Abstract Cylindrical grid shells made of modern composite materials by automated continuous winding that have a high degree of weight perfection and are widely used in aerospace engineering are considered. The problem of using such structures as deep-submergence vehicle bodies operating not under external pressure is discussed. The problem of optimal design of cylindrical grid shells based on the criterion

Abstract— The main focus of this study is to investigate the dynamic responses of a simply supported bridge structure in terms of displacement, speed, and acceleration subjected to vehicles traveling at different speeds. The interaction between a bridge and the vehicles moving on it is a coupled, dynamic problem. Conventionally, most research has been focused on the dynamic or impact response of the

Abstract The problem of refined modeling of ultrafine rods, which arose in connection with the need to explain the known experimental data on the significant dependence of the bending stiffness of such ultrathin structures on their thickness if the thickness becomes very small, commensurate as some authors believe with the characteristic dimensions of the material microstructure, is considered. To

Abstract The use of effective approximations that increase the rate of convergence of numerical results when constructing a finite element model of bearing layers for a more accurate layer-by-layer analysis of the stress-strain state of three-layer irregular cylindrical shells is considered. It is believed that the carrier layers are sufficiently thin and rigid, and two-dimensional finite elements

Abstract A design scheme is considered: a cylindrical shell, which is loaded concentrated through the frame. A classical mathematical model is used for the adopted calculation scheme. Based on the mathematical model, the initial problem is analytically solved and an effective algorithm for multiparameter solution of the corresponding boundary value is constructed. The results of a quantitative analysis

Abstract A spatial non-stationary contact problem with moving boundaries of the interaction region for a thin elastic cylindrical shell and an absolutely solid impactor bounded by a smooth convex surface is considered. A closed mathematical formulation is given and a system of resolving equations is constructed. The latter is based on the spatio-temporal integral equation resulting from the principle

Abstract— The influence of morphological features of nanocomposites based on a polymer matrix and graphene oxide on the effective elastic and electrically conductive properties is studied. The concept of a representative volume element (RVE), the geometry of which is modeled explicitly using specified parameters, is used. A method for analyzing the specific conductivity of a RVE that is based on graph

Abstract— In the present article, we argue a choice of a modifier (filler) for an epoxy binder, namely, carbon nanotubes. The solid-state epoxy adhesive obtained by modification is a 3-phase nanocomposite, where the matrix is epoxy resin, the filler is nanotubes, and the contact layer is the domain of the epoxy resin, molecules of which have been undergone conformation. Next, the effective deformation

Abstract Many features of dynamic fracture caused by shock-wave action are most pronounced under spalling conditions, i.e., when an intense wave pulse is reflected from a free boundary. Therefore, such material tests are one of the main ways to study the fracture processes occurring in a solid under ultrafast dynamic stress. Nevertheless, the geometrical characteristics of the fracture zone formed

Abstract The paper considers differential equations in partial derivatives of an elliptic type with variables, piecewise-smooth coefficients, depending on the coordinates (initial equations). It is shown that the solution of the original equation can be represented as an integral equation through the solution of the accompanying equation with constant coefficients of the same type. This representation

Abstract The problems on determining the design fatigue resistance characteristics of materials and structural elements by using methods of the statistical theory of fatigue failure similarity are considered. The results of vast number of fatigue tests conducted by various researchers and research and production enterprises for samples of different sizes, models and full-scale parts have been subjected

Abstract An elastic inhomogeneous coating is considered for which a simplified deformation model is proposed in the framework of the concept of an asymptotically thin layer. Based on such a model for an inhomogeneous coating, a solution of the contact problem in the presence of intermolecular interaction is constructed and the wear kinetics for the thrust sliding bearing is calculated. It is shown

Abstract— An approach to calculating the stress-strain state during axisymmetric deformation of domes and bottoms by synthesizing two stress states, namely, momentless and edge effect is generalized to the case of arbitrary deformation of cylindrical and conical shells. It is proposed to construct the stress state on the basis of approximate equations describing the so-called elementary stress states:

Abstract An analysis of the properties of the constitutive equations of the theory of plasticity for porous media using Green’s yield criterion is carried out. It is shown that this criterion is one of the possible yield criteria for materials with plastic properties depending on the type of stress state, with the only difference being that the coefficients depend on the porosity parameter. Therefore

