Introduction. The paper deals with the calculation of wooden arches taking into account the nonlinear relationship between stresses and instantaneous deformations, as well as creep and geometric nonlinearity, are considered. The analysis is based on the integral equation of the viscoelastoplastic hereditary aging model, originally proposed by A.G. Tamrazyan [1] to describe the nonlinear creep of concrete.

Materials and Methods. The creep measure is taken in accordance with the work of I.E. Prokopovich and V.A. Zedgenidze [2] as a sum of exponential functions. The transition from the integral form of the creep law to the differential form is shown. The relationship between stresses and instantaneous deformations for wood under compression is determined from the Gerstner formula, and elastic work is assumed under tension. The solution is carried out using the finite element method in combination with the Newton-Raphson method and the Euler method according to the scheme that involves a stepwise increase in the load with correction of the stiffness matrix taking into account the change in the coordinates of the nodes with the sequential calculation of additional displacements of the nodes, which are due to the residual forces. The proposed approach for increasing the accuracy of determination of creep deformations at each step provides using the fourth-order Runge-Kutta method instead of the Euler method.

Results. Based on the Lagrange variational principle, expressions are obtained for the stiffness matrix and the vector of additional dummy loads due to creep. The method developed by the authors is implemented in the form of a program in the MATLAB environment. Calculation examples are given for parabolic arches simply supported at the ends without an intermediate hinge and with an intermediate hinge in the middle of the span under the action of a uniformly distributed load. The results obtained are compared in the viscoelastic and viscoelastic formulation. The reliability of the results is validated through the calculation in the elastic formulation in the ANSYS software package.

Discussion and Conclusions. For the arches considered, it is found that even with a load close to the instant critical, the growth of time travel is limited. Thus, the nature of their work under creep conditions differs drastically from the nature of the deformation of compressed rods. 

Introduction. Currently, the purification of wastewater and technological solutions by membrane methods is considered a promising way to neutralize liquid waste. Therefore, the task of developing an engineering method for calculating baromembrane devices is a challenge. Studies on methods involving calculation of design and process variables, membrane equipment design, research of technological features of membrane devices, selection of design schemes, as well as methods of strength and rigidity analysis, are investigated.

Materials and Methods. Basic elements of the body of the combined membrane apparatus are considered, a design scheme is proposed, and a method for calculating the strength and rigidity of the main load-bearing element, the cover, is described.

 Results. The methods determine the required dimensions of shells and plates for the development of a combined membrane apparatus, and evaluate the strength properties of the devices of this class. The construction elements of the apparatus (primarily, the load-bearing covers) must meet not only the requirements of efficiency and quality of separation and cleaning of solutions, but also the conditions for safe operation. Therefore, the design of the device covers should be based on the optimal design dimensions (thicknesses of round plates, toroidal shells, and support rings). To test the method, the stress-strain state of the membrane apparatus structure was calculated for strength and rigidity. As an example, we consider one cover presented in the form of an open toroidal shell. The evaluation of the application of this technique, taking into account the fact that the shell is mated with a round plate in the inner diameter, and with a ring in the outer diameter, has provided the determination of the required parameters.

Discussion and Conclusions. The obtained method of analytical description of the mechanical impact on the elements of the combined apparatus and the example of calculating the toroidal shell and plate, enables to evaluate the stressstrain state of the structure for strength and rigidity. The results of the calculation of covers made of various materials at different pressures are presented. Loading the combined apparatus with transmembrane pressure made it possible to determine the required dimensions of the shells and plates for its design and development. 

Introduction. In the context of the problem of plane deformation, a finite-element model of a natural landslide slope is developed. It allows for the joint work of a flow slide and a protective engineering structure. The Drucker-Prager model is used to take into account the physical nonlinearity of the slope layer material. To activate the kinematic instability, a viscoelastic interlayer is introduced into the design scheme, along which the landslide layer slides.

Materials and Methods. Numerical experiments were performed using the ANSYS Mechanical software package, which implements the finite element method in the form of the displacement method. Slope discretization is performed on the basis of PLANE42 flat four-node finite elements. To simulate the displacement of the landslide layer relative to the fixed base, the combined viscoelastic elements COMBIN14 were used.

