No 4 (2023)

 The equilibrium of a body supported by rigid and telescopic supports on fixed hinges is considered. It is shown that the addition of a potentially sliding joint may not provide mobility to the design, as well as the addition of a rotary joint. A paradox was discovered for a sliding support: the equations of seemingly obvious equilibrium are not fulfilled. Deviations are introduced to regularize the problem. Internal reactions remain statically indeterminate, while the magnitude of these reactions may be significant. It is shown that external reactions tend to infinity as the introduced deviations decrease. This explains the inconsistency of the equilibrium equations: a pair of infinite forces with zero leverage, generally speaking, is not equivalent to zero force, but can create any moment, including the balancing moment of gravity. It can be assumed that some of the major accidents involving building structures are associated with these features.

A general solution of problems of elasticity theory for anisotropic half-planes and strips with arbitrary holes and cracks is presented, which uses the complex potentials of the plane problem of the theory of elasticity of an anisotropic body, conformal mappings, representations of holomorphic functions by Laurent series, and satisfaction of boundary conditions by the generalized least squares method. The problems are reduced to overdetermined systems of linear algebraic equations solved by the singular value decomposition. The results of numerical studies are described for a strip with a circular hole under its tension or under the action of a uniform pressure along a segment of a rectilinear boundary, as well as for the tension of a strip with a circular hole and a crack in the bridge, including those extending to the border of the strip or to the contour of the hole. An isotropic half-plane and a strip with holes and cracks are considered as special cases of the general problem. The influence of the geometric characteristics of holes and cracks, the physical and mechanical properties of the strip on the values and distribution of stresses material was studied.

 In this article, the mechanical and deformation characteristics of epitaxial films of AlGaN solid solutions formed on silicon substrates of crystallographic orientations (001), (011) and (111) with a silicon carbide (SiC/Si) buffer layer synthesized by the method of the coordinated substitution of atoms were studied using the nanoindentation method. The growth of AlGaN epitaxial layers were carried out both directly on the SiC/Si hybrid substrate and on the SiC/Si substrate additionally coated with an AlN buffer layer. The morphology and structure of the surface of the layers was studied by atomic force microscopy. The structural characteristics of hybrid AlGaN substrates and films grown with and without an aluminum nitride buffer layer were measured. An unambiguous relationship has been established between the mechanical properties (elasticity modulus and hardness) and the surface structure of AlGaN films. It has been found that the AlN buffer layer has a significant effect on the mechanical and deformation properties of AlGaN films at the initial moment of indentation, when the layer is predominantly elastically deformed. The roughness was determined and the surface morphology of the AlGaN films was characterized. For the first time, experimentally, using the nanoindentation method, the hardness parameters and the reduced modulus of elasticity of epitaxial AlGaN grown on hybrid SiC/Si and AlN/SiC/Si substrates were measured.

The behavior of a mechanical system when the parameters characterizing it change is investigated. The analysis shows that stepwise changes (catastrophes) occur in the system in a certain area of control parameters. The considered problem admits an exact (global) analysis of the catastrophe, without involving various expansions and assumptions. The proposed mechanical design can serve to demonstrate the occurrence of a catastrophe.

The article considers a method for forming a rotating tether group of small spacecraft in the form of a regular polygon. To create an external torque acting on the entire system as a whole, low-thrust engines are used, and the directions of the reactive forces are unchanged in the coordinate systems associated with the spacecraft. The release of the cables is controlled by measuring their length and speed in accordance with the nominal program, which assumes that the mechanisms of the release of the cables work only for their braking. The nominal program is built according to a simplified model of the system's motion, built using the Lagrange equations. The feasibility of the deployment program is checked using a more complete model of the spatial motion of the system, written in a geocentric fixed coordinate system and taking into account the extensibility of the cables, the one-sidedness of the mechanical links corresponding to them, the operation of the control system, disturbances associated with the initial conditions of motion, etc. A more complete model of motion takes into account the motion of space vehicles relative to their centers of mass as solid bodies of finite dimensions, which leads to perturbations in the directions of action of reactive forces. Numerical examples are given of the deployment of ring tether groups of small spacecraft in the form of polygons with up to seven vertices, inclusive, under the action of disturbances.

The article considers the issues of optimizing the processes of attenuation of the transverse movements of the trailer, which is attached to a tractor moving at a constant speed with the help of a hinge and taking into account the compliant clutch. As an optimization criterion characterizing the efficiency of this attenuation, the maximization of the degree of system stability is taken. In this case, the distance from the center of mass of the trailer to the point of its adhesion to the tractor acts as an optimized parameter. A detailed analytical solution of the problem is carried out, during which the optimal curve on the plane of dimensionless parameters is determined, which consists of several sections and is located in the region of motion stability. Visual graphic illustrations are given, explaining the meaning of the found solution and its main features. In addition, the obtained results are compared with the variant of the location of the center of mass of the trailer exactly in the middle between the point of its coupling with the tractor and the axle of the wheelset, and an assessment is made of the effectiveness of the obtained optimal solution. The conclusions made in the work are not only of theoretical interest, but can also find some practical application.

The longitudinal motion at a constant speed of a thin continuous elastic web through a system of roller bearings under the action of a given constant tension is considered. One span between adjacent supports is considered. The web is modeled by a thin layered plate hinged on two opposite edges, the remaining two sides of the plate are free. It is assumed that the plate in the process of longitudinal movement can perform small transverse vibrations. The layers of the plate from a given set of materials are arranged symmetrically to the middle surface and fit tightly to each other. The total thickness of all layers is given and is small compared to the span length and plate width. Analytical expressions are derived for the effective characteristics of the plate, as a result of which the initial composite structure can be considered as an isotropic homogeneous plate, for which the known equations for calculating the critical velocity are applied. Within the framework of multi-criteria Pareto optimization, using a numerical method of non-local optimization, the order of the layers and their thickness are determined in order to satisfy a number of selected criteria: the maximum critical divergence rate, the maximum flexural stiffness, and the minimum unit weight of the layered web. An example of the found optimal structure of the plate and the constructed Pareto front for a given set of defining parameters of the problem are given.