Scientific journal TECHNICAL MECHANICS ISSN 1561-9184 (Print), ISSN 2616-6380 (Online) Technical Mechanics is dedicated to advancing scientific knowledge and fostering innovation in the fields of aviation and space engineering, applied mechanics, and material science. Its primary aim is to provide a platform for the dissemination of original research articles, comprehensive reviews, and theoretical developments that contribute to the progress of engineering sciences and their practical applications. In 1993, the Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine started to publish an interdepartmental collection of scientific papers entitled Tekhnichna Mekhanika (the Ukrainian for technical mechanics), which in September 1997 received the status of a scientific journal. In 2017, the institute received a new state registration certificate, according to which the journal has the official English title of Technical Mechanics and has the right to publish papers in English and to be distributed internationally. The journal publishes papers in Ukrainian and English (at authors’ choice). The journal is indexed in Google Scholar та Index Copernicus. The journal is sent to the V. I. Vernadsky National Library of Ukraine to be placed in the Scientific Periodicals of Ukraine database. All papers are assigned a DOI (CrossRef). DOI prefix: 10.15407/itm Abbreviated title: Teh. Meh.; ТМ. Authors retain copyright to their materials published in Technical Mechanics, and the journal does not claim any intellectual property rights to the authors’ content. Authors may deposit the final version of their paper in institutional or any other repositories where the paper will be in open access (at their own choice). Technical Mechanics is in diamond open access, i.e., free both for authors to publish in and for readers to access all papers and issues. Once published, all papers are immediately in open access for reading, downloading, and use without any technical limitations, i.e., without any access delay. The Editorial Board of Technical Mechanics is guided by international ethical standards for scientific publications and adheres to an open access policy. All submitted papers are to be peer-reviewed and checked for plagiarism. Starting with June 2026, the journal is to publish papers of the Mechanical Engineering and Machine Building cluster: G 8 Material Science; G 9 Applied Mechanics; G 12 Aeronautical and Space-Rocket Engineering. Journal website: https://journal-itm.dp.ua Media identifier in the Register of Subjects in the Media Field: R30-03759 In 2020, the journal was included in the list of Ukrainian specialized scientific editions (category B) by the Ministry of Education and Science of Ukraine’s orders No. 886 of July 2, 2020, and No. 1188 of September 24, 2020, in: 113 Applied Mathematics; 131 Applied Mechanics; 134 Aeronautical and Space-Rocket Engineering; 151 Automation and Computer-Integrated Technologies; 104 Physics and Astronomy. Frequency: 4 issues a year Founders: Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine ​ National Academy of Sciences of Ukraine Publisher: Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine ROR ID: https://ror.org/003ed9546 National Joint Register Code: 05539962 Publisher website: https://itm.dp.ua
STUDY OF THE PERFORMANCE OF PLANAR ANTENNA ARRAYS AS A FUNCTION OF THEIR TOPOLOGY AND THE PROPERTIES OF THEIR STRUCTURAL MATERIALS
DOI: https://doi.org/10.15407/itm2026.01.123 The rapid development of unmanned aerial vehicles and the extension of their range of application increase requirements for radar systems, in particular in terms of detecting small-sized targets with a low effective scattering area in a complex interfering environment. One of the promising engineering solutions for such systems is the use of planar antenna arrays, which provide electronic control of the radiation pattern, a high scanning speed, and design scalability. The goal of this work is to assess the effect of the number of radiating elements, the relative dielectric constant, and the physical thickness of the dielectric substrate on the electrodynamic characteristics and radiation parameters of planar antenna arrays. The study analyzes