The paper is concerned with equations and numerical methods for calculation of flexible shaft rotation in a rigid tube. In the very general statement the shaft is represented as a Cosserat rod with an arbitrary dependence of properties on the coordinate. The quasi-static motion is considered in the first. Six equations of motion are obtained for the arbitrary bent and curved rod in the tube of arbitrary geometry. The projection of the equation of moments on the tangent to the curved axis of the rod is shown to be sufficient for describing the shaft motion. This differential equation is expressed in terms of the rotation angle of the rod cross-section. The solution for the quasi-static rotation is obtained both analytically and using the shooting method for boundary-value problem for an ordinary differential equation. The closed form expression for the angles of rotation of the shaft in the rigid tube as a function of the axial coordinates is obtained. The jumps occur for some combination of the parameters and they cannot be explained in the framework of quasi-static analysis. In order to explain the instability, the dynamics statement is applied. The nonlinear dynamic problem is solved by means of differential-difference method which is tested by a comparison with a closed form solution. Solution to the dynamic problem allows one to explain the quasi-static jumps obtained. The dynamic formulation shows that instead of quasi-static jumps the initial stage of rotation is a smooth rotation which jumps are abruptly replaced by intensive vibrations. The laws of rotation at different rotational velocities are determined too. The qualitative difference in the quasi-static and dynamic solutions is exposed. The suggested approach for solving nonlinear dynamic problems of rotation of the shaft with an arbitrary geometry is promising for modeling of processes of the directional deep drilling which is vital for the problems of oil production industry.

This work presents simulated mechanical and frictional properties of polymer composite materials derived from the ultra-high molecular weight polyethylenes which are widely used as units of friction and sealing elements in different types of modern technology and medicine. There authors considered the two-phase polymer composites obtained by modifying the high molecular weight polymers by introducing micro- and nanoinclusions. Such materials tend to clear manifestation of scale effects, consisting of the non-monotonic dependence of the mechanical properties and tribological characteristics on the inclusion concentration and on characteristic size of inclusions. In order to register the scale effects it is proposed in this work to use first order gradient models which describe not only the non-local (gradient) effects in volume but also interfacial effects that affect the formation of transition zones in the vicinity of phase boundaries. Scale and surface parameters of gradient model of mechanical properties allow to take into account the peculiarities of the considered modified polymers, associated with the fact that the effect of fillers on properties is determined not with the own properties of the filler, but with the change of polymer morphology, i.e. with the forming of polymer crystallization zones in the vicinity of particles of filler distributed in volume. In order to simulate scale effects on the frictional properties, we proposed a model based on the analogy of the friction coefficient of inhomogeneous surface structures with mechanical characteristics of compliance of inhomogeneous material, when the "weak" phase defines the effective properties. It is shown that the use of this analogy simultaneously with the use of relations for effective compliances of periodic two-phase composite, found under the gradient model of elasticity in the one-dimensional approximation, allows a good description of typical non-monotonic dependences of the friction coefficient on the concentration of filler for the considered polymer composites. It appears that the proposed equations will be useful for the prediction of the properties of designed anti-friction polymer coatings.

Analysis of power transmission lines (PTL) involves the calculations of static states and vibrations of conductors (and cables) together with spiral accessories, vibration dampers and other devices attached on them. Many of these problems can be properly solved only by taking into consideration the internal structure of the conductors, the design of which is formed by wire layers wound on each other at different angles relative to the longitudinal axis. For example, such reference is required in the design of the systems of power safety and reliability of information-telecommunication supply of aerodromes, aircraft and rocket systems, overhead transmission lines, subject to intense wind, especially in icing conditions. Due to the complex design of the wire structures the known issues arise in the estimates of their deformations, stiffnesses, bearing capacity, etc. For example, the bending stiffness of the conductor can sufficiently vary markedly as its deformation, since the wire layers may slip relative to each other, and a separate wire is movable within the wire layer. Consequently, the values of stiffnesses can be varied both along the conductor axis, and in time. The paper proposes a new deformation model of wires structures which are similar to a PTL conductors. These structures include not only conductors and cables, but spiral clamps intended for tension, suspension, joints, protection and repair of conductors. On the basis of energy averaging, each wire layer is considered as an elastically-equivalent anisotropic cylindrical shell, thus a conductor or a spiral clamp are modeled as a system of cylindrical shells nested into each other and interacting by the forces of pressure and friction. Following this approach the formulae for the flexibility and stiffness matrices of spiral structures have been obtained. The problem of interaction of a tension clamp with the external wire layer of a conductor has been formulated and solved. The mechanism of the force transfer from the clamp on the conductor has been investigated.