Abstract The article considers two problems, one of which is related to the engineering direction, devoted to the study of the resources of bearings with coatings that have received a certain defect. The second relates to the mechanics of natural phenomena and is associated with the phenomenon of subduction. Subduction is the process of moving oceanic lithospheric plates under the continental in the

Abstract The relations of the mathematical model for studying the stress-strain state of structurally anisotropic panels made of composite materials are given. The mathematical model of the reinforcing element is clarified under conditions of one-sided contact with the skin. The influence of panels manufacturing technology is taken into account: residual temperature stresses and prestressing of reinforcing

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AbstractThe axisymmetric torsion of a layer of incompressible Mooney–Rivlin material placed between two rigid coaxial cylindrical surfaces is considered. It is assumed that the ends of the cylinder are fixed to avoid axial displacement and the cross-sections orthogonal to the axis of symmetry do not distort during deformation. In this case, the material points move along arcs of circles with an angular

AbstractThe present article deals with a solution of an analogue of the Prandtl problem on compression and drain (spreading) of a perfectly rigid plastic material in an asymptotically thin spherical layer by taking into account inertial effects. Various compression modes that characterize the transition from a quasistatic process to a dynamic one are considered.

AbstractThe present article claims that by preliminary heat treatment (thermal annealing) of polystyrene in a fixed state at a temperature of 60°C, a slight increase in its light stability can be achieved.

Abstract–A rectangular plate pivotally mounted on two opposite edges is considered. It is shown that one of the plate fastenings at the other two edges is determined up to a permutation of the fastenings at these edges uniquely from five natural frequencies. It is also shown that four eigenfrequencies for such a recovery is not enough. The corresponding counterexample is given. It was previously shown

AbstractIn this work, the evolution of dispersion relations of 2D asymmetric phononic crystals in the low-frequency range is introduced and discussed. Two phononic crystal structures are proposed and calculated using Finite Element method. The first one is a thin plate from PDMS with a circular one-side stubbed from tungsten and the other is a thin plate in the X-shape from rubber and tungsten. The

AbstractBased on the layer-by-layer analysis approach, the construction of a model of two types of finite elements (FE) of natural curvature (two-dimensional FE of the momentary bearing layers and three-dimensional FE of the filler) is considered for refined investigation of the stress-strain state (SSS) in layers of three-layer generally irregular shells of revolution of double curvature.The presented

AbstractWe study the dynamics of a gimbal-mounted gyroscope, which has a vertical external gimbal axis and is equipped with a synchronous electric drive that rotates a gyroscope (electric motor rotor). A mathematical model of the electric motor that includes differential equations for electric currents in the rotor windings is used. Both friction and control torques on the gimbal axes are assumed to

AbstractCurrently, various structural components have coatings of different purposes that are multilayer or gradient structures. During operation these elements are often subjected to compressive loads, as a result of which sometimes the upper part of the coating is delaminated. To analyze this process, we use a simplified model of infinite structure, namely, a modified beam approximation that takes

AbstractA continuum model is proposed and a system of equations is constructed to describe the processes of destruction of a solid. In the framework of the model, a decaying solid is considered as a heterogeneous medium consisting of two phases—solid and gaseous. Based on the analysis of the energy balance equation, in which its surface component is taken into account, the regularities of the onset

AbstractIn a non-standard setting, motion with respect to the center of mass of a spheroid with a cavity filled with a fluid of high viscosity is considered. The moment of forces acting on the body from the side of a viscous fluid in the cavity is determined by the technique developed in the works of F.L. Chernousko. As a result of original asymptotic and numerical calculations, solutions are obtained

AbstractThe present article deals with the problem on constructing a guaranteeing time of a given control beginning for a shock isolator protecting an object on a movable base from impacts acting on this base. The initial moment of control action can either be ahead (anticipation) or lag behind (delay) the moment of the disturbance beginning. It is assumed that the shock shape is unknown, but its duration

AbstractIn the framework of the model of M.A. Lavrentiev, the effect of internal elastic and dissipative forces on the rotational motion of the planet in a central gravitational field in a circular orbit is studied. The averaged equations of the rotational motion of the planet are derived. The stability of plane rotations is investigated. The analysis of the evolution of rotational motion depending

AbstractIn the framework of the theory of large deformations, a solution is obtained for the deformation of a material with nonlinear elastic, plastic and viscous properties located in the gap between two rigid coaxial cylindrical surfaces. The outer surface remains stationary, and the inner rectilinearly moves with variable speed. With uniformly accelerated surface motion, initially irreversible strains