the radiation patterns, the gain, the energy potential, and the operating frequency band at different numbers of array elements. The work is based on numerical simulation in the CST Studio Suite environment using the finite integral method. Use is made of the parameterization of the emitter dimensions for resonance correction and the linear extrapolation method for estimating the characteristics of many-element arrays. The work investigates the electrodynamic characteristics of planar antenna arrays built on the basis of rectangular microstrip radiating elements with a corporate feed system. A 2×2 subarray was chosen as the basic element, which was subsequently scaled to 4×4 and 8×8 element configurations. Particular attention is paid to the effect of the dielectric substrate parameters, in particular its relative permittivity and physical thickness, on the radiation characteristics of the array. It is shown that the use of the Rogers 5880 dielectric substrate of standard thickness provides an optimal balance between radio technical characteristics, mechanical rigidity, and manufacturability. A stable trend is found to gain increase and main lobe narrowing with array scaling and to frequency-band extension in many-element arrays. The scientific novelty lies in a comprehensive justification of the choice of geometric parameters of the substrate and the number of array elements, which is based on a balance between industrial manufacturing standards and the resolution required for detecting targets with a small effective scattering area. The obtained data allow one to design effective radar systems for small-sized object tracking. The use of a standard substrate thickness (1.575 mm) significantly simplifies the industrial process of antenna system production and reduces its cost. REFERENCES 1. Rojhani N, Shaker G. Comprehensive review: effectiveness of MIMO and beamforming technologies in detecting low RCS UAVs. Remote Sens. 2024. V. 16. No. 6. 1016. https://doi.org/10.3390/rs16061016 2. Seidaliyeva U. , Ilipbayeva L., Taissariyeva K., Smailov N., Matson E. T. Radar-Based Drone Detection Technologies. Encyclopedia.pub. 9 pp. https://encyclopedia.pub/entry/53402 3. Xu Z., Zhou Z., Wu D., Xu X., Fellow Y. Z. CKM-enabled joint spatial-doppler domain clutter suppression for low-altitude UAV ISAC. Journal of Latex Class Files. 2021. V. 14. No. 8. 13pp. 4. Liu Q., Song M., Yu J., Liang P., Wang T., Zeng C., Zhang Z., Gao Y., Liu L. A circular fitting clutter suppression algorithm based on ISAC for low altitude UAVs. Sensors. 2025. V. 25. No. 20. 6285. https://doi.org/10.3390/s25206285 5. Ghofur M.J.U., Riyanto E. AI-driven adaptive radar systems for real-time target tracking in urban environments. Journal of Technology Informatics and Engineering (JTIE). 2025. V. 4. No. 1. Pp. 135-155. https://doi.org/10.51903/jtie.v4i1.289 6. Fontanesi G., Guerra A., Guidi F., V'asquez-Peralvo J. A., Shlezinger N., Zanella A., Lagunas E., Chatzinotas S., Dardari D., Djuri'c P. M. A deep-NN beamforming approach for dual function radar-communication THz UAV. IEEE Transactions on Vehicular Technology. 2025. Iss. 1. Pp. 746 - 760. https://doi.org/10.1109/TVT.2024.3453194 7. Costanzo S., Buonanno G. Distributed phased-array radars exploiting collaborative beamforming and diversity techniques for remote sensing applications. IEEE Open Journal of Antennas and Propagation. 2025. V. 6. No.3. Pp. 864-878. https://doi.org/10.1109/OJAP.2025.3552517 8. Norrud H. Antenna design of a radar phased array using drone swarms. Lund University publications. Thesis, printed in Sweden. January 20, 2025. 61 pp. https://lup.lub.lu.se/student-papers/record/9183205/file/9183212.pdf (Last accessed on January 20, 2026). 9. Ghattas N., Ghuniem A. M., Abdelsalam A. A., Magdy A. Planar antenna arrays beamforming using various optimization algorithms. IEEE Access. 2023. Р. 68486-68500. https://ieeexplore.ieee.org/document/10173536 (Last accessed on December 13, 2025). https://doi.org/10.1109/ACCESS.2023.3292792 10. Hou L., Jin L., Huang K., Xiao S., Lou Y., Chen Y. Beamspace spatial smoothing MUSIC DOA estimation method using dynamic metasurface antenna. Entropy. 2025. V. 27. No. 4. 