# Mechanics

## Influence of slipping on viscosimetric flow of a elastoviscoplastic material between rigid coaxial cylinders

The viscoplastic flow of an incompressible elastoviscoplastic material between two rigid coaxial cylindrical surfaces is considered when slipping of a material is possible at one of them. The solution is constructed using the model of large elastoviscoplastic deformations. Reversible deformation, development and braking of a viscoplastic flow, unloading and deformation under rotation in the opposite direction are considered. Laws of movement of elastic-plastic boundaries are received.

## The heat conductivity in the infinite solid of the convection in a cylindrical cavity

The problem of heat conductivity in the infinite solid from gas moving in a cylindrical cavity is solved by the combination of the Green function method and the Laplace transformation.

## Flow of Slibar–Paslay material in a flat channel

The question of the numerical simulation of unstable flow of a viscoplastic material in a flat channel is considered. Defining relations are taken in the form of Slibar–Paslay. The problem is solved in stresses. Theorem about the weak discontinuity at the interfaces between rigid and viscoplastic zones is proved. The original numerical method for solving the problem is offered. Numerical simulation results are presented.

## Application of generalized functions in dynamical contact problems of wing aeroelasaticity

The range of problems dealing with analysis of deformed state of thin elastic wing at the oscillations in limited acoustic medium is considered in this article. The theory of generalized functions was chosen as an instrument for the mathematical research. By results of performed numerical experiment the existence of damp forces in the acoustic medium and resonance effects caused by elastic properties of the wing was confirmed.

## Analysis of algorithms study of stability of thin-walled shells

We consider three variants of algorithms for studying the stability of thin-shell: An algorithm based on the Ritz method and iterative processes, an algorithm based on the method of steepest descent, the algorithm based on a method of extending the solution to the parameter. Analyzes the results of the study of shells produced using these algorithms.

## Mathematical modelling of critical speed of the multistage core at longitudinal blow

Mathematical modeling of longitudinal elastic central blow of a multistage core about a rigid barrier is carried out, at not keeping communications. Mathematical modeling is carried out by the exact analytical decision of the wave differential equation by a method of Dalamber with the task of necessary initial and boundary conditions. With application of the formula of Euler analytical expression for calculation of critical pretonic speed at which there comes loss of stability of a step core is received.