Abstract—A natural phenomenon has been discovered—a natural property of nonlinear oscillations of elastic mechanical structures interacting with the environment. The indicated property, related in view of its objective reality to natural phenomena, is as follows: if the forces of excitation of structural vibrations from the environment exceed the strength of their damping, then the frequency of oscillations

AbstractA mathematical model of a flexible rotor with n degrees of freedom rolling around a flexible stator with slippage between them is proposed, as well as an approach to the exclusion of contact forces for dynamic analysis of the system. The angular velocity and amplitude of the reverse rotor precession are determined by matrix methods. It is shown that the break-in speed is not always equal to

AbstractThe nanoindentation method was used to study the elastic properties of gallium nitride and aluminum nitride films grown on nanoscale silicon carbide on silicon (SiC/Si), a new type of substrate. The values of the Young’s modulus of epitaxial films of such wide-gap semiconductors as GaN and AlN, grown on substrates SiC/Si. were determined for the first time. It was experimentally established

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Abstract—Theoretical models are proposed that describe the initial stage of plastic deformation in metal–graphene composites with a homogeneous ultrafine-grained metal matrix, as well as with a bimodal grain size distribution. The models take into account both dislocation mechanisms of plasticity and the processes of structural transformations of grain boundaries associated with grain-boundary sliding

Abstract—The vacancy growth of a faceted pore in a crystal via Chernov mechanism is studied. It is assumed that the growth is due to the diffusion of excess vacancies arising in the bulk of the crystal under the influence of mechanical tensile stress. In the framework of the formalism proposed by Chernov, the distribution of vacancies in the crystal near the step and its rate of advance are found.

Abstract—Mechanical properties of alloyed steels parts may be improved by precipitation of simple and/or complex chemical combinations (carbides, nitrides, and/or carbonitrides) using thermal and/or thermo-chemical treatments. Nevertheless, the precipitation of transition metal sulphides (TMSs) is considered as an undesirable phenomenon because of the negative influence on the material properties.

Abstract—A reasonably accurate solution of the balance equation for a substance is obtained for a predetermined number of nuclei of a new phase in the nucleation kinetics. This solution is necessary for the adequate description of secondary nucleation and accurate determination of the number of nuclei of a new phase. The approximation is constructed by studying the characteristic properties of the

Abstract—The concepts of nucleation processes occurring near the three-phase contact line are developed under conditions of poor wettability of the vertex (end) face of the threadlike nanocrystal by a liquid catalyst drop.

Abstract—Ab initio calculations for studying electronic band structure of ideal and defective Cd1 – xMnxSe (0.01 ≤ х ≤ 0.07) semimagnetic semiconductors have been performed. It has been defined that with an increase in concentration of Mn in Cd1 – xMnxSe compound, there is a decrease in the band gap. Based on the results obtained we can conclude that ferromagnetic phase is more stable than antiferromagnetic

Abstract—A simple scheme for estimating the adsorption energy of polar molecules on solid state substrates has been proposed within the Harrison bond orbitals method. Analytical expressions are obtained for the ionic and metallic components of the adsorption energy for diatomic and tetraatomic molecules. The adsorption of GaCl and AlCl3 on a semiconductor substrate is considered as an example.

Abstract—In this article, we studied the growth characteristics of AlN epitaxial layers on 3С-SiC/Si(111) templates at various values of atomic flux of aluminum at a constant growth temperature and a constant flow of atomic nitrogen. The AFM method was used to study the morphology of the resulting structures. The minimum roughness was achieved at a growth rate of 150 nm/h on on-axis templates, and

Abstract—Molecular dynamics is used to study the fracture of pseudo-graphenes, namely, allotropic forms of carbon that are modifications of graphene with a high density of periodically distributed disclinations with zero total charge. Disclinations in pseudo-graphenes are associated with improper carbon rings, that is, rings having 4, 5, 7, or 8 members, in contrast to the proper 6-member carbon rings

Abstract—The paper presents the results of experiments on the formation of GPS-var structures using hydrofluoric acid (HF) electrolytes in solutions of ethyl (C2H5OH) and isopropyl alcohol (CH3CH(OH)CH3) at various component ratios. It was experimentally shown that the use of electrolytes based on CH3CH(OH)CH3 allows the formation of a GPS-var structure with a nanoporous layer of silicon, while the

