Introduction. A method for solving the problem of an infinite plate on an elastic foundation is proposed. The plate is affected by a periodic load in the form of a force following an arbitrary closed path. The work objective is to develop a numerical method for solving problems of the elasticity theory for bodies under a moving load. Materials and

Methods. Given the periodicity of the load under consideration, it is decomposed in a Fourier series in a time interval whose length is equal to the load period. The solution to the original problem is constructed by superposition of the solutions to the problems corresponding to the load specified by the terms of the Fourier series described above. The final solution to the problem is presented as a segment of a series. In this case, each term corresponds to the solution of the problem of the impact on an infinite plate of a load distributed along a closed curve (the trajectory of the force motion). To find these solutions, the fundamental solution to the equation of vibration of an infinite plate lying on an elastic base is used.

Research Results. A new method is proposed for solving problems on the elasticity theory for bodies with a load following a closed path of arbitrary shape. The problem of an infinite plane along which a concentrated force moves at a constant speed is solved. It is determined that the trajectory of motion is a smooth closed curve consisting of circular arcs. The behavior of displacements and stresses near a moving force is considered. The energy propagation of the elastic waves is studied. For this purpose, the coordinates of the Umov – Poynting vector are calculated. The effect of the force motion speed on the length of the Umov – Poynting vector is investigated.

Discussion and Conclusions. The method is applicable when considering more complex objects (plates of complex shape, layered plates, viscoelastic plates). Its advantage is profitability since the known problem solutions are used to build the solution. The final decision is expressed in a convenient form – as the sum of curvilinear integrals. The results obtained can be used in the road design process. Studying the energy propagation of elastic waves from moving vehicles will enable to evaluate the impact of these waves on buildings near the road. The wear of the pavement is estimated considering data on the behavior of displacements and stresses

Introduction. In modern production, when performing finishing operations, centrifugal rotary processing in the medium of abrasive plays an important role. High productivity, low costs and extensive technological capabilities are the main advantages of these cleaning and finishing operations. This paper considers the process of abrasive particle – workpiece surface interaction within the framework of the static contact problem of the elasticity theory. Thus, plastic deformation in the contact area comes into account.

Materials and Methods. The abrasive particle (corundum) is simulated with a linearly elastic body, whose Young's modulus is significantly larger than that of the work material. The process material (steel) is simulated with an elastoplastic bilinear body using the von Mises yield criterion.

Research Results. Finite element modeling of the structures under consideration was performed in the ANSYS CAE package. The process of abrasive particle – workpiece surface interaction was simulated; its stress-strain state was analyzed. The results of numerical experiments are presented. They have determined how equivalent plastic strains are distributed at depths of the cone penetration of 0.01 mm and 0.05 mm. The data obtained, as well as the areas of plastic strain values of more than 1%, are visualized in the ANSYS CAE package.

Discussion and Conclusions. It is established that the equivalent plastic deformation is proportional to the depth of penetration (DP). It reaches a minimum value of 0.158 at DP = 0.01 mm, and a maximum of 0.825 at DP = 0.05 mm. The dependences of the plastic region sizes on DP are determined for cases when the plastic deformation exceeds 1%. At the maximum penetration (0.05 mm), the deformation radius is 1 mm, and the depth is 0.8 mm. On the basis of the data obtained as a result of the conducted research, the parameters of the technological process (rotational speed, size of the abrasive surface, mass of abrasive particles) that affect the workpiece – abrasive particle interaction can be selected. A judicious choice of these parameters will increase the processing efficiency

Introduction. The integration of reliability and optimization concepts seeks to design structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to very high computational cost and weak convergence stability. Materials and

Methods. Several methods have been developed to overcome these difficulties. The methods called Reliability Index Approach (RIA) and Performance Measure Approach (PMA) are two alternative methods. RIA describes the probabilistic constraint as a reliability index while PMA was proposed by converting the probability measure to a performance measure. An Optimum Safety Factor (OSF) method is proposed to compute safety factors satisfying a required reliability level without demanding additional computing cost for the reliability evaluation. The OSF equations are formulated considering RIA and PMA and extended to multiple failure case.

Research Results. Several linear and nonlinear distribution laws are applied to composite yarns studies and then extended to multiple failure modes. It has been shown that the idea of the OSF method is to avoid the reliability constraint evaluation with a particular optimization process.

Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of decoupling the optimization and the reliability analyses. It provides designers with efficient solutions that should be economic satisfying a required reliability level. It is demonstrated that the RBDO compared to OSF has several advantages: small number of optimization variables, good convergence stability, small computing time, satisfaction of the required reliability levels.

