# Mechanics

## Descent of Nanosatellite from Low Earth Orbit by Ion Beam

The work is devoted to the problem of contactless CubSat3U nanosatellites removal from low Earth orbit bymean sof anion beam, which is created by the engine of an active spacecraft. The advant age of this methodis that there is no needfor additional mean sof dockingand gripping. A mathematical model of the nanosatellite plane motion under the action of the ion beam and gravitational forces is developed. Two approaches are used to simulate the ion beam impacton nano satellite.The first one involves the use of known dimensionless aerodynamic coefficients.

## A Couple Contact Loading at the Unilateral Contact of Beams

The contact problem for the structure consisting of two beams is considered. The beams have the different lengths and the different variable thicknesses. One end of the shorter beam is clamped coinciding with the hinge dend of the longer beam.The other ends of the beams are free. The given loading is applied to the longer

## Inﬂuence of Doping by Oxygen Atoms of Porous Carbon Nanostructures on Values of Young’s Modulus

Porous carbon structures are actively used in various ﬁelds of science and technology. The mechanical strength of porous carbon structures with a density of 1.4 g /cm3 with different pore sizes and different concentrations of oxygen atoms was investigated. Investigation of the mechanical properties of porous carbon nanostructures was carried out on three models with different sizes of nanopores (0.4–0.8 nm, 0.2–1.12 nm, 0.7–1.3 nm).

## Axisymmetric Problem Lemba for the Cosserat Medium

The article deals with elastic homogeneous isotropic half-space filled with the Cosserat medium. At the initial instant of time and at infinity, there are no perturbations. At the boundary of the half-space, normal pressures are given. All the components of the stress-strain state are supposed to be limited. A cylindrical coordinate system is used with an axis directed inward into the half-space.

## Creep and Long-Term Strength Modeling for Thick-Walled Tubes under Combined Loading with Axial Force, Torsional Moment and Internal Pressure

We have developed a method for solving the boundary-value problem of rheological deformation and creep rupture of thick-walled tube under combined loading with axial force, torsional moment and internal pressure. Energetic variant of the theory of creep and long-term strength is used to describe creep process. Experimental verification of proposed method has been performed using known test data for creep and long-term strength of thick-walled tubes made of D16T alloy and Steel~20. Calculated dependencies for total axial strain and torsion angle on time are obtained.

## Instantaneously not Elongated Directors in Three-Dimensional Kinematics of the Coulomb – Mohr Medium

Three-dimensional flows of perfectly plastic medium are considered within the framework of the Coulomb -- Mohr continuum model. The model is to be used in applied problems related to limit states and flows of sands, rocks and any other kind of granular media. The present study is based on a notion of asymptotic directions of the stress tensor and the strain tensor increment and as well on instantaneously not elongated directors which are orthogonal to the asymptotic directions and lie in the plane normal to the intermediate principal stress axis.

## Stress and Strain Fields in a Plate of Stress State Dependent Material Properties

The paper analyzes the properties of the constitutive relations proposed to describe the behavior of materials whose deformation diagrams depend on the type of external forces. In this case, various forms of nonlinearity arise, related to the dependence of the properties of materials on the type of the stressed state, the nonlinearity of the deformation diagrams, and the relationship between the shear and volume deformation processes.

## Low-Frequency Vibration Modes of Strongly Inhomogeneous Elastic Laminates

The dynamic behaviour of thin multi-layered structures, composed of contrasting “strong” and “weak” layers, is considered. An asymptotic procedure for analysing the lowest cutoffs is developed. A polynomial frequency equation is derived, along with the linear equations for the associated eigenforms corresponding to displacement variation across the thickness. For a five-layered laminate with clamped faces two term expansions for eigenfrequencies and eigenforms are compared with those obtained from the exact solution of the original problem for thickness resonances.

## On the Complex Dynamics in Simplest Vibrational Systems with Hereditary-Type Friction

The dynamics of a number of vibrational systems, accounting for the forces of hereditary-type dry friction and a vibration limiter, are studied in the paper. The interaction between the vibration limiter and the vibrational system is assumed to obey Newton's hypothesis. A general mathematical model has been developed, which is a strongly nonlinear non-autonomous system with a variable structure. The dynamics of the mathematical model is studied numerically-analytically, using the mathematical apparatus of the point mapping method.

## On Some Models of Indentation for Functionally-Graded Coatings

The paper presents approximate models of deformation for an inhomogeneous elastic strip. Approximate models reflect the distribution features of the inhomogeneous structure properties over the thickness. The models are based on hypotheses about the nature of the change in the components of the displacement field, which allows to consider arbitrary laws of heterogeneity: continuous, as well as discontinuous or having a strong gradient. Solutions of the contact problem for different inhomogeneity laws are constructed. Comparative analysis of the models is carried out.