A method for forming multidirectional testing efforts during the mechanical testing of laboratory samples using the typical one-driving testing machine is suggested here. In the proposed method, this system of forces acting on the sample is created by the inclined faces of the sample and the resulting contact reactions on them when it interacts with parallel support having appropriate ramps. The authors consider the scheme of supporting and the loading of the prismatic sample which implements the considered formation of the test efforts. The justification of choice of angles of the sample inclined faces based on the numerical simulation of model deformation using the numerical finite element method apparatus and solving the contact problem of deformable solids is provided here. Recommendations for using optimum angles of inclination of the supporting surface for creating circuitry biaxial stretching have been given. The results of computational analysis of VAT prismatic samples depending on its basic geometric parameters are described here. The testing of the proposed models is described in determining the strength parameters of spring-tempered spring steel 50HFA located in a biaxial stretching. The analysis of the results obtained by the destruction of the samples is based on the limit state equation of Pisarenko-Lebedev. The determination of these parameters is based on the numerical analysis of VAT tested series of samples at the time of their destruction. The analysis includes consideration of the nature of the contact interaction of the sample with the support elements and the possible occurrence of plastic deformation in the sample. It became possible to present the experimental evaluation of reducing the limit value of the first principal stress in the hearth of destruction of samples of steel 50HFA under biaxial stretching compared to uniaxial tension.

The paper studies electroplastic effect in terms of the hypothesis of the healing of defects in the material under the influence of high-energy pulsed electromagnetic fields. The processes occurring in the metallic samples under the impact of electrical current of high density are considered. The electric, temperature fields, stress-strain state and phase transformations in the vicinity of micro-defects with line size 10 microns are studied. Such defects are always present between the grains in a polycrystalline metal after metallurgical casting or appear in it during its deformation under processing. The coupled quasi-stationary model of the impact of high-energy electromagnetic field on the pre-damaged electroplastic material with an ordered system defects are proposed. The model accounts for melting and evaporation of the metal and the dependence of its physical and mechanical properties on the temperature. The problem is solved numerically by finite elements method with adaptive mesh using on the base of alternative Euler-Lagrange’s method. The boundary value problem is solved for a representative element material with a micro-defect in the case of plane strain. The micro-defects in the form of flat cracks with rounded tips are considered. The presence of micro-cracks leads to inhomogeneous physical and mechanical fields in the material. Numerical modeling has shown that in the vicinity of the micro-defects intensive electromagnetic field and current with large fields gradients arise. This causes rapid local heating in the vicinity of the tip of the micro-crack, followed by thermal expansion of metal, and subsequently melting the material. The inhomogeneous heating results in a high compressive stresses and intense plastic flow of the material in the vicinity of micro-crack. The resulting stress field is not only closing the shores of micro-crack, but also reducing its length and ejecting the metal into the crack. Ejection occurs through the formation of the metal jet of molten metal directed into the crack. These processes may be accompanied not only by melting in the vicinity of the tip, but also evaporation of the metal to crack for the micro-cracks located near the outer boundaries of the sample. The simultaneous reduction in the length, the ejection of the molten metal into the cracks and closing of micro-crack shores leads to the fact that the shores of the crack come into contact with the jet stream and finally the jet material completely jams shores cracks. It is the welding of the crack and healing of the micro-defects which takes place.

The target of research is the stress-strain state (SSS) near and directly in the special points of structures with features in the form of flat composite wedges or spatial edges, which are the intersections of the forming bodies surfaces. Boundary conditions, continuity conditions of stresses and strains on the line (surface) connections of structural members and other constraints, posed by the problem statement into structural elements special points, form a mandatory algebraic equality (MAE), which represent a system of linear inhomogeneous algebraic equations. The MAE number, formulated at special points, exceeds the MAE number in ordinary (not special) points of the boundary, which limits the ability to build solutions meeting all of the UAR using usual solid mechanics methods. Therefore, the works purpose is to create an algorithm allowing constructing a solution consistent with all MAE formulated at special points. Substructure iterative mixed finite element method (FEM) is proposed. Substructures are parts of the computational area with continuous state parameters. The main results. The algorithm and software package for the stress state study near and directly in special points of construction elements are suggested. Depending on the considered flat or spatial structure geometric and material parameters properties, problems of elasticity and thermo elasticity are divided into types and subtypes, distinguished by the MAE number. Mixed finite element method version allows calculating nodal stress parameters without the differentiation of the approximate solution or without using any replenishment method. The iterative approach allows building a solution that is consistent with all MAE at special points. The procedure of the proposed algorithm and its Fortran-95 implementation is described. Features, associated with OpenMP technology used in the algorithm implementation are discussed.

