Technical mechanics最新文献

{"title":"Marching algorithm to calculate supersonic flow past a tilting-nose rocket","authors":"V. P. Halynskyi","doi":"10.15407/itm2022.01.016","DOIUrl":"https://doi.org/10.15407/itm2022.01.016","url":null,"abstract":"This paper presents a marching algorithm for the calculation of supersonic flow past a tilting-nose rocket. A feature of the algorithm is that the marching direction of supersonic flow calculation for the nose does not coincide with that for the main part of the rocket surface. Because of this, at first flow past the nose is calculated in a cylindrical coordinate system, the flow field parameters being stored at marching cross-sections. The start and the end of the parameter storage interval in the flow field are determined from the condition of the intersection of the bow shock wave with a plane in which an initial flow field is to be specified for the calculation of flow past the main part of the rocket surface. The flow field is interpolated in two stages, First, in the cylindrical coordinate system bound to the main part of the rocket surface in the initial data plane, the radial coordinates of the bow shock wave are determined at meridional sections. From the radial coordinates of points on the rocket surface and the bow shock wave, new computational grid node coordinates are determined at meridional sections in the cylindrical coordinate system of the main part. Using the new computational grid coordinates specified in the cylindrical coordinate system of the main part, old coordinates specified in the cylindrical coordinate system of the nose are determined with the use of expressions that relate the two coordinate systems to each other. The flow parameters at a point with the calculated coordinates are calculated using linear interpolation of the stored flow field parameters in the cylindrical coordinate system bound to the nose. The calculated flow field is used as initial data for the marching calculation of the main part of the rocket, The paper presents the results of calculation of the aerodynamic characteristics of a tilting-nose rocket in a supersonic flow at different values of the nose angle. The proposed algorithm may be used in a prompt calculation of the aerodynamic characteristics of rockets with tilting elements. In doing so, use may be made of a standard program of rocket flow calculation with an added block for the storage and interpolation of the flow field in a tilted cylindrical coordinate system with a shifted origin, which allows the marching direction to be changed.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123640042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of the elastically deformed state of a wheel-rail pair with different initial profiles and wear degrees","authors":"S. Pasichnyk, N. Bezrukavyi","doi":"10.15407/itm2022.01.067","DOIUrl":"https://doi.org/10.15407/itm2022.01.067","url":null,"abstract":"A topical problem for the Ukrainian railway transport is its integration into the world’s transport system. The Ukrainian and the European railways differ in rail track parameters, which complicates railway communication. As shown by international experience, the most promising way to resolve this problem is to use gage-changeable wheelsets, which may be adjusted to different track gages. Besides, the Ukrainian and the EU railways use different wheel and rail profiles, whose shape greatly affects the rail?vehicle interaction. In service, the profile geometry may change significantly due to contacting pair wearing-in, which may result in a number of negative consequences caused by rail and wheel profile mismatch. The aim of this work is to study the effect of the wear-caused change of the initial rail and wheel profiles on the elastically deformed state of wheel?rail pairs for wheelsets operating on 1,520 mm and 1,435 mm gage railways without truck change. Worn wheel and rail profiles were studied by mathematical and computer simulation. The elastically deformed state of a wheel?rail pair was studied by the finite-element method, which allows one to analyze various complex-geometry engineering structures and perform a 3D simulation of physical processes. The interaction of worn wheels and rails with initial profiles used on 1,520 mm and 1,435 mm gage railways was analyzed to give the contact stress distribution over the wheel and rail profile zones for wheel?rail contact pairs theoretically possible in Ukraine?EU railway communication. This made it possible to assess rail?vehicle interaction conditions in Ukraine?EU railway communication without wheelset change. The results of the study of the effect of wheel profile change on the elastically deformed state made it possible to formulate recommendations on the practicability of existing profiles and direct ways to improving the profile geometry of wheelsets operating on 1,520 mm and 1,435 mm gage railways without truck change.