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A physical model for describing the diffusion creep in perovskite-type material given oxygen non-stoichiometry and tensile–compressive asymmetry is developed. Reference tests for determining the creep parameters in the constitutive equations are discussed. The proposed model is used for combined numerical-and-analytical simulation of diffusion creep in a hollow thick-walled perovskite cylinder under generalized plane strain conditions. The analytical solution for oxygen non-stoichiometry is used. Also, the closed-form general expressions for stresses in a hollow cylinder undergoing diffusion creep at a given oxygen chemical potential gradient are derived. The numerical integration is performed using the-Runge–Kutta–Merson method of the fourth order with automatic step control. The stress redistribution over time in the cylinder under the diffusion creep conditions is analyzed. The numerical results related to tensile–compressive asymmetry and oxygen surface exchange in a perovskite cylinder are discussed.

A new brachistochrone problem of the motion of a material point on a transcendental surface between two given points in a vertical uniform field of gravity is considered. The surface is a cut horizontal cylinder whose directrix is a cycloid, and generatrix is straight lines parallel to the horizontal axis. Energy dissipation is neglected. A time functional is obtained and a differential equation is derived for a single parameter that describes the form of brachistochrons in the problem. Spatial parametric equations of the brachistochronic motion of a material point on a surface are obtained. The fast response time is determined.

A generalized design model is proposed to study the stability and initial post-buckling equilibrium trajectory of sandwich cylindrical shells with elastic core that resists only transverse tension–compression. The model includes nonlinear equilibrium mixed-form equations, asymptotic equations obtained by the Koiter–Budiansky method, and the analytical solution of a homogeneous eigenvalue problem and inhomogeneous problem to find the values of the unknown functions at the critical point. The numerical results obtained indicate that the internal pressure strongly influences the critical load and initial post-buckling behavior of the shells.

Using the finite-element method, the stress–strain state of a tooth crown with a caries cavity acted upon by a vertical force is simulated. The tooth crown is modeled by a two-layer cylinder with outer enamel layer and inner dentinal layer. The effect of the location and geometry of the caries cavity and the mechanical properties of the enamel and dentin on the load-bearing capacity of the tooth crown is analyzed. It is shown that an increase in the length and depth of the cavity in the tooth crown leads to an increase in the stress intensity in the crown layers. The stress intensity peaks in the enamel layer near the walls of the caries cavities located near the tooth neck.

The problem on propagation of axisymmetric electroelastic waves in a hollow layered cylinder made of metallic and radially polarized piezoceramic layers is solved. The lateral surfaces of the cylinder are free of electrodes. The outside surface is free of mechanical loads, while the inside one undergoes harmonically varying pressure Pe. The problem was solved with a numerical-analytical method. By representing the components of the stress tensor, displacement vectors, electric-flux density, and electrostatic potential by traveling waves, the original electroelastic problem in partial derivatives is reduced to an inhomogeneous boundary-value problem for ordinary differential equations. To solve the problem, the stable numerical discrete-orthogonalization method is used. The results of the kinematic analysis of the layered cylinder both with metallic and piezoceramic (PZT 4) layers are presented. The numerical results are analyzed.

The distribution of contact pressure between a sealing element and a cylinder depending on the dimensions and mechanical characteristics of the former when subject to unidirectional compression is studied. The axial load needed to ensure seal tightness is determined. The relationship between this load and the dimensions of the sealing element is established. It is shown that as the height of the element is decreased, the axial load increases substantially. The maximum height beyond which the contact pressure hardly depends on the axial load is determined

The stress intensity factors (SIF) for a plane circular crack in a finite cylinder undergoing torsional vibrations are determined. The vibrations are generated by a rigid circular plate attached to one end of the cylinder and subjected to a harmonic moment. The boundary-value problem is reduced to the Fredholm equation of the second kind. This equation is solved numerically, and the solution is used to derive a highly accurate approximate formula to calculate the SIFs. The calculated results are plotted and analyzed

A method of analyzing the near-edge stress state in mixed problems of the deformation of an isotropic cylindrical body is proposed. The method is based on the expansion of the solution of three-dimensional problems of elasticity into a series of Lurie–Vorovich homogeneous basis functions. An asymptotic analysis is performed to find the principal part of the solution of the infinite systems of linear algebraic systems to which the problems are reduced. The type of the stress singularity at the edge of the cylinder is the same as in the mixed problems for a quarter plane. Kummer’s convergence acceleration method is used. The obtained results are validated by testing the boundary conditions and by comparing with results obtained by other authors

The effect of the tangential components of magnetic-flux density on the stress state of a circular cylindrical shell of variable stiffness is studied following a geometrically nonlinear problem statement. The cylindrical shell is subject to extraneous electric current and nonstationary mechanical loading