Results. A physically nonlinear model of a natural landslide slope consisting of a base, a landslide layer, and a viscoelastic interlayer, is formalized. An engineering technique for analyzing the stress-strain state of the “slopeprotective structure” system has been developed, taking into account the kinematic instability of the landslide layer. A series of computational experiments was carried out.

Discussion and Conclusion. Based on the calculations performed, it is shown that the proposed method enables to specify the force action of the landslide layer on the protective structure and, thereby, to increase the reliability of the risk assessment when activating the landslide process. 

Introduction. The development of machine learning methods has given a new impulse to solving inverse problems in mechanics. Many studies show that along with well-behaved techniques of ultrasonic, magnetic, and thermal nondestructive testing, the latest methods are used, including those based on neural network models. In this paper, we demonstrate the potential application of machine learning methods in the problem of two-dimensional ultrasound imaging.

Materials and Methods. We have developed an experimental model of acoustic ultrasonic non-destructive testing, in which the probing of the object under study takes place, followed by the recording of the response signals. The propagation of an ultrasonic wave is modeled by the finite difference method in the time domain. An ultrasonic signal received at the internal points of the control object is applied to the input of the convolutional neural network. At the output, an image that visualizes the internal defect is generated.

Results. In the course of the performed complex of numerical experiments, a data set was generated for training a convolutional neural network. A convolutional neural network model, which is developed to solve the problem of visualizing internal defects based on methods of ultrasonic nondestructive testing, is presented. This model has a small size, which is 3.8 million parameters. Its simplicity and versatility provide high-speed learning and a wide range of applications in the class of related problems. The presented results show a high degree of information content of the ultrasonic response and its correspondence to the real form of an internal defect located inside the test object. The effect of geometric parameters of defects on the accuracy of the neural network model is investigated.

Discussion and Conclusion. The results obtained have established that the proposed model shows a high operating accuracy (F1 > 0.95) in cases when the wavelength of the probe pulse is tens of times less than the size of the defect. We believe that the combination of the proposed methods in this approach can serve as a good starting point for future research in solving flaw defection problems and inverse problems in general. 

Introduction. One of the ways to improve the accuracy of manufacturing parts by cutting is related to the control of elastic deformations of the tool and the workpiece. This is particularly true for slender parts, whose stiffness law along the tool path is given. In this case, the control parameter, as a rule, is the return flow rate, which affects the cutting forces, whose change causes variations in elastic deformations. To provide the specified accuracy of the diameter, it is required to coordinate the controlled trajectory of the feed drive speed with the feed rate and a priori given law of change in the stiffness of the workpiece or the law of variation of the cutting process parameters. To do this, it is required to determine the law of converting the engine speed into the feed rate, and, ultimately, into elastic deformations. This law depends on the stiffness of the mechanical part of the feed drive and the changing parameters of the cutting process.

Materials and Methods. The paper presents mathematical modeling and, on its basis, analysis of the conversion of the feed rate into cutting forces, taking into account the final stiffness value of the mechanical part of the drive and the evolutionary parameters of the cutting process.

 Results. It is shown that, starting from a certain critical value, the law of converting the feed rate into cutting forces becomes fundamentally dependent on the stiffness of the mechanical part of the drive. At the same time, there is an increase in time for setting a new force value when the feed rate varies, which affects the accuracy of providing forces that are consistent with the stiffness law of the part. The paper presents algorithms for calculating elastic deformations for a given stiffness law, as well as algorithms for calculating the trajectory of the feed rate at which the deformations remain constant. It is shown that the law of conversion is also affected by variations in the cutting parameters.

Discussion and Conclusion. The frequency and time characteristics of the conversion are discussed. A conclusion is made about the accuracy of the diameter formed through cutting, depending on the stiffness of the mechanical part of the feed drive and on some parameters of the cutting process. 

Introduction. Friction stir welding is widely used due to certain advantages of this method. Factors that reduce the strength of joints made of high-strength aluminum alloys are considered. When welding flat sheets, an effective way to increase the strength of the weld is edge thickening. The paper proposes a method for such thickening. A device is developed, calculations and experiments are carried out.

Materials and Methods. Laboratory equipment has been developed to provide simultaneous thickening of two edges to be welded. The main component of this equipment is a steel roller, which is rolled along the edges of two blanks and thickens them due to plastic deformation. The same setup can be used for the friction stir welding process. To calculate the geometry of the thickened edges and the parameters of the deforming roller depending on the value of the edge settlement, a mathematical model based on the contact problem for elastic (roller) and elastoplastic (blank) bodies with a bilinear hardening law has been developed. A three-dimensional simplified geometric model of the facility with account of its symmetry has been constructed. On the contact surfaces, special contact finite elements were selected and the finite element mesh was refined. The numerical implementation of the model was carried out in the ANSYS package.