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131843232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction of a multiplicative-additive criteria convolution in the space of quantitative and qualitative indices to determine the priority of projects","authors":"V. Mamchuk","doi":"10.15407/itm2022.01.077","DOIUrl":"https://doi.org/10.15407/itm2022.01.077","url":null,"abstract":"One of the main problems in scientific activity organization on a competitive basis is to improve methods of R&D project evaluation and priority determination. The project priority level may be determined using approaches based on the multi-attribute utility theory (MAUT), whose development is the subject matter of many studies and publications. Despite of the large number of publications on the subject, the development of a scientifically substantiated mathematical apparatus for multicriteria project evaluation is still a topical and challenging problem. The complexity of the development of project priority determination methods is due to difficulties in the construction of a unified rating scale that would allow one to measure the value of project indices differing in physical content and dimension. That is, what is difficult is the structurization of a decision-making person (DMP)’s preferences and the formalization of preference evaluation. It is also difficult to construct a criterion-target model that would adequately represent the system of DMP preferences in the form of a scalar value function, which is termed a criteria convolution, an integral criterion, or an integral value function (IVF). MAUT-based computational algorithms widely use procedures of common criteria scaling, in which one quality index is replaced with another. Such algorithms have a resolution equal to one; however, they operate with quantitative criteria alone, thus significantly narrowing their application area. Another drawback of theirs is the lack of simple methods to determine the value function at indifference (DMP preference equality) points. The aim of this work is to eliminate these drawbacks in a multiplicative-additive IVF model. To do this, the following was done. Functional relationships between DMP preferences and alternative quality indices were established to give analytical expressions for evaluating local value functions at indifference points. A method was developed for constructing a multiplicative-additive criteria convolution to evaluate and rank alternatives in the space of quantitative and qualitative indices. An algorithm was developed to determine the priority of projects; the algorithm allows one to rank alternatives with a resolution equal to one. In this work, decision theory, multicriteria utility theory, and verbal decision analysis methods were used. The results obtained may be used in R&D efficiency evaluation, competitive project selection, and space program formation in the rocket space industry.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114537275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Verification of analytical antiderivatives forms using correlation analysis for mechanical problems","authors":"A. Alpatov, V. Kravets, V. Kravets, E. Lapkhanov","doi":"10.15407/itm2022.01.026","DOIUrl":"https://doi.org/10.15407/itm2022.01.026","url":null,"abstract":"An analytical search for antiderivative functions (indefinite integrals) is widely used in the mathematical simulation of various engineering, economic, ecological, biological, social, and other processes. In their turn, mechanical problems have many subproblems whose solution involves analytical integration methods. Among these problems is the problem of development of analytical models for navigation and ballistics support and control theory models in space rocket engineering. The advantage of this approach to mathematical simulation is a fast analysis of the state of dynamic systems on different time intervals without calculating all previous states. In their turn, for some classes of functions, antiderivatives may be found in several different ways, as a result of which there exist several different forms of antiderivatives that are hard to verify by the classical method in standard form. This is mainly due to the choice of various combinations of integration methods used in the development of analytical models, in particular in problems of applied mechanics. Taking into consideration these difficulties in the verification of the set of antiderivative functions, this paper proposes a method to check their analytical forms for correspondence with the use of correlation analysis. In doing so, the arrays of the values of each antiderivative form at certain nodal points are represented as a set of random variables. With this in mind, it is suggested that the verification process be conducted with the use of the standard approach based on correlation analysis (using Pearson’s correlation coefficient). The efficiency of the method is shown by the example of verifying the antiderivatives of the reciprocal of a squared quadratic trinomial. This approach will make it possible to check the adequacy of the i-th candidate antiderivative and to adapt the problem to the standard form.