Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Conditions for the solvability of nonlinear equations systems in Euclidean spaces
Get PDFThe solution of many applied problems is to ?nd a solution of nonlinear equations systems in ?nite- dimensional Euclidean spaces. The problem of ?nding the solution of a nonlinear system is divided into two problems: 1. The existence of a solution of a nonlinear equations system; in the case of nonunique of the solution, it is necessary to ?nd the number of these solutions and their surroundings. 2. Finding the solution of a system of nonlinear equations with a given accuracy. Many publications are devoted to solving problem 2, namely the construction of iterative methods, their convergence and estimates of the solution accuracy. In contrast to problem 2, for problem 1 there is no general algorithm for solving this task, there are no constructive conditions for the existence of a solution of a nonlinear equations system in Euclidean spaces. In this article, in ?nite-dimensional Euclidean spaces, the constructive conditions for the existence of a solution of nonlinear systems of polynomial form are found. The connection of these conditions with the linear polynomial interpolant of the minimum norm, generated by a scalar product with Gaussian measure and the conditions of its existence, is given.
Pages of the article in the issue: 74 - 80
Language of the article: Ukrainia
Algorithm of solving of nonstationary thermoelastic problem for two-layered cylinder at time-variety heat transfer coefficient
Get PDFThe nonstationary axisymmetric thermoelasticity problem for a two-layer cylinder at the inner surface of which convective heat transfer with an environment takes place is considered. The solution of this problem is derived for the case of inhomogeneous initial temperature field. The solution is presented in the form of development by the system of eigenfunctions of the boundary value problem for a two-component beam and expressed in terms of the elementary functions. Based on this solution, an incremental algorithm of solving thermoelasticity problems for a two-layer cylinder is proposed for the case that the heat transfer coefficient between the inner surface of the cylinder and environment is time-varied. The idea of the algorithm is to divide the entire transient time interval into a sequence of subintervals, the heat transfer coefficient is considered constant on each. Once the temperature field is determined, the axisymmetric stress field can be founded on the basis of analytical expressions. The proposed algorithm was tested on the example of the thermal shock scenario for a nuclear reactor vessel. The comparison of the obtained results with the numerical solution by the finite element method verified sufficient working accuracy of the proposed approach.
Pages of the article in the issue: 59 - 62
Language of the article: Ukrainia
Computational method for solving boundary problems of the theory of elasticity using non-orthogonal systems of functions
Get PDFA complete system of functions based on non-orthogonal sinuses and cosine was constructed. It has been proven that the continuous function can be approximated by a finite number of non-orthogonal functions in such a way that this amount does not enter the selected function of the non-orthogonal base. The numerical experiment confirmed the high accuracy of approximations of continuous functions by a small number of non-orthogonal functions. The flat problem of the theory of elasticity for the plate with variable elastic characteristics is considered. This equation is simplified when the characteristics of the material change insignificantly depending on the spatial coordinates. A new method of solving a boundary value problem has been developed for the fourth-order equation with variable coefficients. The proposed method is based on the separation of the stress state of the plate from an inhomogeneous material to the main and indignant state, the use of complete systems of non-orthogonal functions and a generalized quadratic form. A criterion under which the constructed approximate decision coincides with the exact solution was found.
Pages of the article in the issue: 101 - 106
Language of the article: Ukrainia
Implementation of the methodology for calculating the contact interaction of teeth of gear wheels made of composite materials
Get PDFBased on the solutions of contact problems for fibrous materials and coatings of composite materials, the article considers the implementation of the method of calculating the pliability of gears of composite materials, determining the contact parameters of coatings of fibrous materials. To calculate the contact deformations of gears made of metals and composites, a program was developed in the Delphi environment, which makes it possible to calculate the coefficients of contact deformation of the gear tooth, as well as the calculation of contact deformations for a tooth with a fibrous coating. An integral equation is presented, which gives a solution of the contact problem of pressing a stamp into an orthotropic coating. To study the influence of the properties of the material and the thickness of the coating on the contact parameters, a computer program was compiled, which was used to calculate for different thicknesses.
Pages of the article in the issue: 50 - 55
Language of the article: Ukrainia
Application of the finite element-differences method for modeling of anisotropic filtration processes
Get PDFWe consider modeling and geophysical interpretation of the obtained results in the oil and gas production problems in anisotropic reservoirs. For solving these practical problems, we use combined finite element-differences method of resolving anisotropic piezoconductivity problem with calculation of heterogeneous filtration parameters distribution of oil and gas productive reservoirs and oil-gas penetration conditions in the borders of investigating areas. We have defined that the anisotropy of oil and gas permeability in the far zone of the well has a greater effect on the filtration processes around the well and, accordingly, on the producing of the raw materials than the anisotropy of permeability in the near zone of the well. We have shown that the intensity of filtration processes in anisotropic reservoirs near the acting well depends significantly on the shear permeability and to a lesser extent on the axial permeability of the corresponding phase. Therefore, for the effective using of anisotropic reservoirs, it is necessary to place production wells in local areas with relatively low anisotropy of permeability of the reservoir, especially to avoid places with shear anisotropy.