Results. The theoretical model provides assessing the stress-strain state of interacting elements. On the basis of the developed finite element model, the parameters of the thickened edges are calculated, and the geometry of the thickened edges is defined. Using the developed laboratory equipment, full-scale experiments on thickening the edges of the blanks were carried out. The experimental results confirm the adequacy of the developed theoretical model and calculations based on it. The possibility of adjusting the size of the thickened edges is shown.

Discussion and Conclusion. A technology for obtaining thickened edges in places of welds is proposed. It will reduce the metal consumption of structures and ensure the bearing capacity of welded joints not lower than similar characteristics of the base metal. A theoretical model of the process is developed, and a numerical experiment providing the selection of the process parameters is carried out. 

Introduction. Elevators in residential and public buildings are the means of vertical transport. An elevator is one of the complex electromechanical devices of increased danger. Therefore, all stages of its life cycle are strictly limited by regulatory documents. The desired levels of safety and comfort are provided through the reasonable choice of the basic parameters and a constant maintenance of the system in good condition. The key factors that affect the implementation of regulatory requirements during the operation of the elevator installation are the quality of manufacturing of critical components, the level of real workload, taking into account the actual value of the spent resource, and the implemented maintenance program. Currently, when determining the maintenance schedule for elevators, such characteristics as the density of occupancy, the level of power loads, the actual operating time of the elevator and the counts of starts of the main drive are not taken into account. This study objective is the scientific rationale of the concept and methodology for developing the program of maintenance of specific elevator installations on the basis of studies of the level and mode of loading of load-bearing units.

Materials and Methods. The use of simulation modeling techniques to assess the load level of power units of an elevator installation and its kinematic indicators under the action of numerous random impacts is validated in the paper. The development of an indicator that characterizes the complex mode of elevator operation, taking into account the joint influence of the level of resource development, net operating time, number of starts, and the power load of the nodes, required the application of an expert method. The final part of the research program is the formation of specific recommendations on the maintenance schedule of elevators. It is based on the ranking of particular indicators.

Results. The performance feature of the elevator installation is that the service time of a customer is a function of many random variables. Mathematical models of the formation of force impacts are based on the representation of an electromechanical elevator as a dynamic one-degree-of-freedom system. Expressions for calculating the static tension of traction ropes and torques on the motor shaft are obtained. The problem of dynamics is solved. The loads whose values are the basis for performing simulation modeling of the operating modes of the elevator installation are determined.

Discussion and Conclusions. Feasibility of the regulations for the maintenance of passenger elevators is an urgent task, the solution to which determines the level of safety and comfort of passengers. Currently, the standards for the design and operation of elevator installations do not link the frequency of maintenance programs with the level of load and the amount of resource development. The paper provides a general statement of the problem and a methodology for the formation of a complex factor of the equivalent load. Mathematical models are given for calculating the power and temporary loads of the elevator, taking into account the nature of numerous random impacts. 

Introduction.The generation of polynomial power laws of motion for the synthesis of cam mechanisms is complicated by the need to determine the coefficients of power polynomials. The study objective is to discover a rational capability of generating рower law swith arbitrary terms number under s with an rbitrary number of terms under the synthesis of cam mechanisms.

Materials and Methods.A unified formula for determining the values of coefficients of power polynomials with any number of integers and/or non-integer exponents is derived through the so-called transfinite mathematical induction.  

Results.A unified formula for determining the values of coefficients, which gives correct results for any number of even and/or odd exponents, is presented. The correctness of the derived formula is validated by the results on the multiple checks for different numbers, even and odd values of the exponents of quinquinomial and hexanomial power functions.  

Discussion and Conclusions. A unified formula for determining the values of coefficients of power polynomials makes it possible to rationally define the laws of motion without finite and infinite spikes in the synthesis of elastic cam-lever systems. This provides a rational determination of the laws of motion without finite and infinite spikes in the synthesis of elastic cam-lever systems, and simple verification of the accuracy of the results obtained. The functions are particularly suitable for the synthesis of polydyne cams, as well as cams, since one polynomial can be used throughout the entire geometric mechanism cycle.

