# Mechanics

## Mechanical Problems in Nanotechnology

During the last decade, production and adoption of nano-aggregations and nano-inclusions have become actual in electronics, medicine, space engineering and many other branches of production. In this connection, the necessity of studying the nano-subject resistance, stiffness, defectology, durability has emerged. Which of the techniques are best applicable? Feasibility of applying the traditional methods of Newtonian Mechanics, which have been developed and tested for centuries, is widely discussed.

## Gasdynamics and Magnetohydrodynamics of the Interplanetary and Interstellar Gas Interaction. Theory and Experiments

A problem of the interaction between interplanetary and interstellar gas flows is the problem of the interaction between the supersonic flow of the fully ionized hydrogen gas flow from a source (solar wind) and the supersonic translational flow of the interstellar gas which has neutral (Hatoms) and plasma (electrons and protons) components. Self-consistent, kinetic-continual model of this interaction, suggested in [8], is described in this paper.

## Three-Dimensional Problem of Perfect Plasticity (Kinematic Equations Determining Three-Dimensional Plastic Flow for a Facet and Edge of the Tresca Prism)

In the present study a system of partial differential equations which describes kinematic of three-dimensional plastic flow for the states corresponding to an edge of the Tresca prism is obtained. The system includes the Cauchy equations and the compatibility equations formulated for the displacements and strains increments. These equations are then analysed by the aid of the triorthogonal isostatic coordinate net. The system of kinematic equations is shown correctly determines displacements increments and be of the hyperbolic type.

## Asymptotic Methods in Dynamics of Shells under Shock Loading

The paper deals with the asymptotic methods, developed for creating a mathematic model of non-stationary wave propagation in shells of revolution under shock impacts of tangential, bending types and shock impacts of normal type; the methods are also aimed at solving the boundary value problems for the strain-stress state (SSS) components with different values of variability and dynamicity indices. Classification of asymptotic approximations is also presented. This classification defines three different types of separation scheme of non-stationary SSS.

## Investigation of the Isotropic Plates Bending Lying on the Complex Two-parameter Elastic Foundation by Boundary Element Method

This work is dedicated to the investigation of the linear deformation problem of plates based on application of the fundamental decision of task of the isotropic plate bending lying on the complex two-parameter elastic foundation by an indirect method of boundary elements. In the issue of resolving system analysis was indicated that the task of isotropic plate bending lying on the simple elastic foundation is a special case of the task declared in the title of the article.

## Numeric Investigation of a Curve Piecewise-Homogeneous Rectangular Plate from an Isotropic Material

In this paper we consider the problem of a curve piecewise-homogeneous rectangular plate from an isotropic material. There are two group of condition on the line of a contact: geometric conditions,describing the continuity and smoothness of midsurfase of composite plate and force conditions, which supply the equality of bending moments and generalized cutting forces in the left and in the right parts of the plate.

## Impact System Motion Modes Simulationat Periodic Force Effect

A model of impact system motion at periodic force effect taking into account possible multiple impacts during the period of the force effect has been developed. Simulation of impact system motion modes has been carried out. Choice of system parameters realizing the required motion characteristics has been made.

## Tricomi Problem for Differential-Difference Equations of Mixed

The paper examines the boundary value problem for mixed type equations with two perpendicular lines of degeneracy and the delay in the derivative.

## The Global Solvability of the Problem of Nonlinear Diffusion and Slow Convection in Slightly Compressible Viscous Fluid

The paper deals with Stokes system, corresponding to the motion of slightly compressible viscous fluid where kinematic viscous depends on the admixture concentration. The system also contains the convective diffusion equation. The article proves the existence of generalized solution of the initial-boundary problem for this system in the limited domain with the homogeneous Dirichlet condition for the fluid velocity and the homogeneous Neumann condition for the concentration of admixture on the boundary of domain.

## Propagation of Pressure Waves in Finite-Size Bubbles Zones

Peculiarities of pressure waves propagation in liquids with bubbly zones have been studied. The problem is studied taking into account two-dimensional effects. Results of the research of a wave impulse influence on the firm wall partially covered with a bubble screen are presented.