# Mechanics

## Asymptotic methods for obtained solutions in vicinities of wave fronts in viscoelastic rod at large time

Non-stationary longitudinal waves in viscoelastic rod at large time are considered. Equations for the wave fronts are derived by means of asymptotic methods. Solutions of these equations are obtained.

## Quaternion Models and Algorithms for Solving the General Problem of Optimal Reorientation of Spacecraft Orbit

The problem of optimal reorientation of the spacecraft orbit is considered in quaternion formulation. Control (vector of the acceleration of the jet thrust) is limited in magnitude. To solve the problem it is required to determine the optimal orientation of this vector in space. It is necessary to minimize the duration of the process of reorientation of the spacecraft orbit. To describe the motion of the center of mass of the spacecraft we used quaternion differential equation of the orientation of the spacecraft orbit. The problem was solved using the maximum principle of L. S.

## Investigation of Strength and Buckling of Orthotropic Conical Shells and Conical Panels

In the construction, thin-walled shell structures are used to cover the buildings of large areas, such as stadiums, hangars, circuses, airports. In this paper, the strength and buckling of closed conical shells as well as their panels are studied. The geometric nonlinearity and transverse shifts are taken into account. A mathematical model is used in the form of a functional of the total potential energy of deformation. Also expressions for deformations, forces and moments are given. The calculation program is implemented in the MatLab environment.

## Thin Film Thermocapillary Motion of Binary Alcohol-Containing Solution

Interphase convection is a widespread phenomenon that occurs in various branches of technology, including chemical technologies. The greatest interest in the case of thin liquid films is the Marangoni convection. Phase transitions significantly affect the convective flow, changing the coefficient of surface tension. In this paper, the behavior of a thin film of an alcohol-containing solution when it is heated is analytically studied.

## T-irreducible extension for unions of complete graphs

T-irreducible extension is one of kinds of optimal extensions of graphs. Constructions of optimal extensions are used in diagnosis of discrete systems and in cryptography. A graph H with n+1 vertices is called an extension of a graph G with n vertices if G can be embedded in every maximal subgraph of H. Any graph Ghas the trivial extension that is the join ng+of G with some outer vertex v. T-irreducible extensions are obtained from the trivial extension by removal of maximal number of edges in such a way that the extension property is preserved.

## Research into the time-depended transactional processes in viscoplastic fluids

The paper presents problem of transition from one steady-state conditions of viscoplastic fluid flow to another between parallel planes. The problem definition is given within the limits of five- parameter model, which permits to take up differences between behavior under stress and without stress and possible slippage along the solid walls. Hysteresis of deformation is considered by means of model of smooth transition from adhesion to slippage. The solution is determined by method of momentary eigenfunctions of Melamed-Grinberg.

## Influence of Residual Stresses on Geometric Parameters of Surface-Strengthened Beam

The сomprehensive study of the formation of residual stresses and plastic deformations in prismatic samples of the EP742 alloy after ultrasonic hardening and their influence on the geometric parameters of the beam was conducted. Phenomenological model for the reconstruction of residual stress fields is proposed, and the verification of its adequacy to experimental data with four hardening modes is performed. The correspondence of the calculated and experimental data is observed.

## On Wave Solutions of Dynamic Equations of Hemitropic Micropolar Thermoelasticity

Coupled equations of hemitropic thermoelastic micropolar continuum formulated in terms of displacement vector, microrotation vector and temperature increment are considered. Thermodiffusion mechanism of heat transport is assumed. Hemitropic thermoelastic constitutive constants are reduced to a minimal set retaining hemitropic constitutive behaviour. Coupled plane waves propagating in thermoelastic media are studied. Spatial polarizations of the coupled plane waves are determined. Bicubic equations for wavenumbers are obtained and then analyzed.

## Extracting Clinically Relevant Data from Biomechanical Modeling of Surgical Treatment Options for Spinal Injury in Damaged Vertebrae Th10, Th11

Two three-dimensional geometric solid-state models of the Th7-L1 spinal segment (Model 1, Model 2) with metal construction were built. Models include the vertebrae Th7, Th8, Th9, Th10, Th11, Th12, L1, intervertebral discs, facet joints and ligaments, and metal construction elements. In Model 1, the cortical and spongy layers are constructed by three-dimensional solids, facet joints and intervertebral discs by three-dimensional bodies, ligaments by one-dimensional objects.

## Creation of Three-Dimensional Solid-State Models of a Spine with Transpedicular Fixation Using a Specialized Software

Biomechanical experiments are widely used to study the mechanical characteristics of spinal elements under various types of loading. The correct construction of three-dimensional models is especially important for studying the behavior of the spine after surgery, for example, the installation of fixing metal structures. There are several approaches to modeling each anatomical component of the spinal column. It is generally accepted to construct vertebral bodies of a simulated spinal segment based on the results of computed tomography.