Introduction. In engineering practice, dynamic processes, with the help of which mechanics of interaction of machine components and structural elements are described and studied, are of great importance. These dynamic processes are the cause of large deformations leading to the destruction. The research objective is to develop a more accurate shock simulation algorithm through the controlled transformation of the mechanorheological shock process model from elasticviscous to elastic-viscoplastic.

Materials and Methods. Differential equations of the model movement are proposed. The conditions for the transformation of the model during the transition from elastic to plastic deformations, from the stage of loading the model to the stage of unloading under the shock interaction with the surface, are considered. When calculating deformations, the assumption is made that elastic and plastic deformations occur simultaneously from the very onset of the impact. The model functioning method is considered in detail, the algorithm of the model operation is developed, the logic of its functioning is described in detail.

Results. To study shock processes, a mechanoreological elastic-viscoplastic model was developed. An important parameter of the model is the force corresponding to the onset of plastic deformation. As a result of the research, a more perfect algorithm was created, and a new computer program was developed to study the shock process using an elasticviscoplastic model with an adjustable elastic-plastic transformation.

Discussion and Conclusions. The results obtained can be used to improve the accuracy and reliability of simulation of shock processes in order to further develop the techniques for determining the physical and mechanical characteristics of materials by shock methods. Knowledge of the mechanical characteristics of materials is required when solving various research problems through mathematical modeling of vibration and shock processes. At the same time, an important task is to adapt the design model to the real shock process, for which it is required to develop appropriate methods and techniques. 

Introduction. The organization of branches and repetitions in the context of logical programming is considered by an example of the Prolog language. The fundamental feature of the program in a logical programming language is the fact that a computer must solve a problem by reasoning like a human. Such a program contains a description of objects and relations between them in the language of mathematical logic. At the same time, the software implementation of branching and repetition remains a challenge in the absence of special operators for the indicated constructions in the logical language. The objectives of the study are to identify the most effective ways to solve problems using branching and repetition by means of the logic programming language Prolog, as well as to demonstrate the results obtained by examples of computational problems.  Materials and Methods. An analysis of the literature on the subject of the study was carried out. Methods of generalization and systematization of knowledge, of the program testing, and analysis of the program execution were used.  Results. Constructions of branching and repetition organization in a Prolog program are proposed. To organize repetitions, various options for completing a recursive cycle when solving problems are given.  Discussion and Conclusions. The methods of organizing branches and repetitions in the logic programming language Prolog are considered. All these methods are illustrated by examples of solving computational problems. The results obtained can be used in the further development of the recursive predicates in logical programming languages, as well as in the educational process when studying logical programming in the Prolog language. The examples of programs given in the paper provide using them as a technological basis for programming branches and repetitions in the logic programming language Prolog.

Introduction. Internet of Things (IoT) is one of the promising innovative technologies. Every year more and more people are involved in the use of smart things. At the same time, a relatively small number of papers are devoted to the study of the social value of technology and the experience of human interaction with this technology. It is important to study the features and prospects of the technology, to analyze the attitude and willingness of people to use it. Materials and Methods. We have conducted an Internet survey, in which special attention is paid to the place of IoT in the life of modern people, their attitude to the concept of devices. The obtained data is processed and systematized. Results. The analysis of the survey results allowed us to draw conclusions regarding the attitude and willingness of young people to apply this technology. In the course of the study, the IoT concept was defined, the conditions required for the existence and functioning of the technology were described, the advantages of IoT technology were generalized, information technologies interacting with this technology were specified, the tasks that require solutions for the successful and effective implementation of IoT into Russian reality were listed. Discussion and Conclusions. The Internet of Things is a technology that, with a consistent and systematic solution to a number of problems, can become a significant factor in the development of both individual spheres of life and activity, and the country as a whole. At the same time, it is important to study and consider the social impact of technology dissemination. This will increase trust in the IoT and eliminate negative impacts. The survey shows that young people tend to use smart things more widely. It is necessary to expand the range of smart things, to more confidently introduce the basics of practical application of IoT technology into educational programs, to discuss issues, ways to solve the tasks and pilot projects related to this technology widely in the media. This will enable to train not only people who are practically interested in IoT, but also qualified personnel who are able to solve problems in a new way.