Axisymmetric contact of anisotropic shells of rotation with rigid and elastic foundations

A class of problems are investigated on determining the stressed-strained state of anisotropic shells of rotation that are in axisymmetric one-sided contact with rigid and elastic surfaces. The shells are under the action of surface and contour loads. For some combinations of these quantities the shell may break away from the surface. To determine the contact zone, the method of successive approximations is utilized. In contrast to most investigations in which the contact zone is first determined, the method proposed makes use of a special quantity characterizing the size of the contact zone. The load on contours is determined from the solution to the problem on the stressed state of the shell and the condition specified on the boundary of the contact zone. Some examples of solving concrete problems are given. Bibliography: 5 titles. Translated fromObchyslyuval’ na ta Prykladna Matematyka, No. 76, 1992, pp 70–74.     

Impression of a semiinfinite stamp in an elastic strip with regard for friction and adhesion

We consider the problem of contact interaction between a semiinfinite stamp with rectilinear base and an elastic strip with one rigid side. Friction forces in the contact region are taken into account. These forces lead to the division of the contact region into slipping and adhesion zones. With the use of the Wiener–Hopf method, a system of integral equations is reduced to an infinite system of algebraic equations. The computational results of stresses and strains at the boundary and at inner points of the elastic strip are presented. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 138–149, January–March, 2008.     

Application of the principle of possible displacements to problems of the dynamics of a “shell-fluid” system

We state in general form the principle of possible displacements for a “shell-fluid” mechanical system, on the basis of which it is possible to solve dynamic problems taking account of a geometrically nonlinear process of deformation of the shell and nonpotential motions of a viscous fluid. It is shown that this principle yields the equations of motion of the shell and fluid as components of this system, confirming the reliability of the principle. The conditions of force contact are taken into account as a load term in the equations of motion of the shell. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 117–123.     

Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling constant is sufficiently small. More precisely, under the assumption that the fiber eigenvectors corresponding to the putative mass shell are differentiable as functions of the total momentum of the system, we show that a mass shell could exist only at a strictly positive distance from the unperturbed embedded mass shell near the boundary of the energy–momentum spectrum.     

Wear resistance of bodies protected by a thin composite coating

The mechanical contact interaction of bodies with a thin composite coating is investigated with account of wear. The thermal effects are not considered. The coating is modeled by a thin plate. Between the body and the coating is an interlayer, which is modeled by a Winkler body with one modulus of subgrade reaction. Under the action of a rigid stamp on the coating, the process of abrasive wear proceeds. The contact interaction of the coating with the base is described by using the model of an intermediate layer. To determine the stress-strain state of the coating, equations of the generalized theory of plates including the shear strains and the compression of normal are utilized. For the contact wear problem formulated, the basic integral equation with a Fredholm-type kernel is derived, and its solution algorithm is proposed. Numerical results are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 319–330, May–June, 2006.     

Contact with break-off under bending of an elastic strip with a rigid disk

We consider the problem of the theory of elasticity of the contact interaction of a rigid circular disk and an elastic strip, which rests upon two supports with disturbance of contact in the middle part of the contact region. On the basis of the Wiener–Hopf method, an integral equation of the problem is reduced to an infinite system of algebraic equations. The size of the zone of break-off of the boundary of the strip from the disk and the distribution of contact stresses are determined.     

Structural damping in an equi-strength cylindrical shell with an elastic filler

We present a method for rational application of the deformation properties of a shell system with an elastic filler: design of a shell with variable thickness while preserving the load-bearing ability of the system as a whole. For the equi-strength shell thereby obtained we state and solve the mixed contact problem taking account of dry friction with nonmonotone loading, making it possible to estimate the structural hysteresis in the system. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 86–91.     

Eigenfrequencies of radial vibrations of a spherical sandwich shell

Free across-the-thickness vibrations of a closed spherical shell consisting of three rigidly connected layers with arbitrary physical constants and thicknesses are studied. A closed-form solution in displacements to a one-dimensional (along the radius) vibration problem for a homogeneous spherical shell is derived and then used in posing a boundary-value problem on free vibrations of a heterogeneous sphere. Based on the degeneration of the sixth-order determinant of a system of homogeneous equations satisfying the corresponding boundary conditions, a transcendental equation for eigenfrequencies is found. Transformation variants for the equation of eigenfrequencies in the cases of degeneration of physical and geometric parameters of the compound shell are considered. The main attention in investigating the lowest frequency is given to its dependence on the structure of shell wall, whose parameters greatly affect the calculated values of the high-frequency vibration spectrum of the shell. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 839–852, November–December, 2008.     

An analysis of contact deformation of auxetic composites

The adaptive mode of frictional interaction has been studied as a self-locking effect upon contact deformation of isotropic and anisotropic auxetic materials with a negative Poisson ratio. This effect manifests itself in the fact that the bearing capacity of the joint rises with increasing shear load. In particular, the parameters of stress state (contact load, tangential stresses, slippage, etc.) were determined for a double-lap joint under conditions of compression with or with out shear. The contact interaction was analyzed by the finite-element method for three profiles of symmetrically located contact elements (plane, cylindrical, and wedge-shaped). The Poisson ratio was varied within the range theoretically admissible for isotropic elastic media. Analogous calculations were also performed for a joint with a deformed element made of an anisotropic auxetic composite, whose reinforcement angle was varied. The maximum loads, tangential stresses, and slippage are obtained as nonlinear functions of Poisson ratio (in the isotropic case) and reinforcement angle of the composite material. The stress concentration and the increased ultimate shear forces are also estimated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 681–692, September–October, 2006.     

