Subject of a study is a difficult stress state of long hollow cylinder which is being bended by its own weight and rotated by turning moment. The stressed state over the cylinder section and the curvature of its longitudinal axis are investigated. The basic assumptions taken in the attention to solve the problem in question are usual common for the mechanics of materials and engineering approximations the hypothesis about the linearity of the physical relationships between the stresses and strains (linear theory of elasticity) and assumption about the small strains. Solution of problem is built on the basis of the differential equation of the elastic flexure of the central axis of cylinder and fundamental relationships between the curvature of this axis, applied loads, strains and stresses in the region of cylinder section. Boundary-value problem for the ordinary differential equation of the fourth order with the appropriate boundary conditions is solved using the method of variations of the arbitrary constants. This made it possible to obtain the exact solution of the task of the long cylinder bending which rotates around the longitudinal axis. This, as a result, made possible to determine the dependence of the curvature of cylinder central axis on the longitudinal coordinate and to find the stress distribution in the of cylinder section. The estimation of the contribution from each of the factors, which act on the subject of study, to the stressed state is executed. Solution of the presented problem made it possible to define equivalent stress in the outlying layers of cylinder as the result of the action of all power factors examined.

In the present paper there is outlined the procedure of stress state calculation for compressor disk of gas-turbine engine during flight-loading cycle (low-cycle fatigue regime – LCF) and under low-amplitude blade vibrations (very high-cycle fatigue – VHCF). The criteria and models of multiaxial fracture are studied in the case of low-cycle fatigue and in the case of very high-cycle fatigue. The model parameters are determined by using the experimental data of uniaxial fatigue tests for various asymmetry coefficients of the cycle. On the basis of the calculated stress state using multiaxial fatigue fracture criteria, the durability estimations for compressor disks are obtained for alternative mechanisms of LCF and VHCF. Two elasticity problems for circular disk are solved for confirmation of the numerical results obtained. In the first problem the centrifugal loading from the blades (analogue of LCF regime) was modeled. In the second problem loading from blade torsion (analogue of VHCF regime) was modeled. The durability estimation also shows that the fatigue fracture in LCF and VHCF regimes can take place for the same period of real time.

A numerical algorithm of the investigation of stress-strain state of the elastic–plastic solids with large deformations is described. The left Cauchy-Green tensor and velocity gradient tensor are used as the tensors describing the deformation and deformation rate. The potential of the elastic strain the specific strain energy, which depends on the left Cauchy-Green tensor is introduced. An isotropic material is considered. The state of stress is described by the Cauchy stress tensor. The linearized constitutive equations of elastic deformation are obtained as a function of the derivative of the Truesdell stress rate on the strain rate. The theory of flow and an additive representation of the total deformation rate are used. The von Mises yield criterion is applied. The research algorithm is based on the incremental method. The principle of virtual work in terms of the virtual velocity is used. After linearization the system of linear equations is obtained, where the unknown is the increment of displacement in the current state. The radial return method with an iterative refinement of the current mode of deformation, based on the introduction to the governing equations of additional power voltages is applied. As an example the potential of elastic deformation is considered. The von Mises yield criterion with isotropic hardening is used. The linearized constitutive relations is obtained. The numerical implementation is based on the finite element method. An 8-node brick element is used. Developed algorithm of investigation of large elastoplastic deformations is tested on the solution of the necking of circular bar problem. The results of solutions and comparison with results obtained by other authors is reduced. Also the deformation of a square plate under internal pressure is investigated.

In this article the technique of definition of optimum angles of the technological tool is offered at pressing combined composite preparations. In an optimization basis the pressure of pressing providing the minimum power inputs is necessary. The problem of improvement and optimization of the production technology of low-temperature composite superconductors for achievement of necessary production volumes of release is actual at compliance to quality requirements. Development of theoretical bases and techniques of design of technological processes in relation to the production technology of the low-temperature composite superconductors which are scientifically proving a choice of technological modes and industrial equipment for improvement of quality of low-temperature composite superconductors and providing high technical and economic rates of their production is important. The pressing process is widely used in metal forming.The essence of the pressing process is extrusion of material placed in an enclosed area through the channel formed by the pressing tool. The advantage of process of pressing is the favorable scheme of a tension with prevailing influence of the squeezing tension providing increased plasticity of the pressed material. Therefore process of pressing is widely used when processing by pressure of low-plastic hardly deformed metals and alloys.

In work the basic processes of machining and their influence on quality and durability of cylindrical products, calculated temperature modes are considered at cutting of pipes, parameters of process of cutting are chosen taking into account size and a sign on temperature residual stresses. By machining understand different types of cutting: turning, drilling, milling, grinding, honing, polishing. In this regard, shows how the processes of machining affect the quality of tubular products. The aim is to give a cutting detail desired shape. Also examined parameters of the cutting process, selected to the value and sign of thermal residual stresses. Residual stresses in metal cutting result from uneven plastic deformation and significant heating of the surface layers. Solving the problem of thermoelasticity can determine the stresses induced by heating. Based on the terms of the onset of plastic deformation is not on the surface of the part after passing through the tool, you can optimize the cutting parameters for the treatment of various axisymmetric metal. Thus, knowing the relationship between these parameters and the mechanical properties of the workpiece material and geometry can estimate the stress intensity as a function of the initial temperature and cutting data processing tube. Then based on the results built relationships and dependencies critical cutting parameters for tubular products of different materials and some limiting parameter ratios machining tube. The paper presents the method of determination of the limit relations parameters of the cutting process for axisymmetric products with temperature heating surface due to friction when turning. The method allows to determine the voltage at the surface of the workpiece and the rational selection of the process parameters, depending on the part geometry and the material.

