# Mechanics

## Double Layer of Polymer Melts in Channels of Dies

Numerical simulation of double-layer nonlinear viscous flow in channels of dies was performed. The fluid motion is described by equations conservation of mass and momentum, supplemented by the rheological equation of state of nonlinear viscous fluid on the Carreau model. The technique of numerical solve the problem based on the finite element method is described. Results the field of velocities, pressure, stresses, position the interface boundary of two-layer flow depending on rheological properties of liquid and flow regimes are presented.

## Using Galerkin Method for Solving Linear Optimal Control Problems

The linear optimal control problem is considered. Duration of the controlled process is fixed. It is necessary to minimize the functional, that characterizes the energy consumption. A method of constructing an approximate solution based on the Galerkin method is proposed. Examples of numerical solutions of the problem are given.

## Simulation of Incompressible Nonviscoussevere Fluid on a Regular Grid in Three-dimensional Space

This study focuses on modification of the method of Davydov (large particles) in the case of incompressible liquid. We consider the simulation of a heavy incompressible nonviscous fluid by Davydov's modified method in a three-dimensional case. Besides, comparison of the received results with a two-dimensional case is carried out. Formulas of modified Davydovs's method for the case of three spatial dimensions are lead out including difference analogue of the three-dimensional Poisson equation for the pressure. The criterion of stability is generalized.

## Flow a Round Cylinder by Waves Extending on the Viscous Liquid Surface

Some marine hydro technical constructions have such support elements as piles in the form of vertical round cylinders. Questions about the incident wave’s interaction with such barriers and identification of wave regime on the fenced water areas has as the theoretical as the practical concern.We shall consider the motion of liquid, caused by the interaction of incoming gravitational wave, spreading on the surface of the viscous incompressible liquid coat with an infinitely long round cylinder.

## Calculation of Meteoroids Masses by Approximating the Trajectories

At processing meteor observations the outdated and insufficiently reliable methods are commonly used. In particular, the finding outward-atmospheric meteoroid masses comes from the luminosity without providing any estimates of accuracy for calculations. However, in recent years a variety of new dynamics methods has been developed that quite good describe a motion of meteoroids in atmosphere, as well as changing their parameters.

## The Stress-strain State of Elastomeric Constructions under Conditions of Abrasive Fatigue Wear

In this paper the mathematical model of the deformation process of elastomeric elements of constructions with regard abrasive fatigue failure has been proposed. Due to the specific properties of material the stiffness matrix of finite element based on the finite element moment scheme for weakly compressible materials. To increase the accuracy of solutions has been envisaged the receipt of expressions for deformations on the base of adding the initial linear approximating polynomial to complete cubic polynomial.

## Influence Topology on Mechanical Properties of Carbon Nanotorov: Predictive Modeling

In this paper the results of theoretical studies of the effect of topological features of the mechanical properties of carbon nanotori are presented. Numerical analysis of the atomic structure and properties of the objects was carried out by the molecular dynamics and quantum tight-binding method. Conclusions about the stability of the investigated nanotori were made on the base of the results of calculations of the enthalpy of the reaction. The first calculations of the elastic modulus carbon nanotori are presented.

## About the Specifics of Identification Thermomechanical Characteristics of Functionally Graded Materials

Functionally graded materials are widely used in engineering fields with large thermo-mechanical loads. Efficiency of application of these materials depends on accurate knowledge of the laws of heterogeneity. Earlier, the authors have proposed an approach for the identification of smooth laws of heterogeneity for thermoelastic rod. To do this, were received operator equation linking activities and measurable functions for the solution of inverse problem and carried out computational experiments.

## Investigation of Harmonic Waves in the Viscoelastic Layer

The paper deals with the study of harmonic waves in the viscoelastic layer. The properties of the material are described by the constitutive equations in the integral form. The fractional exponential function of Rabotnov is chosen as a kernel of integral operator. Two cases are considered: symmetric stress-strain state (SSS) and asymmetric SSS. The properties of modes which change in time harmonically are investigated for the purpose of studying of the free vibrations. Dispersion equations for both cases are derived.

## field, action, least action principle, field equations, transformation group, Lie group, infinitesimal generator, variation, varied domain, constraint.

The finite deformations of the growing cylinder fabricated of an incompressible elastic material of Mooney–Rivlin type are under consideration. We assume that the deformations are axisymmetric and constant along the cylinder axis. The discrete and continuous types of growing are studied. The analytical solutions of the corresponding boundary-value problems are derived.