The problem of a strip, composed by two isotropic elastic layers of different elastic properties and thicknesses, separated by a semi-infinite crack located along the line between the layers, is considered. The mechanical load with nonzero total force and moment is supposed to be applied at infinity. By means of Laplace transformation the problem is reduced to a homogeneous Riemann problem. Under the assumption of possibility to neglect the cross-terms related to the influence of the normal stresses to the shier displacements and the shier stresses to the normal displacements the problem is reduced to two scalar Riemann problems. Such a formulation may be considered as an approximation for the general case (which is not worse than the traditional beam or rode approximation) and as the exact one for the case, when the two layers may slide but may not separate due to cohesion, e.g. by van-der-Waals forces. By means of factorization procedure the exact analytical solution has been obtained for one of the formulated scalar problems, namely, the problem of the normal separation. The asymptotical expression has been derived for the relative displacements of the crack faces far from its tip. It is shown that the leading asymptotic terms of these relative displacements correspond to a beam deflection under the boundary condition of the type of generalized elastic clamping. i.e. the proportionality of the displacement and angle of rotation of the clamping point to the total vector and bending moment of the applied load by means of the matrix of coefficients of compliance. The analytical expressions for these coefficients have been obtained. The asymptotical expression for the stress field near the crack tip (stress intensity factor) was also derived.

We have investigated the contacting interaction of a sandwich structure in the form of plates and beams with small gaps between them. Such systems are integral elements of modern devices. The created mathematical model is based on the following hypothesis: the system is a multi-layer structure; the materials are isotropic. To solve the problem we used the finite difference method with approximation 0 (h2), 0 (h4) and Bubnov-Galerkin method in higher approximations of spatial coordinates, as well as the Runge-Kutta 0 (h4), 0 (h6), 0 (h8) time. In solving problems associated with random variations, it is necessary to solve the challenge of an error, so you need to use different numerical methods to validate the results in order to distinguish the chaos of the numerical error. For the analysis of chaotic dynamics we have applied all methods of qualitative analysis. We have investigated the spatiotemporal chaos based on wavelet analysis. We have studied the effect of white noise in the contact interaction of elements of the multilayer structure. Also, the analysis of the complex vibrations of plates and beams in different intensities depending on the type of noise and load has been made. It was found that by using an external additive white noise, it became possible to control chaotic oscillations and transfer the system from a chaotic state to a harmonious one and enable or disable the contact interaction.

Today the composite materials are widely used in aviation industry for load bearing elements of aircraft engines. The following problems need to be solved for an effective composite application: firstly, choosing the optimal reinforcing scheme for main working area of construction, and secondly, realizing the stress-strain analysis for the most loaded zones with complex geometry such as joints, layer crossings and area connections. The present work is devoted to detailed stress-strain analysis of composite outlet guide vane (OGV) for aircraft engine. The 3D problem formulation of mechanics of anisotropic laminated composite for strength prediction was given. The technological scheme of laying out anisotropic plies and fastening method were taken into account in the model. The scheme of reinforcing for OGV was determined in the previous researches. The maximum stress criterion was used for estimation of strength margin. The numerical simulation of this problem was carried out by finite element method (FEM) with ANSYS Workbench software. Due to the high dimensionality of FE model, the high-performance computing complex was used. The in-depth layered analysis of stress-strain state of the structure was made. The special focus was made on the areas with twisted layers near the flange of vane where the initiation of high interlaminar stresses is most likely to take place. An estimate of the influence of fastening conditions on the stress state for OGV was obtained. It was shown that interlaminar shear stresses are the most dangerous. It was found that the VKU-39 material and [0°/±45°] reinforcing scheme allow to provide the double strength margin under working loads for developed OGV.