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127801059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assessment of thrust chamber stability margins to high-frequency oscillations based on mathematical modeling of coupled ‘injector – rocket combustion chamber’ dynamic system","authors":"O. Nikolayev, I. D. Bashliy","doi":"10.15407/itm2022.01.003","DOIUrl":"https://doi.org/10.15407/itm2022.01.003","url":null,"abstract":"High-frequency instability of a liquid-propellant rocket engine (LRE) during static firing tests is often accompanied by a significant increase in dynamic loads on the combustion chamber structure, often leading to a chamber destruction. This dynamic phenomenon can also be extremely dangerous for the dynamic strength of a liquid-propellant rocket engine. The calculation of acoustic combustion product oscillation parameters is important in the design and static firing tests of such rocket engines. The determination of the oscillation parameters (natural frequencies and stability margins such as oscillation decrement) is one of the problems solved in the LRE design period as part of the development of measures to ensure the engine stability. The main aim of the paper is to develop a numerical approach to determining the parameters of acoustic oscillations of combustion products in liquid-propellant rocket engines combustion chambers taking into account the features of combustion space configuration and the variability of gaseous medium physical properties depending on the axial length of the chamber, acoustic impedance in critical throat and dissipation effects (damping experimental values) in the shell structure and the gas media in the chamber. The approach is based on mathematical modeling of the coupled ‘chamber shell structure – gas’ dynamic system by using the finite element method and the CAE (Computer Aided Engineering) system. The developed approach testing and further analysis of the results for the RD 253 engine using nitrogen tetroxide and unsymmetrical dimethylhydrazine as a propellant pair were carried out. The dynamic system shapes and frequencies of longitudinal, tangential and radial modes are determined. The results of mathematical modeling of the dynamic system indicate a satisfactory agreement of the calculated decrements of the first longitudinal oscillation mode and third tangential oscillation mode with the experimental decrements obtained by hot-fire tests data. From system harmonic analysis of the thrust chamber, it follows that the dynamic pressure gain factor of the gas media in the chamber at the first longitudinal mode frequency is 1.6 times greater than the system dynamic gain in the tangential mode. At the same time, the oscillation decrement for the system tangential mode is 2 times smaller than that of the first longitudinal mode. This means that the thrust chamber tangential mode is more dangerous and can lead to rocket engine combustion instability. The effect of the injector on the high-frequency stability of the combustion chamber and the possibility of partial suppression of combustion chamber thermoacoustic oscillations by adjusting the high-frequency dynamics of the injector are shown theoretically.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128704693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Creep failure time prediction using the reliability theory","authors":"V. Poshyvalov","doi":"10.15407/itm2022.01.036","DOIUrl":"https://doi.org/10.15407/itm2022.01.036","url":null,"abstract":"This paper proposes a probabilistic model of structural material creep failure, which is based on the reliability theory. It is assumed that for specimen failure under the action of a constant load, there exists a functional relationship between the creep strain accumulated to a given time and the nonfailure probability at that time. This assumption and the fact that in most cases the failure rate function and a typical creep strain rate vs. time curve are nonmonotonic and U-shaped made it possible to obtain the nonfailure probability. The creep and the long-term strength equations are adopted in power law form with account for specimen necking in the deformation process, For the power law of creep without strengthening, relationships are obtained for determining the average time to failure and the rms deviation of the long-term strength of a rod tensioned with a constant force in creep. The long-term strength variation coefficient is determined; the coefficient has two finite limits. It is shown that with decreasing strength the brittle zone demonstrates an increase in measured failure time spread at equal stress levels, while in the tough zone this is absent. Theoretical calculations are compared with long-term strength test results for 12Cr18Ni10Ti corrosion-resistant steel at 850°C. The material constants were determined from the results of creep and long-term strength test data processing. The theoretical creep failure time for the linear dependence of the failure rate function on the creep strain rate is less than for the quadratic one, while the rms deviations are greater. In both cases, the theoretical results are in satisfactory agreement with the experimental data both for the failure time and for its rms deviation.