In this paper, an implicit coupling algorithm for fluid–structure interaction problems with under-time steps for the solid is presented. Its implementation on two configurations is achieved by using the CASTEM finite-elements code. First, the free oscillations of a cylinder in an annular fluid domain where its movement is determined by the coupled fluid–solid action is considered in the case of viscous fluid. It should be noted that the implicit coupling algorithm gives the best prediction of the structure oscillations. The under-time steps for the solid are introduced in order to obtain better results. Then, an application whose final objective is to model a floating barrage is studied. The main goal of this application is to predict the displacements of a ring completely immersed and anchored by a cable to the lower boundary of the fluid domain. The finite-element discretization of the Navier–Stokes equations in the ALE formulation is used

Algebraic equations for the line of steepest descent of a cylinder are derived in parametric form. Conditions for rolling without slipping and separation of the cylinder along a brachistochrone are established based on the equations of motion with constraint reaction. The important conclusion is drawn that the center of mass of a cylinder moving along a brachistochrone describes a cycloid

The radial nonstationary vibrations of a piezoceramic cylinder polarized across the thickness and subjected to mechanical dynamic loading are studied. To solve the initial–boundary-value problem, mesh approximations and difference schemes are used. The electromechanical state of the cylinder under an instantaneously applied constant force is analyzed in detail

The paper studies the radial nonstationary vibration of a piezoceramic cylinder polarized throughout the thickness and subjected to a dynamic electric load. A numerical algorithm for solving an initial–boundary-value problem using mesh-based approximations and difference schemes is developed. The dynamic electroelastic state of the cylinder subjected to a constant potential difference applied instantaneously is analyzed

The motion of a heavy homogeneous cylinder is considered as rolling without slipping along an unknown curve. A functional in the form of the total time of rolling is found and minimized by solving a variational problem. The algebraic equation of the quickest-descent directrix is derived in parametric form

The problem of identifying the law of time variation in the temperature of one boundary surface of a two-layer cylinder and its thermal and thermostressed state from the temperature and radial displacement of the other surface is formulated and solved. The inverse problem of thermoelasticity to which the problem posed is reduced is analyzed for well-posedness. The solution of the direct problem of thermoelasticity is used to numerically test the technique of solving the inverse problem

The paper proposes a method to solve the problem of vibrations of a radially polarized piezoelectric cylinder subject to nonstationary electric excitation. The dynamic electromechanical state of the cylinder is analyzed. The time-dependences of electric and mechanical characteristics are plotted. The distribution of these characteristics over the cross section of a short cylinder is examined. The region of end disturbances in a long cylinder is identified

The electroelastic state of a bent inhomogeneous piezoceramic cylinder with sliding restraints at the ends is examined. The boundary-value problem is reduced to a system of 12k (k = 1, 2,...) integro-differential equations. Expressions for stresses characterizing the stress state of the cylinder are derived. Relative hoop stresses are calculated

A technique is proposed for mathematical and numerical modeling of thermomechanical processes in electrically conductive bodies subjected to an external electromagnetic field. The initial relations for the determination of the electromagnetic field are the Maxwell equations. The stress and strain states of the body are described using the equations of nonisothermal elastoplasticity. The model takes into account the coupling of the electromagnetic and thermal fields. All physical and mechanical parameters of the material depend on temperature. The process of high-temperature induction treatment of a ferromagnetic cylinder is considered as an example

Coupled electroelasticity theory, acoustic approximation, and two-wire transmission line theory are used to study the generation of waves by a submerged cylindrical piezoelectric transducer connected by a cable to a source of nonstationary electric signals. The problem is reduced to a system of integral Volterra equations using the Laplace transform and analytical inversion of boundary conditions. The results of calculations for different cable lengths are presented

A coupled dynamic problem of thermomechanics is formulated based on a thermodynamically consistent modification of the Bodner-Partom model. This formulation is used to analyze the thermomechanical state of an aluminum cylinder under axial impulsive loading. The problem is solved by the finite-element method. Time integration is performed by the Crank-Nicholson scheme. Reversible and irreversible thermal changes are studied

The mixed problem of bending of a transtropic thick plate and a short cylinder is solved using the Lur'e-Vorovich homogeneous solutions. The most typical results from numerical experiments for a wide range of physical and geometrical parameters are presented

The monoharmonic radial vibrations and dissipative heating of an infinite hollow piezoceramic cylinder are studied in dynamic formulation, taking into account the temperature dependence of the complex electromechanical characteristics over a wide range of temperatures, including depolarization temperatures. The influence of the heat exchange conditions, the level of electric load, and geometry on the thermoelectromechanical characteristics is studied in the case of forced vibrations at the first resonance

The Fourier method is used to find the analytical solutions to two-dimensional quasistatic problems of stationary polyharmonic vibrations and dissipative heating of a linearly viscoelastic cylinder. The influence of the cylinder thickness and the width of the loading area on the thermomechanical state of the cylinder is studied based on numerical data