335. https://doi.org/10.3390/e27040335 11. Warnick K. F., Spencer J. C. Phased array radar systems for small unmanned aerial vehicles. Google patents. United States. Patent No: US 10, 317, 518 B2. Jun. 11, 2019. https://patents.google.com/patent/US10317518B2/en (Last accessed on December 20, 2025). 12. Jin K., Han S.-S., Baek D., Lee H. L. Small drone detection using hybrid beamforming 24 GHz fully integrated CMOS radar. Drones. 2025. V. 9. No. 7. 453. https://doi.org/10.3390/drones9070453 13. Lee C. U., Noh G., Ahn B. K., Yu J.-W., Lee H. L. Tilted-beam switched array antenna for UAV mounted radar applications with 360 coverage. Electronics. 2019. V. 8. No. 11. 1240. https://doi.org/10.3390/electronics8111240 14. Parveez Shariff B. G., Mane P. R., Kumar P., ALI T., Alsath M. G. N. Planar MIMO antenna for mmwave applications: Evolution, present status & future scope. Heliyon. 2023. V. 9. No. 2. e13362. https://doi.org/10.1016/j.heliyon.2023.e13362 15. Choi B., Oh D., Kim S., Chong J.-W., Li Y.-C. Long-range drone detection of 24 G FMCW radar with E-plane sectoral horn array. Sensors. 2018. V. 18. No. 12. 4171. https://doi.org/10.3390/s18124171 16. Jung J.-I., Yang J.-R. 5.8-GHz Patch antenna with an enhanced defected ground structure for size reduction and increased bandwidth. Journal of Electromagnetic Engineering and Science. 2022. V. 22. No. 3. Рp. 245-25. https://doi.org/10.26866/jees.2022.3.r.83 17. Laabadli A.-A., Mejdoub Y., Elamri A., Tarbouch M. Design of a miniaturized patch antenna for 2.45/5.8 GHz applications. International Journal of Advances in Applied Sciences. 2025. V. 14. No. 1. Рp. 101-110. https://doi.org/10.11591/ijaas.v14.i1.pp101-110
SPACEBORNE THERMAL IMAGING OF THE EARTH SURFACE: THE TRENDS AND THE DEVELOPMENT PROSPECTS
DOI: https://doi.org/10.15407/itm2026.01.102 The spaceborne thermal imaging of the Earth plays a key role in monitoring natural and anthropogenic processes, such as wildfires and volcanic activity. It is used to measure the surface temperature, assess crop moisture levels, and determine the rock composition. However, the availability and spatial resolution of such data have long been significantly inferior to optical counterparts due to a number of technical difficulties. In recent years, the situation has been changing thanks to the development of small commercial Earth remote sensing spacecraft constellations and the application of new technologies. This article analyzes the current trends in and the prospects for the development of thermal infrared imaging by small satellites plus nighttime optical imaging projects. Particular attention is paid to commercial constellations, such as OTC (OroraTech / Spire Global), HotSat (SatVu / Leonardo), Hydrosat, FireSat (Muon Space), EarthDaily, etc. Their size, orbital parameters, imaging frequency, spectral capabilities, spatial resolution, and payload are investigated. It is shown that most thermal imaging constellations have a dual, civilian and military, purpose. A transition to multispectral imaging in the mid-wave and long-wave infrared ranges and the use of synchronous thermal and optical imaging are observed. Less energy-intensive uncooled sensors (microbolometers) are being introduced. Under development is high-detail nighttime optical imaging by American and Chinese companies’ small satellites with traditional optical Earth observation capabilities. Increasing use is made of artificial intelligence (AI) methods for preliminary data processing, improving spatial resolution, and autonomous anomaly detection directly onboard satellites. Research is in progress in the field of autonomous guidance and attitude control of satellites using AI. REFERENCES 1. Khramov D. O., Pyrozhenko O. O. Optical methods of Earth remote sensing and prospects for their use in commercial spacecraft. Teh. Meh. 2024. No. 4. Pp. 17-30. (In Ukrainian). https://doi.org/10.15407/itm2024.04.017 2. Khramov D. O., Maslova A. I., Pyrozhenko O. O. Microwave methods of Earth remote sensing and the prospects for their use. Teh. Meh. 2025. No. 3. Pp. 98-113. (In Ukrainian). https://doi.org/10.15407/itm2025.03.098 3. Botelho R. C., Xavier A. L. A unified satellite taxonomy proposal based on mass and size. Advances in Aerospace Science and Technology. 