# Mechanics

## Application of Program Complex ANSYS to Calculation of the Thick-Walled Pipeline Which is Exposed to High-Temperature Local Hydrogen Corrosion

The way of application of program complex ANSYS to the decision of problems of calculation of the is intense-deformed condition and destruction of the cylindrical constructive element which is in conditions of non-uniform hydrogen corrosion is considered.

## The Second Boundary Problem for the System Hyperbolic Type Second Order for Large T

In the paper we consider the control problem for objects which vibration are described by the system of ware equations with boundary condition of the second kind.

## Investigation of Quasi-Static Bending of the Bar on the Basis of Variation Problem

The investigation of the existence of quasi-static behavior of elastic cantilever bar subjected to potential external effects. For the case when the mathematical model is a variational problem is obtained statically singular point, when crossing the path of loading is a change of type of quasi-static process.

## Stability of the Cylindrical Cover with the Elastic-Viscous-Plastic Filler at Axial Compression

Within the limits of the exact three-dimensional equations of stability of an equilibrium state of a cylindrical cover with a filler is investigated at axial compression. Calculations were spent for a case when the cover material was modelled by an elastic body, and a filler material – environment with difficult rheological properties – elasticviscous-plastic. The estimation of influence on size of critical pressure of parameters of a cover and a filler is given.

## Temperature Distribution Inside the Ring of Liquid with Two Free Borders in the Nonclassical Model of Hydrodynamics

The article deals with the task to determine the velocity field and temperature field inside the insulated ring of incompressible viscous fluid with two free boundaries in the non-classical model of hydrodynamics. The solution to the Navier – Stokes equations and heat equation obtained by numerical methods. Analysis of the results of numerical experiments reveal the effect of nondissipative viscosity on the temperature distribution inside the ring.

## Construction and Stabilization Program Motions of Nonautonomous Hamiltonian Systems

We consider program motion of Hamiltonian system and solve the problem of construction asymptotically stability programm motion. The programm motion can be any function. Control is received in the method and the method of limiting functions and systems. In this case we use the Lyapunov’s functions having constant signs derivatives. The following examples are considered: stabilization of program motions of homogeneous rod of variable length and stabilization of program motions of mathematical pendulum variable length in the rotation plane.

## Influence of the Variable Aerodynamic Moment on Satellite Attitude Motion

Attitude motion of a rigid body in the plane of a circular orbit under gravitational and aerodynamic moments is considered. The mode of the motion of a satellite gravitational stabilization when its long axis moves in the vicinity of a local vertical is investigated. Allowance of variations in the atmosphere density at a satellite orbital motion and in the aerodynamic moment coefficient depending on its orientation to an approach flow is included in the aerodynamic moment model.

## Stress of Heavy-Wall Tubing Cylindrical Pipes Taking into Account the Gravity for Materials with Difficult Rheology

Within a method of small parametre the field of stresses of heavy tubing cylindrical pipes is investigated at modelling of a material by the incompressible elasticis viscous-plastic environment. The estimation of influence on size of a plastic zone physicomechanical design parametres is given.

## Boundary Properties of Generalized Cauchy Type Integrals in the Space of Smooth Functions

The generalized Cauchy type integrals which kernel depends on the difference of arguments are considered on the smooth contour. These integrals cover as potentials of double layer for second order elliptic equations as generalized Cauchy type integrals for first order elliptic systems on the plane. In the paper the sufficient conditions such that these integrals belong C n,μ up to the boundary are found.

## Creeping Flow of Viscoelastic Fluid with Free Surface at Non-Isothermal Condition

Numerical simulation flow of viscoelastic fluid with free surface, which is realized in entrance and output flow in extrusion die was performed. The flow of liquid is described by equations of conservation of mass, momentum and thermal energy with rheological constitutive equation of Giesekesus. On basis of finite element method the stable numerical scheme was developed to solve this problem. Different numerical experiments was performed to define the configuration of outflow jet in various regimes and construction of die.