We obtain and investigate the formulation of the problem of strain gradient plane model of elasticity for the composite layer. We used a synthesis of analytical and numerical methods to solve plane problem of gradient elasticity for an infinite layer to allow the distribution of stresses in the plane of ultrathin coatings. We investigate the problem of the impact of surface compressive normal loading on an infinite layer . To solve the problem we use a Fourier integral transform, and the inverse trnsform is computed using a numerical procedure. It is shown that the proposed model can predict the effects of localization interlaminar stresses in the local interphase zones in the coating and consider the influence of non-classical scale factors – the thickness of the coating layers and gradient model parameters. For simulation it is involved the most simple gradient theory of elasticity – applied model of the interphase layer containing single additional physical parameter determining the "gradient" of the environment and the extent of interfacial zones in the border area of the material. This additional physical constant characterizing the contact of dissimilar materials. For the numerical calculations in this paper we use the hypothetical values of the gradient parameter. To solve the problem of practical importance due to the possibility of reliable modelling and optimization of the structure of ultra microstructure protective composite coatings used in the aerospace industry. Also constructed solution can be used to identify additional physical parameters of the gradient theory of elasticity based on a comparison of simulation results and experimental data on the indentation thin layer structures.

A mathematical model of waves propagation and instability on a surface of a cylindrical column of magnetic fluid of an infinite length, surrounding a coaxial infinite long porous core of the round section is constructed and studied. The conditions are found under which the disturbances of the surface of fluid column become unstable and result in its fragmentation into a chain of connected droplets. The presence of a surface tension is taken into account. The gravity is neglected. The axis of the porous cylinder coincides with the axis of a coaxial solenoid, generating an uniform magnetic field. The problem is solved in a cylindrical coordinate system ( r , θ, z ), in which the fluid column is at rest. The z -axis is directed along the axis of the solenoid. The equations of the motion of magnetic fluid inside and outside of the porous medium and the equations for the magnetic field are written. The boundary conditions for hydrodynamic and magnetic values on discontinuity surfaces are formulated. The disturbances of magnetic field (according to wave propagation) is searched inside and outside of the porous medium, as well as in the air clearance of the solenoid. The full solution of a boundary value problem for hydrodynamic and magnetic values is found. The numerical analysis of the dispersion equation, describing wave propagation on surface is done. The different special cases are considered. The conditions are found under which the disturbances of the surface of fluid column become stable (wave damping) or become unstable (which result to the disturbances growth and the fragmentation of the cylinder into a chain of droplets). It is shown that the size of droplets appearanced in fragmentation process increases with the growth of the magnetic field i.e. magnetic field has a stabilizing influence upon the fragmentation of the fluid column.

The alternative geometrical immersion method for plane problems theory elasticity, based on a finite elements method in term of stresses within the principle minimal additional work of elastic system is considered. The geometrical immersion method consists in reducing an initial problem for linearly elastic body of any form to iterative sequence of problems theory elasticity on some initial area. Iterative procedure for the solution of the variation equation of the geometrical immersion method and a procedure of formulation of its discrete analog by means of the finite elements method in term of stresses for plane problems theory elasticity in the Cartesian system of coordinates are formulated. The alternative finite element method in terms of stresses function for satisfaction of approximating expressions to the balance equations is used. Practical application of the method on the example of the plane problems solution for the elastic plate with rectangular hole is shown. Rather good compliance of results of stresses fields definition in comparison with a traditional finite elements method in movements is obtained. Practical convergence of iterative procedure of the geometrical immersion method is established. We focus our attention to the problem of the static boundary conditions that are the main for this variation formulation. The way of modification of a flexibility matrix of the system of finite elements and Lagrange’s multipliers method is used.

The theoretical model of migration metane bubbles in the conditions of formation hydrate is offered and constructed in work. Influence of various parameters on process of formation hydrate bubbles is studied. The minimum values of mass expenses of gas and the water necessary for process hydrating are received. Found that the migration of gas bubbles in a vertical channel, there are two modes of the process hydrate formation, depending on the mass expenses of water. If the initial value of the mass expenses greater than the critical, then for a given mass expenses of gas sufficient for hydrate formation, gas bubbles become fully hydrated, thus water temperature in the channel doesn't reach the equilibrium temperature of hydrating. If the initial value of the mass expenses is less critical, then gas bubbles are covered hydration shell, and the water temperature in the channel reaches equilibrium, and the process hydrating is completed. Also found that the increase of the initial mass expenses, the height of ascent of hydrate bubbles grow to a certain critical expenses, and a further increase - falls. The analysis of different depths at which gas sources are located is carried out: 800, 1200 and 1500 m. It is found that if there is a process of partial hydrating, the deeper the source is located, the greater the height of the rising bubbles. If there is a process full of hydrating, the picture is quite different: the higher up the gas source - the greater the height of hydrate formation.