The paper studies the interaction of a harmonically oscillating spherical body and a thin elastic cylindrical shell filled with a perfect compressible fluid and immersed in an infinite elastic medium. The geometrical center of the sphere is located on the cylinder axis. The acoustic approximation, the theory of thin elastic shells based on the Kirchhoff—Love hypotheses, and the Lame equations are used to model the motion of the fluid, shell, and medium, respectively. The solution method is based on the possibility of representing partial solutions of the Helmholtz equations written in cylindrical coordinates in terms of partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions at the shell—medium and shell—fluid interfaces and at the spherical surface produces an infinite system of algebraic equations with coefficients in the form of improper integrals of cylindrical functions. This system is solved by the reduction method. The behavior of the hydroelastic system is analyzed against the frequency of forced oscillations.

A new technique is proposed for solving the three-dimensional antisymmetric elastic problem for a thick-walled shell of finite length. The boundary-value problem is reduced to a system of one-dimensional singular integral equations. Characteristic stresses are calculated

Natural vibrations localized at the free edge of a semiinfinite, elastic, orthotropic, circular cylindrical shell of open profile are studied. The cylinder is hinged along the bounding generatrices. Dispersion equations are derived from the classical equations describing the dynamic equilibrium for orthotropic cylindrical shells. It is established that these dispersion equations and the dispersion equations for a semiinfinite orthotropic plate strip are in an asymptotic relationship. A procedure for analysis of the possible types of vibrations at the free edge of the cylinder is described. Approximate values of the dimensionless natural frequency and damping factor are determined for shells of different radii

An approach is proposed to study a collision of a long cylinder with the inside surface of a circular cylindrical cavity in an elastic medium. The problem is solved in plane formulation. A nonstationary mixed initial–boundary-value problem with unknown boundaries moving with a variable velocity is formulated and then reduced to an infinite system of Volterra integral equations of the second kind or, in a simplified formulation, to a sequence of Volterra integral equations. The penetration velocity is determined as a function of the cylinder mass and initial conditions. It is established that the reaction force peaks instantaneously and then dies out

An analytical solution is constructed to describe the reaction of a hollow thick-walled cylinder to dynamic pressure applied to its inside surface. The material of the cylinder is assumed transversely isotropic, and its isotropy plane contains the cylinder axis. Internal pressure of general form is considered as an example, which can be used to simulate loads of different physical nature

A numerical method is developed for analysis of nonaxisymmetric waves propagating in a hollow elastic curvilinearly orthotropic cylinder filled with a perfect compressible liquid. Separating out the phase factor leads to a Hamiltonian system of ordinary differential equations. The spectral problem is solved numerically. Dispersion relations for specific waveguides are studied

A thermomechanical model of reconditioning worn-out hollow cylindrical machine parts by thermoplastic compression is developed. The scheme proposed takes into account the main stages and features of the process, in particular, the contact interaction between the cylinder and a rigid punch under compression. The ultimate and residual stresses and process parameters are determined

A method is presented for solving boundary-value elastic problems on the basis of the variational–structural method of R-functions and Reissner's mixed variational principle. A mathematical formulation is given to problems on the deformation of elastic bodies under mixed boundary conditions and bodies interacting with smooth rigid dies. Solutions satisfying all the boundary conditions are proposed. For undetermined components of these solutions, the resolving equations are derived and their properties are studied. A posteriori estimation of numerical solutions is made. As examples, solutions are found to a problem on the stress–strain state of a short cylinder and to a contact problem on a cylinder interacting with a smooth die. A numerical method of solving such problems is analyzed for convergence, and the accuracy of the solutions is estimated.

An interaction problem is formulated for a spherical body oscillating in a prescribed manner inside a thin elastic cylindrical shell filled with a perfect compressible liquid and submerged in a dissimilar infinite perfect compressible liquid. The geometrical center of the sphere is on the cylinder axis. The solution is based on the possibility of representing the partial solutions of the Helmholtz equations written in cylindrical coordinates for both media in terms of the partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions on the sphere and shell surfaces results in an infinite system of linear algebraic equations. This system is used to determine the coefficients of the Fourier-series expansions of the velocity potentials in terms of Legendre polynomials. The hydrodynamic characteristics of both liquids and the shell deflections are determined. The results obtained are compared with those for a sphere oscillating on the axis of an elastic cylindrical shell filled with a compressible liquid (the ambient medium being neglected).

The Mehler–Fock transformation method is used to study the rolling of a rigid cylinder over a half-plane with initial stresses. The problem is reduced to a system of two dual integral equations, which are then reduced to a system of two integral Fredholm equations of the second kind. The system of integral equations is solved by the method of degenerate kernels. The dependences of the normal and tangential stresses on the elongation are plotted.

