The shock interaction of a spherical rigid body with a spherical cavity is studied. This nonstationary mixed boundary-value problem with an unknown boundary is reduced to an infinite system of linear Volterra equations of the second kind and the differential equation of motion of the body. The hydrodynamic and kinematic characteristics of the process are obtained Introduction. Recently, it has been experimentally proved that it is possible to create underwater vehicles based on supercavitation as a new physical principle of motion of bodies in water [14][15][16]24]. A supercavitating body is fully enveloped by a gas bubble, supercavity, and moves inside it at speeds commensurable with the speed of sound in water. Supercavitation arouses considerable interest of researchers. Recent results on supercavitation can be found in, e.g., [18,19].One of the challenges regarding supercavitation is to ensure stable motion of a body in a cavity [12,[14][15][16]24]. Only the nose of a supercavitating body is in contact with the surface of the cavity. The drag exerted by water on the body within the contact region generates an overturning moment about the body's center of mass, making supercavitation unstable. This instability causes lateral impacts of the body against the surface of the cavity, which strongly affects the behavior of the body. This is why study into the impact of the body on the cavity surface is of importance.The supercavitation of a cylindrical body in a cylindrical cavity was studied in [5,22] and [8,19] considering the liquid to be incompressible and compressible, respectively. The hydrodynamic and kinematic loads (plane problem) were determined there.The motion of a spherical body in a spherical cavity (axisymmetric problem) was studied in a similar way. However, many scientists who studied axisymmetric cavities were mainly interested in their geometry, including the relationships between the cavity length and width, between the cavitation number and the body dimensions, and between the body length and the cavitation number [4,11].A spherical body's penetration of the surface of a spherical cavity in a compressible liquid was studied in [9, 20] and the hydrodynamic and kinematic characteristics of the process were determined there. In [9], an axisymmetric problem was formulated and its asymptotic solution was found for the initial stage of the process in the case of an infinitesimal air gap (the body and the cavity have the same transverse dimensions).In [20], a general problem formulation for an arbitrary air gap (a mixed nonstationary initial-boundary-value problem with an unknown boundary varying with time) was given, infinite governing systems of Volterra equations of the second kind were derived, and asymptotic solutions were obtained for the cases of small and infinitesimal air gaps. The present paper, which is based on the results from [20], gives a general problem formulation for an arbitrary air gap, derives infinite governing systems of Volterra equations of the second kind, and solves them nume...
Modern calculations of layered plates and shells in a three-dimensional formulation are based on a technique where the distribution of the desired functions over the thickness of a structure is sought by the method of discrete orthogonalization. In this article, based on the approaches developed by the authors, the thermally stressed state of layered composite shallow shells with a rigidly fixed lower surface is analyzed. The distribution of the desired functions over the thickness of the structure is found based on the exact analytical solution of the system of differential equations. An approach to studying the thermally stressed state of layered composite shells is also considered, and a spatial model for calculating the thermally stressed state of shallow shells on a rigid basis is constructed. Currently, this is a very urgent task when calculating the pavement of bridges. A feature of this approach is the assignment of the desired functions to the outer surfaces of the layers, which allows one to break the layer into sublayers, reducing the approximation error to almost zero. To build a spatial model, a load option is selected with temperature loads (according to the sine law) and boundary conditions (Navier), which lead to the distribution of the desired functions in terms of a plate with trigonometric harmonics of the Fourier series. A polynomial approximation of the desired functions by thickness is involved. Using the model under consideration, an analysis of flat layered composite shells on a rigid basis under the influence of temperature load was carried out. The considered example showed that the proposed model provides sufficient accuracy in the calculations of layered shallow shells when considering each layer within one sublayer. When dividing each layer into 32, 64, 128 sublayers, almost the same result was obtained. The proposed approach can be used as a reference method for testing applied approaches in calculating the stress states of layered shallow composite shells.
A theoretical assessment of the antioxidant properties of non-enzymatic antioxidants (bioflavonoids and carotenoids) with the declared antioxidant activity was carried out. Using computer modeling software package ChemOfficeBio, the energy values of the highest occupied and lowest free molecular orbital in the molecule of the substance were obtained, the Egap index was calculated. In the course of the study, the maximum activity was found in Astaxanthin compounds (carotenoids), high in Beta-carotene and Lycopene (carotenoids), medium and low activity of compounds of the bioflavonoid group (Quercitin, Epigallocatechin-3-gallate and Resveratrol).
Modern calculations of layered plates and shells in a three-dimensional formulation are based on a technique where the distribution of the desired functions over the thickness of a structure is sought by the method of discrete orthogonalization. In this article, based on the approaches developed by the authors, the thermally stressed state of layered composite shallow shells with a rigidly fixed lower surface is analyzed. The distribution of the desired functions over the thickness of the structure is found based on the exact analytical solution of the system of differential equations. An approach to the study of the thermal stress state of shallow composite shells is considered, and an analytical model is constructed for calculating the thermal stress state of shallow shells on a rigid base with a sliding contact of the layers. Currently, this is a very urgent task when calculating the pavement of bridges. A feature of this approach is the assignment of the desired functions to the outer surfaces of the layers, which allows one to break the layer into sublayers, reducing the approximation error to almost zero. Using the model in question, an analysis of flat layered composite shells on a rigid base with a sliding contact of the layers under the influence of temperature loading was carried out. To build a spatial model, a load option is selected with temperature loads (according to the sine law) and boundary conditions (Navier), which lead to the distribution of the desired functions in terms of a plate with trigonometric harmonics of the Fourier series. A polynomial approximation of the desired functions by thickness is involved. Using the model in question, an analysis of flat layered composite shells on a rigid base with a sliding contact of the layers under the influence of temperature loading was carried out. The considered example showed that the proposed model provides sufficient accuracy in the calculations of layered shallow shells when considering each layer within one sublayer. The proposed approach can be used as a reference method for testing applied approaches in calculating various stress states of layered flat composite shells.
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