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The reliable operation of structures and energy machines is related to ensuring thermal strength and durability of their elements and assemblies. Currently, a difficult situation has developed in the modern energy market; the equipment works in difficult conditions and, as a result, it is operated in variable modes, which causes accelerated wear of the resource. Ensuring the reliable use of power machines and structures of various complexity requires a calculated assessment of the thermal strength and durability of their elements, which is based on the application of new methods and calculation models taking into account a number of important factors, including damage, heterogeneity of material properties, the influence of non-stationary temperature fields and the presence of cracks. This paper is devoted to the development of the methodology for crack growth calculations in plate elements of structures under cyclic loading in an elastic-plastic setting using the concept of the accumulation of dispersed damage in the material. At the top of the crack, the processes of sign-changing elastic-plastic deformation and crack resistance of the material are simulated using data from fatigue tests of smooth samples. The thermal stress state of the structure at different loading modes is determined using finite element software for several fixed crack depths. The kinetics of a surface crack in a plate, from both edges of which cracks grow symmetrically under non-zero cyclic loading by tensile stresses, is considered in the paper. Elastic-plastic problems were solved for the cases of plane deformation and plane stress state, the amplitudes of deformation intensities and the number of loading cycles were obtained depending on the depth of crack growth. It was established that the type of stress state significantly affects the destruction of the material. Evaluation of crack development using the concept of accumulation of dispersed damage in the material has advantages for flat and axisymmetric problems, since it has no limitations for the size of the plastic zone and small crack depth. After some improvements, the calculation method can be used for three-dimensional problems of thermoplasticity

Introduction. The paper proposes a method of accounting for energy dissipation for the Timoshenko beam by constructing a damping matrix based on a modified Rayleigh function in the numerical solution of the problem. In this modification, the velocity of displacements is replaced by the velocities of linear and angular deformations. This approach allows us to take into account energy dissipation due to internal friction in the material when both its volume and shape change. The presented technique is promising in practical calculations of structures when shear stiffness has a significant impact on their stress-strain state.Materials and methods. Several proven methods of energy dissipation accounting are considered, including those that make it possible to take into account the energy loss of a moving structure during friction with the external environment (external damping) and dissipation due to friction in the material of the structure deformed in motion (internal damping). Methods for determining the damping coefficients for each of them are presented. The finite element method is used to calculate rod systems. Damping matrices are derived from the condition of stationarity of the total energy of deformation of a mechanical system in motion, including linear and angular deformation rates.Results. Damping matrices proportional to strain rates obtained on the basis of the modified dissipative Rayleigh function are given. A method for determining the damping coefficient taking into account the rates of angular deformation is proposed.Conclusions. The damping matrices presented in the paper describe the energy dissipation during vibrations of mechanical systems due to internal friction in the material. The internal damping matrix was obtained taking into account the influence of linear and angular deformation rates to simulate the dynamic behaviour of short bending structural elements, the deformation of which is described using the Timoshenko model. The performed dimensional check additionally confirms the correctness of the damping matrix construction. Moreover, the dimension of the proposed shear damping coefficient is the same as that of the widely used viscosity coefficient.

The pivot jewel bearing is an important node of some classes of industrial equipment; at nominal operating modes, the speed of relative rotation of the contact surfaces can reach 103 revolutions per second, while the operating time can be measured in years; under such conditions, it is necessary to take into account the wear of the contact surfaces; in this paper, a technique for modeling the dry friction wear of a fast-rotating support pair is proposed, taking into account changes in the properties of materials due to surface heating, based on solving the wear contact problem in a stationary formulation using Archard’s law; the effect of taking into account the temperature dependence of material properties in wear modeling process is demonstrated.

Introduction. Claw pole machines (CPM) are commonly used in the automotive industry. Recently, importance has focused on the use and introduction of permanent magnets (PM) in this type of machine to increase the power density. This paper studies the performance of permanent magnet claw pole machines (PM-CPM) used in hybrid electric vehicle applications. The structure considers that the PMs are placed between the claws of the rotor. Purpose. The influence of the PM magnetization effect on the performance of synchronous PM-CPM is analyzed. Radial and tangential magnetizations are applied to obtain the best possible sinusoidal shape of the electromotive force and an acceptable cogging torque. Then, the electromagnetic performance of the PM-CPM is analyzed and evaluated. Furthermore, due to the complexity of the rotor armature, it seems difficult to give a direct relationship between the PM parameters and the machine torque. This led us to study the effects of magnets geometrical dimensions variations on the torque and its ripple. Method. 3D nonlinear model of the machine is analyzed using the finite element method and comparisons between some electromagnetic performances are processed. Results. It was found that the tangential magnetization of PMs makes it possible to obtain a better distribution of the flux density and a minimum of cogging torque mainly responsible for vibrations and acoustic noise. Also, we observed a non-linear variation between the torque and its ripples depending on the dimensions of the PM. In fact, electromagnetic torque increases linearly with PM size but this is not the case for torque ripples. References 22, tables 2, figures 16.