Introduction. Nowadays, vacuum-type dough dividers are used in industries with a production volume of up to 4,000 loaves per day. In the dough divider operation, due to wear of the working surfaces of the piston, chamber, and drum, the gap between them goes beyond the value equal to 50 microns, which provides vacuum in the suction chamber. As a result, the suction process becomes unstable; the dough divider disturbs the weight accuracy of bakery goods. Repair of such equipment is carried out mainly through a full or partial replacement of worn parts and assemblies with new ones. To increase their durability, there is a need to develop a new highly efficient technology with the restoration of worn part surfaces using the welding and surfacing methods.

Materials and Methods. A new technique of determining the number of objects for research using the “STATISTICA” program is presented. Wear surfaces of the vacuum dough divider parts are determined.

Research Results. Micrometric studies of the dough divider components were carried out. They showed the presence of appreciable size distortions due to the local wear of the working surfaces. In this case, a side gap between the suction chamber and the main piston and between the drum and the suction chamber is 6 times higher than the permissible one, and a vertical gap between the division box and the piston exceeds the permissible gap by more than 10 times. Wear of the working surfaces of the dough divider parts is local in nature, while the range of values is as follows: for the main piston, it is 10-200 microns; for the gaging piston, it is 250- 900 microns; for the suction chamber and division box, it is 300-400 microns; for the drum surfaces, it is 280-300 microns.

Discussion and Conclusions. The conducted micrometric studies showed the presence of appreciable size distortions due to the local wear of the working surfaces. Based on the results obtained, it can be argued that the most productive and economically viable technique for the restoration of worn surfaces of dough divider parts is, for example, the electrospark machining.

Introduction. The durability and performance of hydraulic machines is determined through life tests. At that, various braking devices (mechanical, electric, hydraulic, etc.) are used for strength loading of the hydraulic motor, as a result of which a significant amount of energy is lost. This can be avoided if the method of rotational motion with energy recovery is used during life tests. This approach is applicable for hydraulic pumps, motors, and hydraulic cylinders.

Materials and Methods. A test bench is presented, the design of which provides recreation of the conditions most appropriate for the field operation of hydraulic cylinders. In this case, energy recovery is possible. To solve the research problems, methods of mathematical modeling were used, the basic functional parameters of the proposed design were calculated. The determination of the pressure increment at various points in the hydraulic system is based on the theory of volumetric rigidity. When modeling the motion of the moving elements of the bench hydraulic system, the laws of rotor motion are used.

Research Results. In the structure of the test bench, the cylinders in question are located in the pressure main between the hydraulic pump and the hydraulic motor. This enables to significantly reduce the bench itself and to save a significant amount of energy due to its recovery. A basic hydraulic diagram of the test bench for piston hydraulic cylinders is presented, in which the operation of the moving elements of the system is shown. A mathematical modeling of the hydraulic system of the bench is performed. A kinematic diagram of the mechanism for transmitting motion between test cylinders is shown.

Discussion and Conclusions. The system of equations presented in the paper shows how the increment of pressure at the selected nodal points of the energy recovery system is determined (in particular, how the increment depends on time, reduced coefficient of volumetric rigidity, operating fluid consumption, and piston areas). The velocities of the hydraulic pistons are determined according to the kinematic scheme of the mechanical transmission of the bench. Thus it can be argued that, thanks to the solution presented in the paper, the life test results of hydraulic cylinders will adequately reflect their operation under rated duties.

Introduction. Efficient leak detection methods and gas flow metering are analyzed. The work objective is to select an automatic system of methods providing the improvement of the quality of leakage monitoring and gas flow metering in gas pipelines.

Materials and Methods. The following techniques for detecting gas leakage in the pipeline are considered: according to the pressure profile, volume balance method, acoustic emission method, variable-pressure drop method on the forcing device, ultrasonic method.

Research Results. The analysis shows that all techniques for monitoring leakage and gas flow are dependent on the environmental parameters. Therefore, an important task is to achieve independence of the measurement results from changes in the environmental parameters. In most flow meters, changes in density, pressure and temperature affect drastically the measurement results. An additional error that arises in this case can reach large values.

Introduction. Threshing is a multifactorial process which is affected, in particular, by the feedrate of the crop, the specific weight of the threshed grain and return, separation rates, weediness and moisture of the crop. From this point of view, the issues of optimizing the profile of the transporter cut, which allows for threshing and separation with the least effort, are also relevant. It was also experimentally established that the threshing process is affected by the volume of grain material delivered per second (second feed) and the unit velocity.

