
energy-closed model is studied. The peculiarities gained by
plane and spherical harmonic waves and by a nonstationary
spherical wave in the presence of homogeneous gravity
field are shown.

The behaviour of the
SD material under elasto-plastic
bending.

Finite element simulation
of a stress field near the tips of an insulated
arc-shaped crack in a thick cylindrical shell
subjected to thermal loading.

The mathematical model of the shell of a boiler drum
with laminations is considered. The solution of considered
problem is obtained by means of finite element method.
Interaction of the layers under thermal load is examined.

Computer modeling of non-stationary
flow in a sea gas pipeline.

In the report the mathematical model of non-stationary
non-isothermal flow of multicomponent chemically inert
mix of gases in a sea gas pipeline, with taking into account
the form of the pipeline and heat-exchange conditions is
presented. Various computing algorithms for the solution of
system of equations of model are analyzed. A calculation of
a periodic flow regimen in a gas pipeline
in real conditions is given as an example.

New Year party

New structural-kinetic approach in fracture mechanics.

The fundamentals of incubation time approach in fracture dynamic problems will be outlined. The continual (kinetic) formulation of incubation time based fracture dynamics will be discussed. It provides the investigation of microscale incubation processes anticipating the macrofracture event as well as the dynamic-strength criterion at the macroscale.

On one method of space mirrors production.

The report covers the mathematical model of expansion process of a
layer of liquid in the state of weightlessness. This process
underlies one of methods of producing space mirrors.
The solution of the system of equations for the model
is obtained. In particular, the comparative analysis of
computational algorithms to solve differential equation
that simulates behaviour
of the inner radius of the layer is made.

"Mathematical modelling of
currents in subsurface hydrodynamics (II)".

Analysis of Mechanical Properties of
Asbestos Nanotubes.

Dynamic Stability of Plates and Shells
due to the Theory of Timoshenko-Reissner.

Dynamic and Stability of Thin Plates
due to Different Perturbations.