# Mechanics

## Elastic-plastic deformation of nanoplates. The method of variational iterations (extended Kantorovich method)

In this paper, a mathematical model is constructed based on the deformation theory of plasticity for studying the stress-strain state of Kirchhoff nanoplates (nanoeffects are taken into account according to the modified moment theory of elasticity). An economical and correct iterative method for calculating the stress-strain state of nanoplates has been developed — the method of variational iterations (the extended Kantorovich method).

## Contact problem for functionally graded orthotropic strip

Within the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to transformants of the displacement vector and stress tensor components is constructed.

## Dynamic thermal stability of a geometrically irregular shallow shell of constant torsion under the action of a load periodic by its time coordinate

In the framework of a Love type model, a geometrically irregular isotropic shallow constant torsion shell is considered. It is based on a strict continuum-shell-rib model. It is assumed that the geometrically irregular shell is heated to a constant temperature $\theta_0$, two opposite edges are exposed to a tangential load periodic by its time coordinate, the amplitude and frequency of which are known ($p(t)=p_0 \cos \vartheta t$).

## 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

## 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.