Materials and Methods. The studies were conducted on a test bench equipped with a threshing-separating device in the form of a single-cavity hyperboloid. When performing the work, the width of the drum was divided into three zones, and the length – into five cells. Wheat grain, obtained through threshing and separation in each zone and cell, came to individual containers. Straw was collected separately. Then, the grain and straw were weighed. The resulting data was processed by statistical and mathematical methods.

Research Results. The lengths of each cell were calculated based on the ratio of the total separation and the amount of grain mass per unit length. The lengths of each cell were calculated depending on changes in humidity. Indicators of the ratio between mass humidity and cell length are presented in the form of a table. By the given table values for different moisture levels of the grain mass, graphs were constructed, each of which was described by a mathematical model considering the drum length and width. An averaged cut profile is presented for the treated plant mass with humidity of 8%, 12%, 16%, 20%, and 24%.

Discussion and Conclusions. Analysis of the data in this paper and earlier ones provides the comparison of the graphic expression of the dependences of the transporter cut profile on the second volume and humidity of the grain mass entering it. It has been established that the cut profile curves are identical along the entire length of the drum. The confidence factor is close to 1, which indicates the accuracy of the model. The identity of the averaged cut profiles is obviously dependent on moisture of the plant mass and on the second feed.

Introduction. Technologies of mathematical and logical modeling of problem solving according to the existing practice of their distribution are divided into two areas: widespread mathematical modeling and infological modeling which is currently underdeveloped, especially for sophisticated systems. Fundamental differences between these technologies, in particular for the machining preproduction, are that logical modeling is informationally and logically related to organization systems, and mathematical modeling is associated with control processes in the organization systems. Logical modeling is used to operate with geometric objects in the technological schemes of their interaction through basing methods, geometric shaping in a static (ideal) setting of the corresponding schemes. Mathematical simulation is used to operate material objects in the control processes of their transformations through cutting methods, i.e. imperfectly, considering heterogeneous errors. Between the organization systems under study and management processes in them, there are information and logical links of their organic unity, which deny their separate consideration. In the information deterministic technology for solving problems of a high-level automation, the distinction between the concepts of “mathematical” and “logical” modeling is relevant; it has scientific novelty and practical significance.

Materials and Methods. To characterize the properties of the concepts of “mathematical modeling”, “logical modeling” and the knowledge functions resulting from the formulation of these concepts, fundamentally different methods and appropriate tools are used. The differentiation of the concepts under consideration is based on the differentiation of technologies (methods, appropriate tools, algorithms, operations) for solving applied problems of any knowledge domain.

Research Results. The ideas of “logical modeling” and “mathematical modeling” are conceptual general-theoretical notions with invariant properties required for solving practical problems of any application domain. In accordance with the distinction between these concepts, the problem solving technologies are divided into two types: system engineering technology – in the organization of information object systems, and system science – in the management processes of transformation of the corresponding material objects. These areas should exist in the information and logical link of their organic unity.

Discussion and Conclusions. The author distinguishes between the concepts of “logical modeling” and “mathematical modeling”, which is a key condition for a successful transition to the deterministic information technology of a high-level automation in solving practical problems of any knowledge domain, for example, of the production design machining

Introduction. The paper presents a theoretical study on binary salt ion transport considering the water dissociation/recombination reaction. The work objectives are as follows: to build a mathematical model; to develop an algorithm for the numerical solution to the boundary value problem corresponding to the mathematical model; to work out the similarity theory including the transition to a dimensionless form using characteristic quantities; to determine a physical meaning of trivial similarity criteria; to find nontrivial similarity criteria; to build and analyze the volt-ampere characteristic (VAC).

Materials and Methods. The theoretical study and numerical analysis of the transport of binary salt ions consider the dissociation/recombination reaction of water. In this case, the heat transfer equation and the mathematical model of electrodiffusion of four types of ions simultaneously (two salt ions, as well as ????⁺ and ????????⁻ions) in the diffusion layer of electromembrane systems with a perfectly selective membrane are used. For the first-order differential equations, a singularly perturbed boundary-value problem is set. In the equation for the electric field, the right side is independent of the intensity. In the numerical solution to the digitized system of equations by the Newton-Kantorovich method, this causes the stability of the method. In this regard, the boundary-value problem is reduced for numerical solution: a transition to a system of the second-order equations is provided, and the missing boundary conditions for the electric field strength are calculated.

Research Results. A new mathematical model, a numerical algorithm to solve a boundary value problem, and software are developed. A numerical analysis is carried out, and fundamental laws of the transport of salt ions are determined considering the dissociation/recombination reaction of water molecules, temperature effects, and Joule heating. The VAC is built and analyzed.

