Alexey M. Kolesnikov

Southern Federal University | sfedu · Department of Elasticity Theory

In this work, we consider the problem of finite deformations of a dielectric tube under the action of an electric field. The tube consists of two layers, each of which is helically reinforced with fibers. The winding angles of the fibers in each layer are different. Flexible electrodes are deposited onto the inner and outer surfaces of the tube and...

In this paper the problem of finite deformations of a dielectric tube under the action of an electric field is considered. The tube consists of two layers, each spirally reinforced with fibres. The angles of the fibres in each layer are different. On the inner and outer surfaces of the tube and between the layers are flexible electrodes. The electr...

This paper deals with the problem of ball indentation of a thin flat circular highly elastic membrane with a hole in the centre. The aim of this paper is to investigate the effect of friction on the passage of the ball through the hole. The problem is investigated within the framework of the theory of non-linear elastic membranes. The Gent model is...

In this paper, the theory of nonlinear electroelasticity is used to examine deformations of a dielectric elastomer tube, reinforced by two families of helical fibers with different angles, with closed ends and compliant electrodes on its side surfaces. To illustrate the behavior of the fiber-reinforced tube, a specific form of electroelastic energy...

In this paper we consider the problem of frictional contact between an elastic thin-walled tube and a massive solid body in the form of an ellipsoid. The ellipsoid is placed inside the tube. The tube is modeled by a cylindrical membrane of highly elastic material. The ellipsoid is modeled by a rigid body. We assume that friction obeys Coulomb’s law...

We study an inflation of an inhomogeneous thin-walled hyperelastic tube. Either the thickness of the tube or the material properties of tube the change on its cross section. The inhomogeneity leads to a bending of tube subjected by an internal uniform pressure. We analyse the effect of the magnitude of the inhomogeneity, the size of its area and th...

In the paper we investigate the effect of friction on the stress-strain state of a hyperelastic membrane in contact with a massive solid body. We consider the axisymmetric indentation of a thin circular rubber membrane by a cylindrical indenter for different contact conditions: dry contact, liquid lubrication, and gel lubrication. We present experi...

In this paper the theory of nonlinear electroelasticity is used to examine deformations of a dielectric elastomer tube, reinforced by two families of helical fibers with different angles, with closed ends and compliant electrodes on its side surfaces. To illustrate the behaviour of the fiber-reinforced tube, a specific form of electroelastic energy...

In this work we consider a frictional contact between a thin-walled hyperelastic tube and a rigid body. One edge of the tube is partially worn on the body of revolution. The friction in the contact area obeys Coulomb law. An axial force is applied to the other end of the tube. In this paper we analyze the relationship between the minimum contact le...

In this article we obtain exact solutions of finite inhomogeneous deformations of three-dimensional micropolar elastic bodies. We consider a model of the physically linear isotropic compressible material with six material parameters. The obtained solutions describe following types of finite deformations: cylindrical bending of a rectangular plate,...

We consider the problem of a contact between an initially cylindrical hyperelastic membrane and a rigid rough cylinder. One end of the cylindrical membrane is partially stretched over the rigid cylinder. A uniform internal pressure is applied on that part of the membrane which is not in contact with the cylinder. The membrane is in equilibrium and...

We discuss large flexure of an inflated curved thin‐walled tube within the framework of the nonlinear theory of elastic membranes. Wrinkling of the membrane is taken into account by using a relaxed strain energy density derived from a strain energy function of incompressible hyperelastic material. We consider curved tubes with elliptical cross‐sect...

This paper aims to analyze the closing of a helical spring with a rectangular cross-section in the framework of analytical nonlinear elasticity and investigate whether there is any potential for utilizing the closed spring instead of a regular tube. Different closing deformations allow for flexibility to tune the stress state and mechanical respons...

We study finite inhomogeneous deformations of a helical spring with a rectangular cross-section and a long cuboid. Two surfaces of the spring or the cuboid are joined to obtain a hollow cylinder. When body forces are absent the equilibrium equations reduce to ordinary differential equations. The stress-strain states are the same in each cross-secti...

A contact problem of friction for a hyperelastic long thin-walled tube is studied here. One end of the tube is placed over an immovable, rough, rigid cone. The deformation of the tube is assumed finite and axisymmetric. The tube is modeled by a semi-infinite cylindrical membrane composed of an incompressible, homogeneous, isotropic elastic material...

We study a contact problem with friction for a hyperelastic long thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder and an axial force is applied to another end. We assume the deformation of the tube is finite and axisymmetric. The tube is modeled by a semi-infinity cylindrical membrane. The axial force tends t...

We consider the equilibrium problem of a hyperelastic thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder. We assume the deformation of the tube is finite and axisymmetric. The tube is modeled by a cylindrical membrane. The membrane is composed of an incompress-ible, homogeneous, isotropic elastic material. We u...

The problem of the inflation of a curved tube for large elastic strains using a nonlinear membrane theory is investigated. This problem is the special case of a pure bending. The boundary-value problem reduces to a system of ordinary differential equations with periodical boundary conditions. Tubes with an elliptical cross-section are considered. T...

The goal of this research is to construct a mathematical model of the micromechanical experiment: an aspiration of spherical cells. Such experiment is often used to study properties of cells and their membranes. In our model the cell is considered as a fluid-filled membrane with solid-like behavior. The membrane is modeled by a hyperelastic isotrop...

This research treats the pure bending of a pressurized curved tube.We call a curved tube a sector of toroidal shell. The material of a tube is incompressible, isotropic and hyperelastic. The bending stiffness of a tube wall is neglected due to its small thickness. The problem is solved in the framework of a nonlinear membrane theory. Using the semi...

In this work the effect of the unbending of a curved tube under a uniform normal pressure is investigated. The problem is considered within the framework of the nonlinear membrane theory. It is shown that the inflation of a curved tube is the special case of pure bending. The tube with a circular cross section made of a Mooney-Rivlin material is st...

IN THIS PAPER, THE PROBLEM of large pure bending deformations of membrane is considered. The membrane is a sector of torus with a closed cross-section. This membrane is called a curved tube for short. We consider the homogenous, incompressible, isotropic and hyperelastic material. The external load is a constant pressure and bending couples acting...

This paper considers the problem of equilibrium of a nonlinearly elastic spherical shell filled with a heavy fluid and resting on a smooth, absolutely rigid, flat surface. The weight of the shell is assumed to be negligible in comparison with the weight of the fluid filling it. The contact region with the supporting plane is one of the unknowns in...

This paper treats the plane-strain free-boundary problem describing equilibrium of a closed cylindrical non-linear elastic membrane that is inflated by an internal pressure and that is compressed between a rigid plane and a rigid cylinder. The material points of the membrane in contact with the rigid surfaces are unknowns of the problem. The proble...

We consider the large bending of a thin-walled cylinder made of a rubberlike material. It is loaded by internal pressure and bending moments at the ends. The exact formulation of the problem is given within the framework of the nonlinear membrane theory taking into account large strains of the cylinder. Using the special substitution describing the...

In this paper the nonlinear problem of the bendingby end moments of the closed cylindrical shell loaded by internal pressure is considered. The shell consist of the incompressible isotropic hyperelastic material. The nonlinear membrane theory of the elastic shell is used. The resolving equations are derived from the variational principle of the sta...

Large deformations of the shell of revolution under the action of uniformly distributed pressure are investigated. The momentless elastic shell is considered as material surface with special properties. Equilibrium equations and the variational principle of Lagrang are obtained for the two-demensional material continuum. The resolving system for th...