# Mechanics

## Covariant field equations and d-tensors of hyperbolic thermoelastic continuum with fine microstructure

A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained. Constitutive equations of microstructural hyperbolic thermoelasticity are discussed.

## Modeling of the shock system motion with impacts about hard barriers

Abstract: We have developed a model of a shock system with a resilient member under periodic force action including impacts about hard barriers. In order to model the shock system we have developed a program providing a computational solution for differential equations of a subject motion taking into account conditions of periodicity and collision, graphical and numerical reproduction of motion parameters in the simulation process. We have performed simulation of modes of the shock system.

## The equilibrium equations of shells in the coordinates of the general form

A mathematical model of homogeneous elastic shells is consider under kinematics Reissner–Mindlin type. Through direct (coordinateless) methods of the tensor calculus equations of equilibrium are obtained in terms of displacements in an arbitrary (not necessarily orthogonal) coordinate system, taking into account the asymmetry of the location of the front surface. For a spherical shells proposed procedure for constructing solutions, based on the method of spectral decomposition, which describes the stress-strain state at the potential power and torque static loads.

## 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

## 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.