Discussion and Conclusions. The transport of binary salt ions through a diffusion layer near a cation exchange membrane is considered. A mathematical model of this process is proposed. It takes into account the temperature effects due to dissociation/recombination reactions of water molecules and Joule heating in a solution. The basic laws of the transport of salt ions are established considering the dissociation/recombination reaction of water molecules and temperature effects. The temperature effects of the dissociation/recombination reaction and the Joule heating in the electroneutrality region (ENR) are almost imperceptible (with the exception of the recombination region, RR). The Joule heating in the space-charge region (SCR) is by two orders of magnitude larger than the cooling effect of the water dissociation reaction. Upon recombination, approximately the same heat is released in the RR as during Joule heating in the expanded SCR. However, due to the small size of the RR, the effect of this heat is imperceptible. Therefore, we can assume that there is only one heat source at the interface in the SCR, which, due to its noticeable size, causes a significant increase in temperature in the entire diffusion layer. It follows that the emergence and development of gravitational convection is possible. General conclusions, following from the results obtained, open up the possibility of intensifying the process of transport of salt ions in the electrodialysis machines.

Introduction. In the mathematical finite element modeling, an average value of the mechanical characteristics of the deformable solid material is used. In aircraft, machine building, construction engineering, medicine and other fields, polymer composite materials and materials of natural origin are increasingly used. In the latter case, the actual change in the mechanical characteristics differs significantly from the averaged change; therefore, when using the averaged parameters to build and analyze finite element models, the results can be significantly distorted. This paper describes the creation of mathematical methods for studying changes in the mechanical characteristics of a material of inhomogeneous deformable solids. The results obtained in this way are used to construct finite element models and analyze their stress-strain state.

Materials and Methods. Naturally occurring materials and composites are considered as inhomogeneous deformable solids. To study the changes in the mechanical characteristics of the material, a method was developed based on the use of two components: the pixel characteristics of raster images scanned by a computer tomograph and the experimental data of field tests of standard samples.

Research Results. A complex of mathematical methods has been developed for modeling the interpretation of scanning raster images by a computer tomograph, which allows for the study of any complicated structures of real deformable solids. The results are used in the construction of finite element models of such bodies considering the heterogeneity of the mechanical characteristics of the material. The analysis of the stress-strain state of finite element models of test samples has proved the accuracy and convergence of the numerical solution of the finite element method in modeling the property of heterogeneity of the mechanical characteristics of the material.

Discussion and Conclusions. The developed approach can be applied to any physical principles of scanning (X-ray, ultrasound, laser, etc.) and for any types of materials if the data obtained as a result of scanning is developed in the form of a digital (raster) image.

Introduction. A rapid development of the systems such as Yandex, Google, etc., has predetermined the relevance of the task of searching substrings in a string, and approaches to its solution are actively investigated. This task is used to create database management systems that support associative search. Besides, it is applicable in solving information security issues and creating antivirus programs. Algorithms of searching substring in a string are used in signature-based discovery tasks.

Materials and Methods. The solution to the problem is based on the Aho-Corasick algorithm which is a typical technique of searching substrings in a string. At the same time, a new approach regarding preprocessing is employed.

Research Results. The possibility of constructing the transition function and suffix references through suffix arrays and special mappings, is shown. The relationship between the prefix tree and suffix arrays was investigated, which provided the development of a fundamentally new method of constructing the transition and error functions. The results obtained enable to substantially shorten the time intervals spent on the preelection processing of a set of pattern strings when using an integer alphabet. The paper lists eight algorithms. The developed algorithms are evaluated. The results obtained are compared to the formerly known. Two theorems and eight lemmas are proved. Two examples illustrating features of the practical application of the developed preprocessing procedure are given.

Discussion and Conclusions. The preprocessing procedure proposed in this paper is based on the communication between the suffix array built on the ground of a set of pattern strings and the construction of transition and error functions at the initial stages of the Aho-Corasick algorithm. This approach differs from the traditional one and requires the use of algorithms providing a suffix array in linear time. Thus, the algorithms that enable to significantly reduce the time for preprocessing of a set of pattern strings under the condition of using a certain type of alphabet in comparison to the known approach proposed in the Aho- Corasick algorithm are described. The research results presented in the paper can be used in antivirus programs that apply searching for signatures of malicious data objects in the memory of a computer system. In addition, this approach to solving the problem on searching substrings in a string will significantly speed up the operation of database management systems using associative search.