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Том 212, № 1 (2016)
- Год: 2016
- Статей: 8
- URL: https://journals.rcsi.science/1072-3374/issue/view/14705
Article
Solvability of the Neumann Problem in a Disk for Fourth-Order Properly Elliptic Equations
Аннотация
We establish and study sufficient conditions of solvability of the Neumann problem for fourth-order properly elliptic equations of the general form in a unit disk K in the space \( {C}^4(K)\cap {C}^{3,\upalpha}\left(\overline{K}\right) \).
1-15
On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions
Аннотация
We study the problem of local convergence of the accelerated Newton method for the solution of nonlinear functional equations under generalized Lipschitz conditions for the first- and second-order Fréchet derivatives. We show that the accelerated method is characterized by the quadratic order of convergence and compare it with the classical Newton method.
16-26
On the Separation of Singularities in the Numerical Solution of Integral Equations of the Potential Theory
Аннотация
We propose new procedures for the separation of singularities in the kernel and in the potential density for weakly singular Fredholm integral equations for the simple-layer potential in the case where the boundary surface has edges, ribs, and corner points. These procedures are based on the projection methods for the solution of these equations and finite-element approximations of the required potential density.
27-37
A Semiring in the Spectrum of the Algebra of Symmetric Analytic Functions in the Space ℓ1
Аннотация
We consider a semiring of numerical sequences in the spectrum of the algebra of symmetric analytic functions in the space ℓ1 and study the problem of continuity of complex homomorphisms of this semiring and the problem of extension of homomorphisms to the corresponding ring.
38-45
Domain Decomposition Schemes Based on the Penalty Method for the Problems of Perfect Contact of Elastic Bodies
Аннотация
On the basis of the penalty method, we propose a number of continuous parallel domain decomposition schemes for the solution of the problems of perfect mechanical contact of elastic bodies. For some of these schemes, we prove the theorems on convergence. We study the problem of optimal choice of the iterative parameters. The relationship between the proposed schemes and the domain decomposition methods without penalty is established.
46-66
Axisymmetric Problem for an Elastic Cylinder of Finite Length with Fixed Lateral Surface with Regard for its Weight
Аннотация
We consider an elastic cylinder with regard for its weight. The conditions of sliding fixing are imposed on the lower base of the cylinder, its upper base is subjected to the action of an axisymmetric normal load, and the lateral surface is fixed. The Hankel integral transform is used to reduce the problem to an integral equation of the first kind for normal stresses acting on the fixed cylindrical surface. After finding the singularities of the unknown function, the solution of the integral equation is sought in the form of a series in Jacobi polynomials. The results of numerical evaluation of the normal stresses on the fixed surface of the cylinder are obtained both with regard for its weight and by neglecting its weight.
67-82
Elastic Equilibrium of a Space Containing a Thin Curved Elastic Inclusion in Longitudinal Shear
Аннотация
We study the problem of antiplane deformation of an isotropic medium containing a thin elastic curved inhomogeneity. The methods used for the solution of this problem are based on the application of the method of jump functions and the conditions of interaction of the matrix containing a thin curvilinear inclusion and the solution of the resultant system of singular integral equations with Cauchy-type kernels by the collocation method. Numerous examples are considered. The results of evaluation of the stress intensity factors for a crack and an absolutely rigid inclusion along a circular arc are compared with the corresponding analytic results. For a crack along a symmetric parabolic arc, the stressed state is thoroughly investigated. We also study the influence of the modulus of elasticity and the shape of the curvature of inhomogeneity (circular arc, parabola, or a half of a cosine curve) on the generalized stress intensity factors. It is shown that, for the stress intensity factors near the tip of the inhomogeneity, the inclination of the tangent at the tip to the plane of application of the shear forces is of determining importance.
83-97
Stressed State of a Shell of Double Curvature with Two Collinear Cracks Under Bending
Аннотация
We study an isotropic shell of double curvature weakened by two through collinear cracks whose faces are in contact in the case of bending of the shell. The solution of the problem is obtained by the method of singular integral equations and the numerical method of mechanical quadratures. We perform the numerical investigations of the dependences of force and moment intensity factors on the sizes of the cracks, the distance between them, and the curvature of the middle surface of the shell.
98-105