# Mechanics

## Axisymmetric Stress Field Near a Circular Cut in a Solid with Stress State Dependent Plastic Properties

The paper analyzes the properties of the constitutive relations of the theory of plasticity for a continuum, which plastic properties depend on the type of stress state. The plasticity condition

## Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift

A theory of nonlinear dynamics of a flexible single-layer micropolar cylindrical shell of a network structure is constructed. The geometric nonlinearity is taken into account by the model of Theodor von Karman. We consider a nonclassical continuum shell model based on the Cosserat medium with constrained particle rotation (pseudocontinuum). It is assumed that the displacement and rotation fields are not independent. An additional independent material length parameter associated with the symmetric tensor of the rotation gradient is introduced into consideration.

## Threshold Values of Morphological Parameters Associated with Cerebral Aneurysm Rupture Risk

Numerous studies have shown that morphological parameters of aneurysms are associated with their rupture. However, literature data on the values of these parameters vary significantly. The objective of this study is to identify image-based morphological parameter values which correlate with cerebral aneurysm rupture and can be used during preoperative planning to detect aneurysms prone to rupture. Mean values of the morphological factors such as aspect ratio and size ratio were chosen from the literature. These factors were sampled for ruptured and unruptured aneurysms.

## The Effect of Bubbles on the Structure of Flow and the Friction in Upward Turbulent Gas–Liquid Flow

This paper presents the computational study results of the ascending gas-liquid flow local structure in a vertical pipe. The mathematical model is based on the use of two-fluid Eulerian approach taking into account the inverse influence of bubbles on averaged characteristics and turbulence of the carrying phase. The equations conservation of mass and momentum quantity of motion in the form of Navier-Stokes equations averaged over Reynolds for each phase are written down. For turbulent stresses the relations under the assumption of the Boussinesq hypothesis are written.

## 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 beam. The beams undergo the weak joint bending with the unilateral (receding) contact. There is no friction between the beams.The bending of each beam is described by Bernoulli–Eulermodel.The contact problem is to find the contact loading, i.e.

## 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.