ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

# Mechanics

## Bending of an elastic circular three-layer plate in a neutron flux by a local load

The bending of an elastic circular three-layer plate asymmetric in thickness by local loads uniformly distributed in a circle in a neutron current is considered. Polyline hypotheses are used to describe the kinematics of the package. Kirchhoff's hypotheses are valid in thin load-bearing layers. In a relatively thick incompressible filler, Timoshenko's hypothesis about the straightness and incompressibility of the deformed normal is fulfilled. The work of the tangential stresses of the filler is taken into account. Deformations are small.

## Evaluation of the influence of white spot lesion on the mechanical properties of human tooth enamel and dentine

In the present paper the influence of early caries (white spot lesion) on the mechanical properties of human tooth enamel and dentine was ex vivo investigated. Optical microscopy made it possible to study the shape of the enamel caries area on a prepared longitudinal section of a human molar.

## Influence of the modulation of the blood flow velocity in peripheral vessels on the temperature of the outer wall of the vessel: Finite element modeling of the adjoint problem

A finite element modelling of the process of the heat transfer from blood to the wall of an arterial vessel was carried out in order to solve a more general problem of determining the relationship between the amplitude-frequency characteristics of fluctuations in the volumetric blood flow velocity in peripheral vessels with temperature oscillations on the skin surface. A model was built in the ANSYS software with Fluid Flow CFX module which includes domains related to blood, the wall of a cylindrical vessel, and skin (bio-tissue).

## Generalized pseudotensor formulations of the Stokes’ integral theorem

Oriented continua play an important role in micropolar elasticity modelling. All realizations of micropolar theories are conceptually possible only within the framework of the pseudotensor formalism and the orientable manifold notion. This particularly concerns the theory of micropolar hemitropic elastic media. In this paper, a pseudotensor description is used in contrast to Kartan's formalism. The pseudotensor formulation of Stokes' integral theorem is almost unknown in the current scientific literature.

## Generalized model of nonlinear elastic foundation and longitudinal waves in cylindrical shells

A non-integrable quasi-hyperbolic sixth-order equation is derived that simulates the axisymmetric propagation of longitudinal waves along the generatrix of a cylindrical Kirchhoff – Love shell interacting with a nonlinear elastic medium. A six-parameter generalized model of a nonlinear elastic medium, which is reduced in particular cases to the models of Winkler, Pasternak, and Hetenyi, is introduced into consideration.

## Solution of the inverse problem of two thermomechanical characteristics identification of a functionally graded rod

An approach to solving the inverse problem of the simultaneous identification of two thermomechanical characteristics of a functionally graded rod is presented. Two problems of thermoelasticity with different heat loads at the ends of the rod are considered. The input information is the temperature measurement data at the end of the rod over a finite time interval.

## Numerical study of the influence of the parameters of dispersed particles on the deposition of the solid phase of an electrically charged polydisperse gas suspension

The work is devoted to the study of the laws governing the deposition of particles of the dispersed phase of an electrically charged dusty medium moving in a channel onto an electrode plate. The aim of the study is to reveal the influence of the size of dispersed inclusions and the density of the material of particles on the process of settling of fractions of a polydisperse gas suspension on the surface of the electrode plate.

## Biomechanical support for the physician’s decision when choosing a treatment option based on quantitative success criteria

Preoperative planning for the treatment of the consequences of diseases and injuries of the spino-pelvic complex surgical treatment is a mandatory procedure and should ensure the selection of implants, modes and techniques for their installation, as well as the reconstruction of the optimal biomechanics of the operated segment. For each individual patient, the surgeon chooses a treatment variant based on his qualitative and quantitative individual parameters.

## Nonlinear deformation of axisymmetrically loaded rotation shell based on FEM with different variants of definitional equations

A curvilinear finite element of the median line of an axisymmetrically loaded shell of revolution with a stiffness matrix of $8{\times} 8$ size is used when choosing nodal unknowns in the form of displacements and their first derivatives is used. The constitutive equations at the loading step are implemented in two versions. In the first version, the relations of the deformation theory of plasticity are used, which consist of expressions for the elastic and plastic parts.

## Numerical method for calculating the stress-strain state in a prismatic surface-hardened spacemen with a notch in elastic and elastoplastic formulations

The problem of calculating the stress-strain state in the region of through stress concentrators in the form of a transverse notch of semicircular, through and V-shaped shape in a prismatic sample after advanced surface plastic deformation in elastic and elastoplastic formulations based on the finite element method is solved. The initial formulations are reduced to fictitious problems of thermoelasticity and thermoelastoplasticity using the method of initial deformations.