A promising mathematical model for the creation of wide-purpose acoustoelectronic devices has been developed for a piezoactive heterostructure consisting of a W-cut lithium tantalate crystal plate deposited through a silicon dioxide buffer layer onto a (0001)-cut ɑ-sapphire substrate, where W defines the normal to the crystal cut surface. The model takes into account the crystal cut orientation, the direction of propagation of a horizontally polarized shear wave, and the geometric dimensions of the heterostructure's constituent elements. This allows for a wide range of parameter variations to achieve maximum values of the electromechanical coupling coefficient. The heterostructure's properties have been studied with and without a buffer layer. For the latter case, the analysis allowed for determining the optimal orientation of the lithium tantalate plate cut and its thickness, which would ensure the optimal level of electromechanical coupling. The maximum value of this coefficient, for a given cut orientation and specific geometric parameters of the heterostructure, is achieved by selecting the wave propagation direction. A study of a heterostructure with a silicon dioxide buffer layer revealed that its introduction significantly increases the electromechanical coupling coefficient. A detailed study of the acoustic wave amplitude and energy flux density distribution across the heterostructure's depth was conducted. Calculations revealed that both the wave amplitude and the degree of elastic energy localization in the piezoactive layer depend on the presence of the buffer layer and the thickness of the piezoactive layer, which directly affects the electromechanical coupling coefficient. Its maximum is observed at a small piezoactive layer thickness. Thus, optimal heterostructure parameter values exist that allow for achieving the maximum electromechanical coupling coefficient. This study is of interest to developers of acoustoelectronic devices and general-purpose devices.achieving maximum EMCC. This study is of interest to developers of acoustoelectronic devices and general-purpose devices.

The first part of the study, published in the previous issue of the journal, was devoted to estimating fatigue limits using a fatigue curve in tests conducted at several levels of alternating stress amplitudes over a wide range of life spans, as well as tests conducted to estimate the parameters of the fatigue failure similarity equation for subsequent combined statistical modeling with elements of bootstrap estimation and the Monte Carlo method. This article (part two) continues this research. For the same purposes, an up-down fatigue limit assessment is considered. The up-down method is not intended to construct a complete fatigue curve over a wide range of life spans, but it allows for a forced determination of the fatigue limit distribution corresponding to a certain fixed (base) life span. The mathematical model of the “up-down” testing method has a rigorous probabilistic-statistical justification. It is based on the maximum likelihood method and, unlike other accelerated fatigue testing methods such as Pro, Enomoto, and Locatti, does not require a priori information about the characteristics of random variables. It is only necessary to approximately specify the initial stress amplitude level of the cycle and the range between levels during the experiment, which is maintained constant throughout the test. The hypothetical distribution functions considered are the normal law, the log-normal law, and the Weibull law for the fatigue limit. A significant time savings compared to a full-scale fatigue experiment and high accuracy allow this method to be recommended for fatigue limit assessment. Generating a nonparametric fatigue limit distribution function for comparative evaluation of different groups of observations using the binomial criterion is performed using Monte Carlo statistical modeling, as in the first part of the paper.

This paper provides the results of numerical simulation of high-speed impact interaction of a non-deformable hemispherical body with a granular medium, which is a dense packing of steel spheres. The granular medium is considered as a set of individual particles, the motion and deformation of which is described by the discrete element method. This method uses the representation of the modeled material as a set of individual particles, with given set of elastic constants. This approach allows more efficient simulation of processes accompanied by large deformations and violations of the continuity of the medium than when using grid methods. Main principles of the numerical discrete element method, which have been widely used in recent years due to the development of computer technology are described with references to primary sources. An example of calculating the contact force between two interacting elastic spherical particles in the approximation of small deformations is given by decomposing it into normal and tangential components. In the simplest approximation, this force is the representing Hooke's law where the deformation of particles is considered as their spatial intersection. A general description of the numerical model and calculation methods is given. The results of modeling the process of normal high-speed impact interaction of a rigid rod with a hemispherical head with a deformable granular medium consisting of steel spherical spheres are presented taking into account the friction forces. An estimate is given of the contact forces from the discrete medium on the solid hemisphere. The results of numerical studies are compared with experimental data.