The paper examines the natural frequencies of prismatic thin shells, the cross-section of which is the regular polygon. Spectra of free vibration frequencies of such shells are analyzed as the number of cross-section sides increases, provided that the perimeter is preserved. The relation between fundamental frequencies of the prismatic shells with the regular polygonal cross-section and a circular cylindrical shell is discussed. For a small and large number of polygon sides analytical and asymptotic solutions are compared with numerical solutions obtained by the finite element method (COMSOL). The convergence of the numerical method is studied for the prismatic shell with a large number of facets.

Introduction. In the current climate change conditions, the protection of irrigation structures, especially dams, is a very important task. Seepage is one of the main causes of dam failure, so it is very important to investigate the seepage regimes and find solutions to prevent dam failures as a result of the seepage processes in earth dams. In this paper, the analysis of the seepage regimes in the body of earth dams is performed by means of mathematical modelling using numerical finite element models. A homogeneous earth dam with an imperfect diaphragm on an impermeable foundation is taken as the object of study. The purpose of the study is to determine the influence of relative parameters: diaphragm height, diaphragm location in the dam body, their number. In addition, the influence of diaphragm parameters on the seepage flow through the dam body and its velocity is analyzed.Materials and methods. The study was carried out with the help of numerical modelling using PLAXIS 2D software. The model of the dam is based on typical design solutions used in practice.Results. The results of the study show that the placement of the diaphragm in the dam body reduces the seepage flow through the dam and the height of the diaphragm is inversely proportional to the seepage rate. The maximum seepage rate was recorded at the upper end of the diaphragm and its magnitude is directly proportional to the height of the diaphragm. When the diaphragm is displaced towards the downstream side, the filtration rate slightly decreases. The value of maximum velocity increases when the diaphragm is displaced towards the downstream end.Conclusions. Dam failure due to seepage can result in serious property damage and loss of life. Implementing methods that reduce seepage discharge and seepage velocities is important to ensure safe dam operating conditions

Relevance. The need to determine a reliable pressure distribution field and fluid filtration velocity vectors inside the perforation hole and the reservoir rock surrounding it. Aim. On the basis of numerical finite element modeling of the fluid flow inside the perforation holes and its filtration in the surrounding reservoir rock, to reveal the patterns of pressure distribution and fluid filtration vectors in the perforation hole, on its walls and in the near-wellbore zone. Objects. Near-wellbore zone of a limestone reservoir of one of the oil fields in the south of the Perm Region, including perforations. Methods. Numerical finite element method for calculating the flow and filtration of liquid in the near-wellbore zone, taking into account the geometry of perforation holes. Results. The paper considers the main relationships used in numerical simulation of fluid flow and filtration in the ANSYS finite element modeling software package. The authors have developed the finite element scheme of the near-wellbore zone, including cumulative perforation holes and taking into account their geometric parameters, as well as the fact that inside the holes the fluid flow is modeled in open space using the Navier–Stokes equations, and in the surrounding reservoir rock based on the filtration equations and Darcy's law. Numerical calculations were carried out, on the basis of which the distribution of pressure, flow velocities and fluid filtration inside the holes and in the near-wellbore zone as a whole was obtained. Calculations were made with varying pressure in the well (or pressure drawdown), as well as for different values of reservoir permeability. The calculation results showed that for the actual drawdown values of 10 MPa and the reservoir permeability of 50 mD, the value of pressure change inside the perforation holes will not exceed 0.01 MPa, i.e. it can be assumed that it practically does not change inside the hole. It is noted that the maximum value of the filtration rate corresponds to the top of the perforation holes and then its value decreases as it approaches the borehole wall. It is concluded that in further modeling of the stress-strain state of the near-wellbore zone, taking into account the holes of cumulative perforation on the surface of the holes, it is permissible to set a constant pressure value equal to the pressure in the well, and not logarithmic or any other distribution of it.