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Том 240, № 1 (2019)
- Год: 2019
- Статей: 7
- URL: https://journals.rcsi.science/1072-3374/issue/view/15011
Article
Solvable Extensions of Some Nondensely Defined Operators and the Resolvents of These Extensions
Аннотация
In terms of abstract boundary conditions, we study a class of extensions of finite-dimensional restrictions of closed densely defined linear operators acting in Hilbert spaces. By the methods of the theory of linear relations, we find the resolvent sets and construct the resolvents of the analyzed extensions. The set of these extensions is parameterized by a certain auxiliary operator. In the case where this operator is normally solvable, we present certain improvements of the basic results.
1-20
21-33
34-47
Construction of a Refined Model of the Dynamic Behavior of Flexible Reinforced Plates of Nonlinear Elastic Materials Based on the Explicit Numerical “Cross” Scheme
Аннотация
In the von Kármán approximation, we formulate the initial-boundary-value problem of dynamic deformation of flexible reinforced plates with nonlinear elastic behavior of the materials of the components of composition. We deduce the equations for the determination of the stress-strain states of these plates with different degrees of accuracy with regard for their weakened transverse-shear resistance. As a special case of these equations, we get the relations of the nonclassical Reddy theory. For the numerical integration of the posed problem, we use the method of time steps with application of the explicit numerical “cross” scheme. We investigate the dynamic response of relatively thick and thin annular composite plates containing a rigid internal washer under the action of loads caused by an air-blast wave. The plates are rigidly fixed along the outer contour and rationally reinforced in the radial and radial-circumferential directions. It is shown that, in the case of application of the “cross” scheme, the numerical procedures based on the equations of refined theories have a higher practical stability than within the framework of the Reddy theory. It is also discovered that, for times of about one second and longer, the computed dynamic behavior of the reinforced plates determined according to the Reddy theory strongly differs from the behavior determined according to the refined theories.
48-69
Mathematical Modeling of the Mean Concentration Field in Random Stratified Structures with Regard for the Jumps of Sought Function on the Interfaces
Аннотация
We study the diffusion processes of an admixture in a two-phase stratified strip of randomly inhomogeneous structure with regard for the jumps of the concentration function and its derivative on the contact boundaries of the phases. A new representation of the operator of equation of mass transfer for the entire body is proposed. We formulate an equivalent integrodifferential equation whose solution is constructed in the form of a Neumann integral series. The obtained solution is averaged over the ensemble of phase configurations with uniform distribution function. It is shown that the computational formula for the mean concentration with explicit account of its jumps on the interfaces contains an additional term. It is demonstrated that the ratios of the diffusion coefficients, the concentration dependences of the chemical potentials in different phases, and their relationships affect the sign of this term. We find the ranges of parameters of the problem for which this term is negligibly small.
70-85
Solutions of Axisymmetric Problems of Elasticity and Thermoelasticity for an Inhomogeneous Space and a Half Space
Аннотация
We developed a technique for the construction of solutions of axisymmetric problems of elasticity and thermoelasticity in stresses for a space and a half space whose elastic properties are arbitrary functions of the coordinate z. By using the direct integration method and the Hankel integral transformation, the problems are reduced to governing integral equations accompanied by a local boundary condition and an integral condition in the case of the half space. The solutions of the deduced equations are constructed in the explicit form by using the resolvent-kernel method.
86-97
Axially Symmetric Vibrations of Elastic Annular Bases and a Perfect Two-Layer Liquid in a Rigid Annular Cylindrical Vessel
Аннотация
We deduce a frequency equation for the natural coupled axially symmetric vibrations of elastic bases (in the form of annular plates) and a heavy two-layer incompressible perfect liquid in a rigid annular cylindrical vessel. We consider different limiting cases: the case of degeneration of annular plates into membranes, the case of absolutely rigid or circular plates, and the case of absence of the upper plate (liquid with free surface). For a broad range of parameters of the analyzed mechanical system, we investigate the frequency spectra and obtain a series of mechanical effects in the problem of hydroelasticity.
98-112