An original modification of the Kolsky method for studying the dynamic strength of brittle media under tension by splitting a sample in the form of a cube or parallelepiped in the split Hopkinson pressure bar system has been developed and implemented. The setup includes a gas gun as a loading device and a set of steel measuring bars (loading and support) with a diameter of 20 mm made of high-strength steel, equipped with strain gauges for measuring elastic deformation pulses. The SHPB system was loaded with a 150 mm long steel striker, which made it possible to obtain a falling compression pulse with a duration of about 100 ?s in the loading measuring bar. By varying the striker velocity, different amplitudes of the incident wave were achieved, which provided different sample loading rates. To test brittle materials (rocks) that have a nearly linear stress-strain diagram dependence up to failure, a non-dispersive smoothly increasing pulse in the loading bar is required. In the work, a ring of thin copper wire placed on the impact end of the loading bar was used as a former. A feature of the setup is that the pulsed compressive load is applied to the side surfaces of the sample through wedge-shaped attachments on the ends of the measuring bars. When loading a brittle material sample with a compression pulse, it splits along the plane of application of the dynamic compressive load. Since it is extremely difficult to measure the strain of the sample under tension in this type of testing, as a result of tests by measuring the pulse in the supporting measuring bar, only the dependence of the development of the compressive force Pc(t) acting in the sample is obtained. Then, the process of development of the tensile stress σₜ(t) in the the sample is determined, the peak of which is the sought-after tensile strength of the rock. A cycle of dynamic tests on splitting of igneous rock samples of gabbro-diabase of cubic shape with edge size of ~20 mm was carried out. Dependences of splitting strength and time to failure (time of “life”) on the rate of growth of stresses were constructed. The obtained dependences correspond to the known tendency of increasing strength properties and decreasing incubation time during destruction of rocks with increasing rate of growth of stresses and can be used for equipping the Morozov – Petrov structural-time criterion of fracture.

The article analyzes the advantages and disadvantages of three-layer orthotropic slabs. It is shown that when developing the design of such slabs, it is necessary to work out the technology of connecting the elements in the structure. The use of laser welding for connections is effective for connecting elements of small thicknesses. Such welding of sheet elements with a thickness of 12–50 mm has a number of limitations, and the strength characteristics of the joints have not been sufficiently studied. Therefore, when developing slabs with a large load-bearing capacity, it is advisable to design a steel three-layer orthotropic slab using electric arc welding. It is shown that a large number of intersections of welded seams in the joints of elements of such slabs requires performing work using techniques that reduce welding deformations and prevent cracking in such slabs under low operating temperatures, quasi-static and variable loads. The stress-strain state analysis of the slab has been completed. The model and full-scale slabs are tested for transverse loads. It is found that due to welding deformations, deviations of the actual geometry of the slab from the design one appear. This can explain the differences in the experimental and calculated values of vertical displacements. No failures of the slotted welds used to connect the elements were detected during the slab testing. Cracks at the maximum load on the slab model appeared only in the welds located along the perimeter of the cover slab. It was found that the welded 3-layer slab has intersections of welds in which cracks originate. This requires identifying crack-hazardous zones in the slabs using non-destructive testing methods and experimental research into the strength of structural forms containing structural and welding stress concentrators.

The proposed article provides a brief overview of publications devoted to solving problems of granular media mechanics using the discrete element method. These publications discuss the conditions for the successful application of algorithms and software developed for the effective functioning of computing systems implementing the discrete element method. It is noted that the most labor-intensive aspect of modeling deformation processes using the discrete element method are calculations associated with determining contact forces. The key problem is the evolutionary nature of contacts: during deformation of the medium under study, discrete elements can come into contact, which can subsequently be interrupted depending on the loading conditions. In this regard, it is necessary to carefully study the organization and management of memory associated with computer modeling of contacts. The main attention in the article is paid to algorithms for searching for discrete elements coming into contact. These algorithms should be robust (i.e. reliable), easy to implement; effective in terms of speed and use of RAM. Two variants of the algorithm based on the use of auxiliary (screening) grids are compared: the screening contact detection algorithm and the Munjiza-NBS contact detection algorithm. A brief description of these algorithms and their software implementation is given. The results of verification of the algorithms on test problems and a comparative analysis of their performance are presented. It is shown that the selected algorithms provide reliable information about discrete elements contacting during motion and can be successfully used in the software implementation of the discrete element method as applied to problems of granular media dynamics.