2019. V. 4. No. 4. Pp. 57-73. https://doi.org/10.4236/aast.2019.44005 4. Gillespie A. et al. A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images. IEEE Transactions on Geoscience and Remote Sensing. 1998. V. 36. No. 4. Pp. 1113-1126. https://doi.org/10.1109/36.700995 5. Sobrino J. A., Jiménez-Muñoz J. C. Minimum configuration of thermal infrared bands for land surface temperature and emissivity estimation in the context of potential future missions. Remote Sensing of Environment. 2014. V. 148. Pp. 158-167. https://doi.org/10.1016/j.rse.2014.03.027 6. Li X. et al. ECOSTRESS estimates gross primary production with fine spatial resolution for different times of day from the International Space Station. Remote Sensing of Environment. 2021. V. 258. 112360. https://doi.org/10.1016/j.rse.2021.112360 7. ASTER: Advanced Spaceborne Thermal Emission and Reflection Radiometer. URL: https://asterweb.jpl.nasa.gov (Last accessed on December 4, 2025). 8. Abrams M., Yamaguchi Y. Twenty years of ASTER contributions to lithologic mapping and mineral exploration. Remote Sensing. 2019. V. 11. No. 11. 1394. https://doi.org/10.3390/rs11111394 9. Chen Q. et al. ASTER and GF-5 Satellite data for mapping hydrothermal alteration minerals in the Longtoushan Pb-Zn Deposit, SW China. Remote Sensing. 2022. V. 14. 1253. https://doi.org/10.3390/rs14051253 10. Gomez C. et al. Using ASTER remote sensing data set for geological mapping in Namibia. Physics and Chemistry of the Earth, Parts A/B/C. 2005. V. 30, No. 13. Pp. 97-108. https://doi.org/10.1016/j.pce.2004.08.042 11. Lee C. M. et al. An introduction to the NASA Hyperspectral InfraRed Imager (HyspIRI) mission and preparatory activities. Remote Sensing of Environment. 2015. V. 167. Pp. 6-19. https://doi.org/10.1016/j.rse.2015.06.012 12. Portela B. et al. Landsat Next current design for geological remote sensing: VNIR-SWIR-TIR data continuity and new opportunities. Science of Remote Sensing. 2025. V. 12. 100258. https://doi.org/10.1016/j.srs.2025.100258 13. Cawse-Nicholson K. et al. NASA's surface biology and geology designated observable: A perspective on surface imaging algorithms. 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Jilin-1GP01_02 - Chang Guang Satellite Technology Co., Ltd. URL: https://www.jl1.cn/EWeb/product_view.aspx?id=676 (Last accessed on December 20, 2025). 19. NOVI Sensor Suite. URL: https://www.novispace.ai/sensor-suite (Last accessed on December 25, 2025). 20. Canadian Space Agency: WildFireSat data sheet. URL: https://www.asc-csa.gc.ca/eng/satellites/wildfiresat/data-sheet.asp (Last accessed on December 27, 2025). 21. Li L., Yu J., Chen F. TISD: A three bands thermal infrared dataset for all day ship detection in spaceborne imagery. Remote Sensing. 2022. V. 14. No. 21. 5297. https://doi.org/10.3390/rs14215297 22. Xie Y. et al. The potential of using SDGSAT-1 TIS data to identify industrial heat sources in the Beijing-Tianjin-Hebei Region. Remote Sensing. 2024. V. 16. No. 5. 768. https://doi.org/10.3390/rs16050768 23. Su Z. et al. High sensitive night-time light imaging camera design and in-orbit test of Luojia1-01 satellite. Sensors. 2019. V. 19. No. 4. 797. https://doi.org/10.3390/s19040797 24. Zhu X. et al. Assessment of a new fine-resolution nighttime light imagery from the Yangwang-1 ("Look up 1") satellite. IEEE Geoscience and Remote Sensing Letters. 2022. V. 19. 15. https://doi.org/10.1109/LGRS.2021.3139774 25. de Meester J., Storch T. Optimized performance parameters for nighttime multispectral satellite imagery to analyze lightings in urban areas. Sensors. 2020. V. 20. No. 11. 3313. https://doi.org/10.3390/s20113313 26. Combs C. L., Miller S. D. A Review of the far-reaching usage of low-light nighttime data. Remote Sensing. 2023. V. 15. 623. https://doi.org/10.3390/rs15030623 27. Schifano l., Hélière A. Advancements and challenges in nighttime light remote sensing. Proc. SPIE 13699, International Conference on Space Optics - ICSO 2024, 136992F (28 July 2025). https://doi.org/10.1117/12.3071580 28. Wu H. et al. National-scale nighttime high-temperature anomalies from Landsat-8 OLI images. 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ACCOUNTING FOR THE EFFECT OF PULP PARAMETERS WHEN SIMULATING THE FINE SCREENING PROCESS