An asymmetric quasistationary problem for a strip with initial stresses is formulated and solved. Resolving differential equations are derived and then reduced to five functional equations by the Hankel integral transform. Two of these equations are reduced to the Fredholm integral equations of the second kind, which are solved by the method of degenerated kernels. The normal and tangential stresses are plotted versus the elongation.

A nonclassical theory of the stress–strain state of composite beams in bending is developed. Both transverse shear and transverse compression are taken into account. The results demonstrate the high accuracy of the theory in investigation of short transversally isotropic beams

The problem on the interaction between a spherical body that oscillates in a prescribed manner and a thin elastic cylindrical shell filled with an ideal compressible liquid is formulated. It is assumed that the geometrical center of the sphere is located on the cylinder axis. The problem is solved based on the possibility of representing a partial solution of the Helmholtz equation written in cylindrical coordinates in terms of partial solutions in spherical coordinates, and vice versa. By satisfying the boundary conditions on the surfaces of the sphere and the shell, we obtain an infinite system of linear algebraic equations to determine the coefficients of expansion of the liquid-velocity potential into a Fourier series in terms of Legendre polynomials. The hydrodynamic characteristics of the liquid filling the cylindrical shell are determined and compared with the cases where a sphere oscillates in an infinite liquid and in a rigid cylindrical vessel

The formation of flow patterns in liquid and granulated media is studied experimentally. Many phenomena such as segregation of particles different in dimensions, surface properties, and density are observed only in granulated media. However, there exist many effects typical of flows in both liquid and granulated media in a horizontal circular cylinder rotating about its axis. Eight classes of the following similar patterns in fluids and granulated mixtures were studied experimentally: vortex-like patterns, deformation of the trailing and leading edges of a layer, shark-teeth patterns, fish-like patterns, formation of rotating layers, ring-like patterns, and cellular patterns

An approach is proposed to determine the three-dimensional stress–strain state of hollow orthotropic cylinders with elastic characteristics variable in the circumferential direction. The solution of the problem is represented as a double Fourier series in the axial and circumferential coordinates. A resolving system of ordinary differential equations of high order is derived. An analysis is made of the stress state of a cylinder made of a composite with reinforcement density variable in the circumferential direction

A numerical–analytical approach is proposed to solve a problem on the free vibrations of cylindrical bodies. The approach is based on three-dimensional elastic theory and the semianalytic finite-element method. The free vibrations of isotropic and anisotropic solid cylinders of finite length are examined. It is studied how boundary conditions and mechanical and geometrical parameters affect the distribution of dynamic properties. The efficiency of the approach proposed is tested by comparing results produced by different approaches

The problem on the interaction between a spherical body oscillating by a definite law and a rigid cylinder filled with an ideal compressible liquid is formulated. The geometrical center of the sphere is located on the cylinder axis. The solution is based on the possibility of representing the particular solutions of the Helmholtz equation in cylindrical coordinates in terms of particular solutions in spherical coordinates, and vice versa. As a result of satisfaction of the boundary conditions on the surfaces of the sphere and cylinder, an infinite system of linear algebraic equations is obtained to determine the coefficients of expansion of the potential of liquid velocities into a Fourier series in terms of Legendre polynomials. The use of the reduction technique for solving the infinite system obtained is substantiated. The hydrodynamic characteristics of the liquid filling the cylindrical cavity are determined and compared with the case of a sphere vibrating in an infinite liquid.

A conjugate electroelastic field in a piezoceramic cylinder with a parabolic crack under static loading is investigated. Uniformly tensile stresses and an electric potential are applied to the end faces of the cylinder. The following two types of electric conditions are considered at the crack boundary: the electric potential is continuous across the crack and the normal component of the electric-displacement vector on the crack surface is equal to zero. For each of these cases, expressions for some quantities characterizing the disturbed field in the crack plane and formulas to calculate the stress intensity factors are presented.

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered

The transient operation conditions of a thin-walled piezoradiator containing a viscous compressible fluid and immersed into an acoustic medium are considered. The problem is solved using the integral Laplace time transformation. Originals of the general solution of the linearized Navier-Stokes equations are constructed for the interior of the domain. These originals are used to find the unknowns from a system of integral Volterra equations. Numerical examples are presented.

The problem of interaction of a rigid body and a boundary of a viscous fluid under acoustic wave propagation is investigated. An example of the motion of a cylinder in the vicinity of a flat rigid wall caused by acoustic field forces is examined.

The problem of the pulsed loading of a multilayer cylinder has been solved. The simulation is based on the linear elastic theory for homogeneous and isotropic substances. The manner in which the problem is solved guarantees exact fulfillment of motion equations and systems of initial and boundary conditions. The numerical results presented show the wave pattern of the deformation of the inside surface of a multilayer cylinder, and describe the strain state of this cylinder.