Pages of the article in the issue: 63 - 66
Language of the article: Ukrainia
Towards the analysis of stress relaxation in thin-walled cylindrical shells made of linear viscoelastic materials
Get PDFThe problems of stress relaxation analysis in thin-walled cylindrical shells made of linear viscoelastic materials under uniaxial and biaxial loading have been solved. The analysis is based on a there-dimensional model of viscoelasticity starting from the hypothesis of the deviators proportionality. The viscoelastic properties of a material are given with relationships that establish the dependence between stress and strain intensities as well as between the mean stress and volumetric strain by the Bolzmann-Volterra type equation. The kernels of relaxation intensity and volumetric relaxation are given with the Rabotnov exponential-fractional functions. The parameters of relaxation kernels are determined from creep test result using the relationships between creep kernels under the complex stress state and creep kernels under the one- dimensional stress state. The problems of the analysis of normal and tangential stresses relaxation in thin-walled cylindrical shells made of high density polyethylene “PJeVP” under uniaxial tension, pure torsion and combined tension with torsion loading have been solved and experimentally approved.
Pages of the article in the issue: 29 - 34
Language of the article: Ukrainia
Mathematical model of erythrocyte in the capillary motion
Get PDFPractical medicine requires new research to better understand the processes of blood flow through the vascular system. In particular, the processes of blood movement in capillaries, when their diameter is smaller than the diameter of erythrocytes, are of interest. It is believed that the center of mass of the erythrocyte lies on the midline of the capillary. While in the arterioles, the erythrocyte releases nutrients, so its mass decreases. When moving in the venule, the mass of the erythrocyte increases because it receives spent substances from the tissue space. The vascular wall of the capillary and its midline are modeled using the equation of the parabola, which makes it possible to calculate within the specified limits the length of the wall and the midline. The movement of an erythrocyte is described by the Meshchersky equation for bodies with variable mass. The proposed article is devoted to the construction of static models of capillaries in the norm and a dynamic model of movement in the capillary of an erythrocyte with variable mass.
Pages of the article in the issue: 56 - 61
Language of the article: Ukrainia
Eigenfrequencies and eigenforms of regular chain oscillatory systems
Get PDFThe classical approach in the investigation of natural oscillations of discrete mechanical oscillatingsystems is the solution of the secular equation for finding the eigenfrequencies and the system of algebraic equations for determining the amplitude coefficients (eigenforms). However, the analytical solution of the secular equation is possible only for a limited class of discrete systems, especially with a finite degree of freedom. This class includes regular chain oscillating systems in which the same oscillators are connected in series. Regular systems are divided into systems with rigidly fixed ends, with one or both free ends, which significantly affects the search for eigenfrequencies and eigenforms. This paper shows how, having a solution for the secular equation of a regular system with rigidly fixed ends, it is possible to determine the eigenfrequencies and eigenforms of regular systems with one or both free ends.
Pages of the article in the issue: 88 - 93
Language of the article: Ukrainia
Extrapolation problem for periodically correlated stochastic sequences with missing observations: Extrapolation problem for periodically correlated stochastic sequences
No full textThe problem of optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence from observations of the sequence at points , , is considered, where is an uncorrelated with periodically correlated stochastic sequence. Formulas for calculation the mean square error and the spectral characteristic of the optimal estimate of the functional are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of functionals are proposed in the case of spectral uncertainty, where the spectral densities are not exactly known while some sets of admissible spectral densities are specified.
Pages of the article in the issue: 39 - 52
Language of the article: Englis
The impact of management on the behavior of an isolated logistics population
Get PDFThe article considers the isolated population described by the logistic equation and studies the influence of management on the change of its number. Depending on the value of the control parameter, there are three different cases of behavior of an isolated population. In the first case, when the quota is equal to the corresponding value, depending on the initial value, the population either goes to a stationary value, or dies out. In the second case, when the quota does not exceed the established value, depending on the initial population size, the population either goes to the largest stationary point, or dies out. And in the third case, when the quota exceeds the established value, regardless of the initial population size, the population dies out. Stationary points for stability in all three cases are studied and graphs of population behavior depending on different initial conditions are presented.
Pages of the article in the issue: 81 - 84
Language of the article: Ukrainia