# Mechanics

## Unsteady Electromagnetic Elasticity of Piezoelectrics Considering Diffusion

The paper considers a model of the linear theory of deformation of elastic continuum with diffusion and piezoelectric effect taken into account, which describes the relationship between mechanical deformations, mass transfer, and the internal electric field. A one-dimensional model of electromagnetic diffusion in a rectangular Cartesian coordinate system is used.

## Biomechanics of Human Carotid Artery with Pathological Tortuosity

Pathological tortuosity of carotid artery ranks second among the causes of cerebro-vascular insufficiency. In their previous researches authors have described the influence of pathological tortuosity type on carotid artery behaviour. In this article we discuss the influence of different anatomic (bending angle, bulb size) and rheological factors on haemodynamics and stress-strain state of carotid artery with pathological tortuosity. Decreasing of the bending angle leads to blood volume reduction in brain and possible formation of septal stenosis in bending area.

## The Problem of a Hydroelasticity for a Tube Ring-type a Profile with Elastic, Geometrically Irregular Outer Shell at Pressure Influence

The mechanical model presented in the form of a tube of ring section, formed by two surfaces of coaxial cylindrical shells cooperating with viscous incompressible liquid is considered. The mathematical model of this system consisting of the differential equations in private derivatives of describing dynamics of viscous incompressible liquid and an elastic ridge shell together with boundary conditions is constructed.

## Stress-strain State of an Elliptical Cylinder with an Ellipsoidal Bottoms of Dissimilar Materials Based FEM

The algorithm of calculating the construction in the form of an elliptical cylinder with ellipsoidal bottom of different materials based on the finite element method with the use of scalar and vector fields interpolating movements is described. As part of the sampling using rectangular curved finite elements with eighteen degrees of freedom in the node. Calculations of a circular cylinder with an articulated ellipsoid of rotation the verification of the algorithm and shows its effectiveness.

## 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.

## Synthesis of Asymptotically Stable Motion of a Robot Arm Manipulator

The paper is about an active control problem. It solves the inverse problem of dynamics and concerns with construction of program motions of non-autonomous mechanical systems. This study is important and necessary in software design of automated systems for control of mechanisms. In particular, it is used in various modeling problems of robot-manipulators. Here, we construct all possible asymptotically stable program motions for a model of robots arm-manipulator, which is simulated by a mechanical system with three degrees of freedom.

## Investigation of surface roughness at micro-scale and mechanical response in the contemporary bio-polimer sutures by the nanoindentation

An investigation of properties of contemporary suture materials (surgical threads) is the state-of-art challenge in biomechanics. To improve an effectiveness of sutures application, an analysis of structure and elastic properties by the atomic force microscopy and scanning electron microscopy is necessary to be performed.

## 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.