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126483076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental and numerical analysis of the stress state of honeycombs made by additive technologies","authors":"I. Derevianko, B. Uspensky, K. Avramov, O. Salenko","doi":"10.15407/itm2022.01.042","DOIUrl":"https://doi.org/10.15407/itm2022.01.042","url":null,"abstract":"This paper proposes an approach to the experiment-and-calculation analysis of the tension of honeycombs made by FDM additive technologies. The approach includes experimental tension analysis. Tension tests of honeycombs were conducted on a certified TiraTest 2300 universal tension testing machine. To do this, sets of honeycomb samples were prepared. The method of honeycomb manufacturing by FDM additive technologies is described. The vertices of a honeycomb cell row are fixed in the vise-type clamps of the tension testing machine. The experimental analysis is accompanied by a numerical finite-element simulation of tension tests. To simulate honeycomb tension, nine mechanical characteristics of the material in material axes must be known. These nine parameters are considered in the paper. A direct finite-element simulation of a honeycomb with account for the deformation of all its cells was performed. To provide the uniformity of sample deformation in a physical experiment, the sample is loaded by setting the displacement of one of its ends to a constant value. In doing so, the other end is clamped. As follows from the experimental analysis, before failure the honeycomb cell end displacements are comparable with the honeycomb cell thickness. Because of this, the geometrically nonlinear deformation of the honeycomb cells in tension is accounted for in the calculations, and a nonlinear problem is solved using ANSYS. The direct simulation of honeycombs and the analysis of their homogenized model give different results. In the direct simulation of honeycombs, they are considered as thin-walled beams working in bending. In this case, the geometrical nonlinearity contributes significantly to the structural deformation. For plate tension (homogenized model), the contribution of the geometrical nonlinearity is very small, Because of this, the stress-strain response is close to linear.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126319514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asessment of dynamic loads on a motor-car train with a passive safety system in its collision with a large road vehicle","authors":"M. Sobolevska, D. Horobets","doi":"10.15407/itm2022.01.051","DOIUrl":"https://doi.org/10.15407/itm2022.01.051","url":null,"abstract":"A topical problem of the home railway transport is motor-car train renewval, speed increase, and safety improvement in accordance with the Ukrainian State Standards DSTU EN 12633 and DSTU EN 15227, which specify the passenger car crashworthiness and passive safety, respectively, in emergency collisions with various obstacles. Relying on the world experience, researchers of the institute of Technical Methanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine developed a passive protection concept for home high-speed passenger trains in emergency collisions according to the DSTU EN 15227 requirements, proposals on the passive propection of a home motor-car train head car, lower- and upper-level honeycomb energy-absorbing devoces (EAD 1 and UL EAD, respectively) for the head car front part, and EAD 2 and EAD 3 low-level devices to be installed in intercar connecteions. The upper- and lower-level protective devices for home motor-car trains were developed based on finite-element simulation results using previous experience in the development of a passive protection device for a high-speed passenger locomotive and the results of a successful crash test of its proptotype. For Scenario 3, which chraracterizes a collision of a reference motor-car train at 110 km/h with a 15 t large road vehicle at a railway crossing, a model of a large deformable obstacle (LDO) was developed in compliance with the DSTU EN 15227 requirements. Finite-element models were developed to determine the force characteristics of interaction between the proposed head car passive protection devices and an LDO. The aim of this paper is to determine dynamic loads on a motor-car train equipped with passive protection devices in its collision with a large road vehicle. Based on a mathematical collision model for identical motor-car trains, a mathematical model was developed for a collision of a reference train with a large road vehicle at a railway crossing (Scenario 3) with account for the determined force characteristics of obstacle ? two EAD 1 low-level devices and obstacle ? two UL EAD upper-level devices interaction and the in-collision work of the head car structure. Dynamic loads on the cars of a reference train with a passive safety system (a head car mass of 80 t and intermediate car masses of 50 t or 64 t) were analyzed for its collision by Scenario 3. Two EAD layouts in the head car front part were studied. It was found that the proposed passive protection of the reference train cars meets the DSTU EN 15227 criteria for Scenario 3 for both EAD layouts and the determined variants of lower- and upper-level EAD use according to the intermediate car masses. The proposed mathematical model of dynamic loads on a passenger train with a passive safety system in its collision with a large road vehicle and the results obtained may be used in designing an up-to-date high-speed motor-car train to the DSTU EN 15227 requirements.