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The numerical modeling of wave flows of
heterogeneous media with a three-
temperature scheme of interphase heat
and mass transfer involves the problem
of equation stiffness. A discrete model
of improved stability was developed to
describe these processes. Test
calculations of the interaction of a
shock wave with a bounded layer of a
mixture of a gas and droplets assuming a
discrete model over a wide range of
initial data showed that the stability
conditions do not depend on the rate of
interphase interaction (C-stability).

This paper studies the dynamic behavior
of simply and doubly connected elliptic
ideal rigid-plastic plates with simply
supported or clamped contours under
short-time intensive dynamic loads. It
is shown that there are several
mechanisms of dynamic deformation of
plates. For each mechanism, equations of
the dynamic behavior are obtained.
Operating conditions of these mechanisms
are analyzed. Analytical expressions for
the ultimate, "high" and "superhigh"
loads and the maximum final deflection
are obtained. Numerical examples are
given.

A model is proposed to calculate
stresses in a glass layer with gas
impurities heated by thermal infrared
radiation. Calculations were performed
for a layer with a diatomic impurity of
nitric oxide and a triatomic impurity of
water. It is shown that for the
radiation parameters and impurity
concentrations considered, the presence
of nitric oxide in the layer does not
influence its stress state, whereas the
presence of water leads to a certain
increase of stress. The stress state of
the layer is determined by the level of
thermal stresses, and the concentration
stresses and the stresses due to the
mass forces of radiation are negligible.
An increase in the rate of diffusion of
the diatomic impurity due to a change of
the radiation spectrum is accompanied by
an increase of thermal stresses.

This paper studies the dependence of the wavelength of localized plastic strain at the parabolic stage of strain hardening on the grain size in polycrystal aluminum. This dependence is determined in the grain-size range 10^-2 – 10 mm. The effect of the grain size on the character of the plastic-flow curve is studied.

This is a study of the effect of structural and mechanical characteristics of a composite material on the stress–strain state of a reflector antenna shaped as a composite thin shell of revolution subjected to gravity, wind, and temperature loads. The boundary-value problem for the system of partial differential equations governing the behavior of this structure is reduced to a sequence of boundary- value problems for inhomogeneous systems of ordinary differential equations with variable coefficients. The resulting stiff systems of equations are solved by Godunov's method of discrete orthogonalization.

Fragmentation of the structure of
lattice disorientations at high plastic
strains of metal crystals is studied.
The medium is modelled by the
geometrically nonlinear elastoplastic
Cosserat continuum. The points of the
continuum are identified with
dislocation cells with a frozen crystal
lattice.

New systems of pretwisted bars are
suggested, and their stability under a
conservative load is investigated. In
this paper, closed-form relationships
are obtained for the direct evaluation
of critical loads of pretwisted cross
bracings with different end connections
and an arbitrary ratio of the
dimensionless parameters of tension and
compression elements. The equation for
the critical loads is derived for
tension and compression braces with
different section properties, lengths,
and axial loading. It is found that the
critical load of a twisted brace is
higher than that of a nontwisted brace.
Parametric solutions are graphically
displayed to clarify the distinct
behavior, including the boundary
separating symmetric and antisymmetric
modes of buckling.

The plane problem of dynamic interaction of a laminar viscous fluid flow and an inextensible pliable fiber of finite length is solved using the perturbation method. Two types of rheological two- dimensional flows — pure shear and simple shear — are considered. Formulas are obtained for the evolution of the tensile force and the shape of the fiber. Results of asymptotic and numerical calculations are compared.

Elastic characteristics and propagation velocities of ultrasonic waves in a TiC– TiNi composite material are determined by the ultrasonic resonance method. The values of the elastic moduli of the solid composite obtained are used to estimate its plastic properties. The effect of various additives on the elastic and plastic properties of the composite is studied.

Main problems and trends in mathematical modeling — a new line of research into various processes and phenomena — are formulated. The status and future prospects are analyzed using as an example the mechanics of continuous media. Emphasis is on two stages of modeling — the selection of physicomathematical models of the mechanics of continuous media and numerical algorithms of solution.