DOI: https://doi.org/10.15407/itm2026.01.113 Fine screening is an important constituent of magnetite quartzite dressing, whose improvement is largely associated with a further development of the industry. Available mathematical models of dry fine screening allow one to control the process parameters. For wet fine screening, it is necessary to take into account the features of the pulp characteristics effect, which makes this study important. The goal of the work is to determine the effect of the main pulp parameters in developing a model of iron ore screening. As distinct from dry screening, pulp or suspension particle sieving on a hydraulic screen involves the presence of an aqueous medium, whose main characteristic is viscosity. Pulp viscosity is a measure of the internal friction of the suspension, which depends on the concentration, the solid particle size and density, and the viscosity of the liquid phase. It determines the fluidity of the pulp, its ability to transport material particles, and the effect on the process of size separation on the screen. To take into account the features of wet fine screening, the main pulp characteristics are identified and combined into a pulp coefficient. A regression analysis is used to determine the type and value of this coefficient. The level of effect of each of the selected pulp parameters is shown, and the calculated hypersurfaces of the pulp coefficient as a function of the analyzed factors are presented. The form of the pulp coefficient as a function of the pulp characteristics is determined. The adequacy of the obtained screening model is confirmed by a high value of the coefficient of determination R2 = 0.972 and a small value of the standard estimate error SE = 0.00793. The fine screening process was simulated for a stochastic ore pulp inflow specified as an estimated-parameter distribution using Tikhonov’s fine screening model. To determine the pulp characteristics and the pulp coefficient, a regression analysis was made using the STATGRAPHICS Plus package. The simulated results were compared with those of experimental screening to estimate the simulation accuracy. The results of the mathematical simulation, which relate the ore pulp inflow parameters to those of the fine screening process characteristics, allow the proposed approach to be used in the solution of practical problems. REFERENCES 1. Andreev E. E., Tikhonov O. N. Raw Material Fragmentation, Grinding, and Predressing. Saint Petersburg: Saint Petersburg State University of Technology, 2007. 439 pp. (In Russian). 2. Oliinyk T. A., Rumnytskyi D. O., Skliar L. V. Particle segregation in the gravity separation of mineral aggregates un an aqueous medium. Journal of Kryvyi Rih National University. 2023. Iss, 56. Pp. 47-54. (In Ukrainian). https://doi.org/10.31721/2306-5451-2023-1-56-47-54 3. Oliinyk T., Rumnytskyi D., Skliar L. Determination of the influence of pulp viscosity on the enrichment process of magnetite suspensions in screw separators. Technology Audit and Production Reserves. Chemical and Technological Systems. 2025. V. 1. No. 3(81). Рp. 6-18. https://doi.org/10.15587/2706-5448.2025.323268 4. Richards R. G., MacHunter D. M., Gates P. J., Palmer M. K. Gravity separation of ultra-fine (−0.1 mm) minerals using spiral separators. Minerals Engineering. 2000. V. 13. No. 1. Рp. 5-77. https://doi.org/10.1016/S0892-6875(99)00150-8 5. Nzeh N., Popoola P., Okanigbe D. et al. Physical beneficiation of heavy minerals - Part 1: A state of the art literature review on gravity concentration techniques. Heliyon. 2023. V. 9. No. 8. e18919. https://doi.org/10.1016/j.heliyon.2023.e18919 6. Tikhonov O. M. Mechanisms of Effective Mineral Separation in Mineral Dressing. Moscow: Nedra, 1984. 208 pp. (In Russian). 7. Oliinyk T. A., Nevzorov V. V. Analysis of the effect of key parameters of raw iron ore on the fine screening process using mathematical models. Technical Engineering. 2025. Iss. 2(96). Pp. 259-272. (In Ukrainian). 8. Sergieiev P. V., Biletskyi V. S. Computer Simulation of Mineral Processing. Mariupol: Eastern Publishing House, 2016. 119 pp. (In Ukrainian).