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127418904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Refinement of the rail–wheel contact pair to improve rail–wheel interaction conditions for railway vehicles with an increased axle load","authors":"T. Mokrii, I. Malysheva, N. Bezrukavyi, I.M. Ladyhin","doi":"10.15407/itm2021.04.129","DOIUrl":"https://doi.org/10.15407/itm2021.04.129","url":null,"abstract":"At present, one of the global trends in railway transport development, which becomes clearer and clearer, is increasing the axle load of freight cars, which gives a considerable economic benefit. In this connection, of importance is not only the car design, but also the car capacity utilization factor: the higher this factor, the more economically efficient the car use. Because of this, one of the priority global lines in increasing the volume of fright traffic and the railway operation efficiency is increasing the carrying capacity of freight cars. Preparing the railways for cars with increased axle loads calls for the development of measures to decrease the track deformability, in particular by choosing appropriate wheel and rail profiles. The aim of this work was to develop recommendations on refining the wheel?rail contact pair to improve curve negotiation by railway vehicles with an increased axle loads on the Ukrainian railways. This paper presents the proprietary R-ITM wear-resistant railhead profile. The effect of the new profile on wheel?rail interaction in negotiating a curve of radius 300 m at a constant speed was studied for different cars. In doing so, emphasis was on wheel?rail interaction for a new-generation freight car on 18-9817 trucks with an axle load increased to 36 tf. The studies conducted made it possible to formulate the following recommendations: to improve curve negotiation by railway vehicles with increased axle loads, reduce the adverse effect on the track and improve traffic safety, new proprietary contact pair profiles are recommended: the ITM-73-03 wheel profile for cars, and the R-ITM railhead profile for outer rails together with the standard R65 railhead profile for inner rails.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129276068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptation of gas-dynamic characteristic arrays to automated ballistics support of spacecraft flight","authors":"T. H. Smila, L. Pecherytsia","doi":"10.15407/itm2021.04.089","DOIUrl":"https://doi.org/10.15407/itm2021.04.089","url":null,"abstract":"The current level of the design and use of new-generation spacecraft calls for a maximally automated ballistics support of engineering developments. An integral part of the solution of this problem is the development of an effective tool to adapt discrete functions of gas-dynamic characteristics to the solution of various problems that arise in the development and use of space complexes. Simplifying the use of bulky information arrays together with improving the accuracy of approximation of key coefficients will significantly improve the ballistics support quality. The aim of this work is to choose an optimum method for the approximation of a discrete function of two variable spacecraft aerodynamic characteristics. Based on the analysis of the advantages and drawbacks of basic methods of approximation by two fitting criteria: the maximum error and the root-mean-square deviation, recommendations on this choice were made. The methods were assessed by the example of the aerodynamic coefficients of the Sich-2M spacecraft’s simplified geometrical model tabulated as a function of the spacecraft orientation angles relative to the incident flow velocity. Multiparameter numerical studies were conducted for different approximation methods with varying the parameters of the approximation types under consideration and the approximation grid density. It was found that increasing the number of nodes of an input array does not always improve the accuracy of approximation. The node arrangement exerts a greater effect on the approximation quality. It was established that the most easily implementable method among those considered is a step interpolation, whose advantages are simplicity, quickness, and limitless possibilities in accuracy improvement, while its significant drawbacks are the lack of an analytical description and the dependence of the accuracy on the grid density. It was shown that spline functions feature the best approximating properties in comparison with other mathematical models. A polynomial approximation or any approximation by a general form function provide an analytical description with a single approximating function, but their accuracy of approximation is not so high as that provided by splines. It was found that there exists no approximation method that would be best by all criteria taken together: each method has some advantages, but at the same time, it has significant drawbacks too. An optimum approximation method is chosen according to the features of the problem, the priorities in approximation requirements, the required degree of approximation, and the initial data organization method.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134148310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}