Abstract—To determine the cracking susceptibility for amorphous metal alloys (AMAs) or metallic glasses, a method based on the determining the dependence of the relative crack resistance (χ) on the load applied to intender of PMT-3 microhardness tester is proposed. In the method, the relative crack resistance at a load of 160 g is set equal to unit. At lower loads, crack resistance has been determined

Abstract—Van der Pol equations describing self-oscillations in a quasilinear one-dimensional oscillator are generalized to the case when the generating isotropic oscillator has an arbitrary number of degrees of freedom. Two-dimensional (flat) and three-dimensional (spatial) cases are specifically considered. In contrast to the classical problem, in which a given amplitude of oscillations was stabilized

Abstract—Non-point vacancy-gas defects (VGD) (pores, blisters) in the crystal lattice arise as a result of its irradiation with an inert gas Xe++, the process is considered as the formation of first-order phase transition nuclei by means of computational mathematics, kinetic theory, and the theory of stochastic dynamic variables and Wiener random processes. The characteristics of disordered porosity

Abstract—A theoretical model for changing the plasticity mechanism in bimodal materials with graphene inclusions has been developed. Within the framework of the model, a theoretical study on the transition of plastic deformation from a nanocrystalline and/or ultrafine-grained matrix to the coarse-grained phase, which is inherent to bimodal materials has been performed. In particular, a theoretical

Abstract—This issue of the journal “Mechanics of Solids” publishes the proceedings of the International conference “Mechanisms and Non-linear Problems of Nucleation and Growth of Crystals and Thin Films” (MGCTF 2019), dedicated to the memory of the outstanding physicist theorist Vitaly Valentinovich Slezov.

Abstract—The loading of a metal rod whose material contains impurities and is described on the basis of a two-component continuum model is considered. The proposed two-component model allows us to take into account the role of dynamics in the transition of a material from one state to another, using source terms in mass balance equations. The obtained solution demonstrates the significant influence

Abstract—The results of growing polycrystalline (PC) films (FL) of luminophore (LP) based on a solid solution of Cd0.1Zn0.9S: Cu, Аg, sodium salt compounds (Nа2SO4, Na6Cd7S10 = 3Na2S · 7CdS) in an aqueous colloidal solution containing zinc acetate, cadmium nitrate and sodium sulfide compounds on the surface of a new material, a hybrid Si substrate (nano-SiС), under normal physical conditions are presented

Abstract—This paper deals with the quality prediction of the Single Point Incremental forming (SPIF) process. The quality prediction can be evaluated through five parameters: Roughness surface, thickness, springback, circularity and position errors. Despite the contribution of many researchers on the development of sheet metal forming process, the geometric accuracy of the formed part remains less

Abstract–In the dynamic theory, the formation of twin martensite crystals is the result of a coordinated propagation of relatively long-wave (\(\ell \)-waves) and short-wave (s-waves) displacements. The matching condition is analyzed for the γ–α martensitic transformation in iron-based alloys, taking into account the quasi-longitudinalness of the \(\ell \)-wave carrying compression deformation. It

Abstract—The dependence of the thermodynamic surface tension of a small droplet formed on a molecular-size condensation nucleus on the droplet size, nucleus size, molecular field parameters, and nuclear charge in the case of an ion is investigated. Calculations have been performed for molecules of supersaturated argon vapor at different values of the chemical potential of the molecules in the framework

To identify the strength properties of a block structure including a bearing pair cage and the lubricated bearing itself, a model of a bearing with a defect is considered. The cage is a deformable base with a thin coating having defects. The coating is under the influence of a lubricant, which under operating conditions loses viscosity and can be modeled by a thin layer of an ideal incompressible fluid

Within the framework of simplified nonlinear models, the initial nonlinear-elastic stage of obtaining hollow gear parts from the circular shells by the method of hydrostatic compression from circular circles is studied by analytical and numerical methods. It is shown that a suitable choice of a rigid rod inside the shell allows one to control the corrugation of the cross section of the pipe billet

A natural generalization of the von Mises flow criterion is obtained taking into account anisotropy on single-crystal materials with a hexagonal crystal lattice. Boundary-value problems are posed for plane deformation by compression with back pressure, for uniaxial tension, compression, and for pure shear. A special case of solving boundary value problems for hexagonal magnesium with a purity of 99