# Mechanics

## Mechanical properties study for graphene sheets of various size

We studied mechanical properties of large graphene sheets. The Young's modulus was found for each of the considered nanoparticles and sheets. To this end, the deformation was applied in two orthogonal directions – zigzag and armchair directions of the graphene atomic framework. It was established that there exist a size effect on the Young's modulus of graphene.

## Theoretical investigation of the deformed graphene nanostructures

The results of the theoretical investigations of properties of the deformed graphene structures are presented in this work. We investigated mechanical properties of the bi-layer graphene structures by means of the molecular dynamics method. To evaluate mechanical properties of graphene we applied a compression load to graphene. As a result of the investigations it was found that graphene became a wave-like with the increase of the compression. The number of half-wave, generated on the graphene surface depends on the size of graphene.

## On precisely conserved quantities of coupled micropolar thermoelastic field

The paper is devoted to the 4-covariant formulation in fourdimensional space-time of dynamics of non-linear hyperbolic micropolar thermoelastic continuum. Theory ofmicropolar continuum are due to E. Cosserat and F. Cosserat and their study of 1909. The complement microdeformations and microrotations of an element are described by a non-rigid trihedron (the case of deformable micropolar directors).

## The conformal contact between punches and coated solids with complicated surface profile

The contact interaction between system of rigid punches and viscoelastic foundations with thin coatings for the cases in which the punches and coating surfaces are conformal (mutually repeating) is studied. Such problems can arise, for example, when the punch immerses into a solidifying coating before its complete solidification. The shapes of punches surfaces could be described by a fast oscillating functions. Basic system of mixed integral equation is obtained. The solution of this system is constructed by using the generalized projection method.

## The transformation of longitudinal the strain wafe having a linear form and increasing intensity in conjugation of rods with elastic gacket

The paper gives a review of transformation of longitudinal strain wave at the boundary of heterogeneous rods with elastic gasket. The article describes a technique for calculating the transformation of the strain wave of linear form. Parameters of the wave, which have passed through connection of rods are defined.

## The new approach to investigation of multilayer graphene mechanical properties by the finite-element method

A new approach to investigate the mechanical properties of multilayer graphene was suggested. The method is based on the idea that the van der Waals interaction between the graphene sheets can be simulated by a fictitious layer of continuum. The stress-strain state of multilayer graphene is described by stationary equations of Navier–Lame. This approach has been successfully tested on graphene deflection. The graphene layers were considered as linear-elastic material.

## A mathematical theory of plane harmonic coupled thermoelastic waves in type-I micropolar continua

The present paper is devoted to an analysis of plane harmonic coupled thermoelastic waves of displacements, microrotations and temperature propagating in continua.The analysis is carried out in the framework of linear type-I (GNI/CTE) theory of thermoelastic micropolar continuum. Additional microrotations and moment stresses are taken into consideration. Propagating wave surfaces of weak discontinuities of displacements, microrotations, and temperature are studied by compatibility conditions technique due to Hadamard and Thomas.

## Dual matrix and biquaternion methods of solving direct and inverse kinematics problems of manipulators for example Stanford robot arm. II

The methology of solving the inverce kinematics problem of manipulators by using biquaternion theory of kinematics control is shown on the example of Stanford robot arm. Solving of the inverce kinematics problem of Stanford robot arm is performed using the simplest control law. The analysis of numerical solution results is made. The efficacy of applying the theory of kinematics control for solving the inverce kinematics problem of manipulators is proved.

## The stability of the constructive-orthotropic heterogeneous cylindrical shell under uneven radial load

On the base haft-momentum Vlasov theory the problem of stability of cylindrical homogeneas shell with variation of thicknees atv radial symmetrical ractial pressure variated onalong axe distance. At one reletion between thickness and pressure values the accurate solution was produced for one values in pressure variation law when stability of shell is sailed.

## The restoration of functional relationships with a given singularity

Provided methods recovery of functional dependence with a specified discontinuity. Application of the algorithm of building function with given discontinuity is shown. The first method is based on a formal function minimization by random search. The second uses the information content of the data.