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Vol 228, No 1 (2018)
- Year: 2018
- Articles: 7
- URL: https://journal-vniispk.ru/1072-3374/issue/view/14876
Article
Sufficient Conditions for the Equivalent Convergence of Sequences of Different Approximants for Two-Dimensional Continued Fractions
Abstract
By the method of fundamental inequalities, we study the equivalent convergence of two figured approximants for two-dimensional continued fractions, namely, the approximants obtained from the problem of correspondence of two-dimensional continued fractions to some formal double power series and the problem of equivalence of two-dimensional continued fractions. We also establish sufficient conditions under which the indicated two approximants of two-dimensional continued fractions converge to the same limit.
1-10
11-25
26-34
Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane
Abstract
The bases in the spaces of functions analytic in simply connected domains are constructed with the help of conformal mappings of these domains onto a circle. The obtained basis functions are biorthogonal to the Faber polynomials. By using the expansions of analytic functions in series in systems of basis functions, we determine the solutions of boundary-value problems for the Helmholtz equation whose boundary values coincide with the boundary values of these functions.
35-52
Eccentric Form of the Loss of Stability of a Rotating Elastoplastic Radially Inhomogeneous Stepped Circular Disk
Abstract
We propose a procedure for the investigation of the possible loss of stability of a rotating elastoplastic radially inhomogeneous stepped circular disk by the method of small parameter. The characteristic equation for the critical radius of the plastic zone is obtained in the first approximation. The values of the critical angular rotational velocity are numerically found for various parameters of the disk.
53-65
Nonlinear Deformation and Branching of the Solutions of Boundary-Value Problems of the Theory of Shells with Delaminations Under External Pressure
Abstract
We consider the structure of branching of the solution of a nonlinear boundary-value problem of the theory of shells in the case of cylindrical shell with delamination area subjected to the action of external pressure. To find the solution, we use the generalized Kantorovich method applied to the analysis of the corresponding boundary-value problem. The complete structure of branching is presented for the solutions of the problem. We establish the existence of branches of the solution both with forms of deformation and joint deformation of the layers and with forms of deformation and separate deformation of the layers in the delamination region.
66-79
Analysis of the Stress State of Hollow Cylinders with Concave Corrugated Cross Sections
Abstract
In the three-dimensional statement, by the method of approximation of functions by discrete Fourier series, we perform the analysis of the dependence of the stress state of a hollow cylinder whose cross section has the form of joined concave semicorrugations subjected to the action of internal pressure under certain conditions imposed on the end faces on the thicknesses and curvatures of the cross sections of the cylinders caused by the changes in the number of semicorrugations. The results of the solution of the problem are presented in the form of the plots of distributions of the fields of displacements and stresses.
80-89