Self-adhesion of amorphous polymers and their miscible blends

The amorphous film surfaces of polystyrene (PS), poly(2,6-dimethyl 1,4-phenylene oxide) (PPO), and their miscible blends are brought into overlap contact below the glass transition temperature T _g for 10 min and 24 h in order to obtain PS—PS, PPO—PPO, and blend—blend self-adhesive joints. It is shown that after the contact of the blend surfaces, i.e., when the molecules of both PS and PPO are present at the interface, it is possible to attain higher values of shear strength as compared with those at PS—PS and PPO—PPO interfaces. This points to the contribution of a specific interaction between the segments of PS and PPO to the strength development at the interface. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 127–135, 2000.     

The vibrations of a conical shell filled with a variable volume of fluid

We consider the vibrations of a conical shell filled with a fluid. We obtain a system of differential equations that describes the interaction of a variable volume of fluid with the shell. We solve the problem of determining the natural frequencies for a completely full shell. We obtain a formula for computing the fundamental frequency as a function of the geometric parameters of the shell. One figure. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 85–88, 1991.     

Plane problem of interaction between an elastic longitudinal wave and a cylindrical shell with axial cut

We have proposed a procedure for investigating the stressed state of a thin-walled round cylindrical shell with a cut along its generatrix, which is placed into an elastic space. A longitudinal elastic wave is incident on the shell. The procedure is based on the use of the Rayleigh expansion in partial waves. We have obtained relations for determining the displacement jumps and angle of rotation at the lips of the shell cut, the radial component of the displacement vector and the normal force in the cylindrical shell, as well as the stresses and displacements in the elastic medium. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 131–137, January–March, 2008.     

Postbuckling of a shear-deformable anisotropic laminated cylindrical shell under external pressure in thermal environments

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments. The material properties are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear-deformation shell theory with the von Karman-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. The boundary-layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling region, and the initial geometric imperfections of the shell, is extended to the case of shear-deformable anisotropic laminated cylindrical shells under lateral or hydrostatic pressure in thermal environments. The singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The results obtained show that the variation in temperature, layer setting, and the geometric parameters of such shells have a significant influence on their buckling load and postbuckling behavior. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 789–822, November–December, 2007.     

Deformations of pressure vessel domes in asymmetric winding

The deformation of pressure vessel domes in asymmetric winding with the use of two families of yarns is accompanied by shear deformations and torsion. For the case of large deformations, a system of equations for describing the stress-strain state of an asymmetrically reinforced netlike shell of revolution loaded with an internal pressure is obtained. It is shown that the shear deformations depend on the deformations of both the yarn families and the deformations of meridians and parallels of the shell. As an example, the dome of a pressure vessel in a deformed state is calculated for an initial equilibrium shape determined on the assumption that the yarns are inextensible. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 425–432, July–August, 2006.     

A dynamic unilateral contact problem with adhesion and friction in viscoelasticity

The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples are presented.     

Stability of Composite Cylindrical Shells with Noncoincident Directions of Layer Reinforcement and Coordinate Lines

The stability problem is solved for cylindrical shells made of a laminated composite whose directions of layer reinforcement are not aligned with coordinate axes of the shell midsurface. Each layer of the composite is modeled by an anisotropic material with one plane of symmetry. The resolving functions of the mixed variant of shell theory are approximated by trigonometric series satisfying boundary conditions. The stability of the shells under axial compression, external pressure, and torsion is investigated. A comparison with calculation data obtained within the framework of an orthotropic body model is carried out. It is shown that this model leads to considerably erroneous critical loads for some structures of the composites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 651–662, September–October, 2005.     

Limiting state of a multilayered nonlinearly elastic long cylindrical shell under the action of nonuniform external pressure

The buckling of a long multilayered nonlinearly elastic shell made of different materials and subject to the action of external pressure is investigated. The load is not hydrostatic and greatly varies in value and direction. Neglecting the effect of end fastening of the shell, the problem is reduced to an analysis of the loss of load-carrying ability of a ring of unit width separated from the shell. The solution is based on a variational method of mixed type formulated for heterogeneous nonlinearly elastic bodies, taking into account the geometrical nonlinearity, in a combination with the Rayleigh–Ritz method. The initial analysis is reduced to solving the Cauchy problem for a nonlinear ordinary differential equation resolved for the derivative. Numerically, using the Runge–Kutta method, the effect of the number of layers and of the parameter of nonuniformity of the external pressure on the critical buckling force is revealed. The urgency and importance of the problem are connected with the research of reserves in the saving of materials with a simultaneous possibility of increasing the load-carrying ability of a structure.     

Plane contact problem of the indentation of a stamp into an elastic wedge

We consider the contact interaction of a stamp with rectilinear base and an elastic wedge. One of the wedge faces is fixed, and the stamp edge touches the wedge vertex. Using the Wiener–Hopf method, we have obtained an exact solution of this problem. We have also determined the stress distributions in the contact region and on the wedge fixed face as well as the displacements of its free boundary.     

Multicriteria optimization of a composite cylindrical shell subjected to longitudinal thermal stresses and buckling under the action of torque

The multicriteria optimization of the structure and geometry of a multilayer cylindrical shell under the action of external torque and longitudinal thermal stresses is considered. From known monolayer properties of the composite and given values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined. The criteria to be optimized — the critical external torque and thermal stresses — depend on two variable parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 223–230, March–April, 2009.