The study presents the results of experimental modeling of elastoplastic deformation of bent massive concrete filled steel tube beams under three-point bending. It has been shown that local deformations and local crushing in such structures have a significant impact on their behavior. The applicability of the theory of bending of a hollow steel beam according to the Bernoulli model is analyzed. A comparison has been made of the bearing capacity and stress-strain state of hollow steel tubes (according to the Bernoulli model and the results of experiments) and concrete filled steel tube beams, and the contribution of the concrete core to the bending resistance during elastoplastic deformation has been quantitatively assessed. The actual load-bearing capacity of a hollow pipe during three-point bending does not exceed 50% of the calculated theoretically determined one, which indicates the impossibility of using the classical bending model when designing systems of this kind. In this case, the concrete filled steel tube beam not only ensures the full functioning of the metal during the deformation process, preventing its disruption, but also provides some increase in load-bearing capacity due to the inclusion of a compressed zone in the concrete work. The increase in the load-bearing capacity of a beam due to the introduction of a concrete core can reach 70%. Despite their significant weight, bendable tube-concrete rods can be recommended in conditions of a complex stress-strain state, in which, in addition to transverse bending loads, significant longitudinal forces arise, as well as local force factors that contribute to the occurrence of local crushing deformations, since, unlike a thin-walled hollow tube, concrete the core significantly prevents these effects. Based on the results of the study, the potential effectiveness of flexible tube-concrete elements for a number of structures was proven.

The inverse problem of elastoplastic deformation of a thick-walled cylindrical shell of finite length under internal pressure is solved. For a given displacement of the outer surface of the shell, it was necessary to construct a numerical technique to determine the internal pressure providing this displacement. The problem being solved is a boundary value problem of a mixed type. The cylindrical shell under study is in a plane stress state and a volumetric deformed state. The mathematical formulation of the problem was based on the provisions of the deformation theory of plasticity. The strain state of the shell was described using nonlinear Hencky strains. The constructed model of elastic-plastic deformation of the shell took into account the compressibility of the material and the nonlinear law of hardening. The numerical calculation method is based on the method of variable elasticity parameters using the method of successive approximations, taking into account changes in the geometry of the shell during deformation. To assess the adequacy of the constructed numerical method for solving the inverse problem, a comparative calculation of the direct problem of elastoplastic deformation using the finite element method in the ANSYS 19.0 software package was carried out. The results obtained for radial and circumferential stresses, stress intensity, radial displacements of the boundary surfaces of a cylindrical shell at internal pressure calculated when solving the inverse elastoplastic problem showed sufficient consistency. The stress distribution patterns in the cylindrical shell wall according to the method of variable elasticity parameters and the finite element method are qualitatively the same. The differences in the quantitative results obtained according to the two approaches are no more than 10%. The proposed calculation method can be used in the field of aircraft engineering in order to calculate the required pressure when deforming cylindrical shells to the required geometry, taking into account the physical and geometric nonlinearities of the material under the condition of monotonic loading.

For homogeneous isotropic annular plates with a rigid insert resting on an incompressible liquid base, a comparison was made of the solutions obtained analytically by Hodge and the numerical method previously developed by the author. Specific examples demonstrate the convergence of the numerical solution and its good agreement with the complete exact solution. In this case, the accuracy of determining the limit value of the transversal load applied to the rigid insert is 1-2%. It is shown that the numerical solution is not complete, since it allows one to calculate only the limiting value of the external active load applied to the bending plate, but does not allow one to determine the magnitude of the fluid resistance in the limit state of the structure. The influence of plate reinforcement parameters on the limiting value of the transverse force applied to a rigid insert is analyzed. Options for laying reinforcement along logarithmic spirals, along rectilinear trajectories and along radial and/or circumferential trajectories have been studied. It is shown that plates with a radial-circumferential structure have the greatest load-bearing capacity when at each point the total reinforcement density is equal to the maximum permissible value. For the first time, an unconventional version of the boundary conditions on the outer edge of the plate, which exploit under the specified conditions, is considered - the free edge. It has been demonstrated that in the case of the design of the product, when in the limit state of the plate it is impossible for liquid to flow from one of its front surfaces to another, the load-bearing capacity of a plate with a free outer edge is several times less than with a supported outer edge. The possibility of the emergence of an absolutely rigid annular subregion adjacent to the internal insert in the limit state of reinforced plates is shown.