ON THE RESEARCH RESULTS OF THE SCIENTIFIC SCHOOL AT THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE "DYNAMICS OF SPACE TECHNOLOGY OBJECTS" IN 2021–2025
DOI: https://doi.org/10.15407/itm2026.01.003 This article presents a review of the work carried out from 2021 to 2025 by scientists from the National Academy of Sciences of Ukraine (NAS) representing the "Dynamics of Space Technology Objects" research school. Some of this work concerns a systems analysis of Ukraine's space industry. Research of spacecraft dynamics and systems was conducted in several areas. These areas are: the development of machine learning methods in spacecraft control, optimization of spacecraft controlled motion, systems for remote sensing of the Earth's surface, deorbiting of space debris, a methodology for conceptual design of an industrial space platform, the problem of space service technology and the formation of a paradigm for stabilizing the Earth's climate based on space systems for shading its surface. A multiscale model of any signal/variable based on multiformalism, experience, and consensus management was generalized. The model allows for diversification of computational methods and means of obtaining primary information. A scheme for applying morphological calculations to integrate and generalize primary information was developed. The application of modern information technologies to solve problems of spacecraft (SC) dynamics was considered. It was shown that free open-source software (GMAT, Basilisk, OreKit, etc.) is an effective alternative to proprietary packages for modeling the orbital motion of SC, trajectory optimization, and visualization. An algorithm for preliminary selection of a set of image features used as input information for neural networks was created. This approach allows one to significantly reduce the dimensionality of input data, thereby reducing computational requirements. The advantages of using artificial intelligence methods for space applications were shown. They make it possible to reduce the requirements for control system elements, such as sensors, actuators, to abandon the use of special benches for testing systems, and to reduce development time and cost. A method was developed for onboard estimation of the relative spatial motion parameters of a non-cooperative orbital servicing target with unknown geometry, based on LiDAR-derived point clouds of the target surface. The algorithm operates on a reduced subset of the point cloud data. The target’s motion parameters are determined as the arguments of an objective function. A formulation of this objective function was proposed such that its extremum corresponds to the correctly identified spatial pose of the target. A number of current problems related to the development of new technologies used in the creation of satellite systems were considered. This makes it possible to significantly increase the efficiency of Earth remote sensing satellites and their constellations. Increasing their efficiency is associated with solving the problems of designing satellite working orbits, controlling the motion of satellites along these orbits, and forming constellations. A new approach was proposed to solving the problem of the growth of space debris in Earth orbits. It is based on the storage of space debris as raw material in special storage orbits for further processing. A number of mathematical models were developed to provide a comprehensive assessment framework for a space-based solar radiation mitigation system. The framework enables investigation of the long-term dynamical stability of individual orbital clusters and the structural coherence of the global distributed shading configuration. REFERENCES 1. Prokopchuk Yu. O. Intuition: The Experience of Formal Research. Dnipro : PSACEA Press. 2022. 724 pp. (In Ukrainian). 2. Prokopchuk Y., Nosov P., Ben A. Problems of meaning, understanding, computability and adaptability in artificial cognitive systems. Proceedings of the 16th Scientific and Practical Conference Modern Information and Innovative Technologies in Transport (MINTT-2024), Odesa, May 29-30, 2024. Odesa: Kherson State Maritime Academy, 2024. Pp. 19 - 25. 3. Prokopchuk Yu. Sketch of the autonomous/cognitive system behavior model. Automatics 2024: Abstracts of the XXVII International Conference of Automatic Control. Dnipro, November 20-22, 2024. Dnipro: DNU, 2024. Pp. 176 - 177. (In Ukrainian). 4. Prokopchuk Y. Designing ecosystems of intelligence: Logic of fast distinction. Materials of the 17th International Scientific and Practical Conference "Modern Information and Innovative Technologies in Transport (MINTT-2025), Odesa, May 28-30, 2025. Odesa: Kherson State Maritime Academy, 2025. Pp. 29 - 34. 5. Prokopchuk Y. Combinatorial, expanding phase space of cognitive dynamic systems. XXVII International Scientific and Practical Seminar "Combinator Configurations and Their Applications", Zaporizhzhia-Kropyvnytskyi-Kiev, Ukraine: National University "Zaporizhzhia Polytechnic", 2025. Pp. 175 - 183. 6. Prokopchuk Yu. O. Open-ended evolution of self-improving systems/agents: LGP-Machine. Materials of the XX Scientific Readings "Dneprovskaya Orbita-2025", Dnipro, October 22-24, 2025. Dnipro: NCAOM named after O.M. Makarov, 2025. Pp. 117 - 124. (In Ukrainian). 7. Prokopchuk Yu. O., Poshyvalov V. P. Development of a methodology for analyzing the functioning, development, and management of complex dynamic intelligent systems. Proceedings of the Fifth International Scientific and Practical Conference "Problems of Sustainable Development of the Maritime Industry (PSDMI-2025)". Odesa, Ukraine: Kherson State Maritime Academy, 2025. Pp. 46-50. (In Ukrainian). 8. Prokopchuk Y. A mathematical model of the meaning/gist of the signal/variable. 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Quantitative assessment of the risk level of increasing costs for the development of space technology samples. Teh. Meh. 2022. No. 4. Pp. 51-66 (In Ukrainian). https://doi.org/10.15407/itm2022.04.051 12. Alpatov A.P., Marchenko V.T., Khorolsky P.P., Sazina N.P. Status and directions for improving regulatory and procedure framework for rocket and space technology development in Ukraine. Sci. Innov. 2022. V. 18. No. 1. Pp. 76 - 88. 13. Sazinа N. P., Zhukova L. G. Features of calculating the expected cost of experimental design work on the creation of spacecraft. Teh. Meh. 2023. No. 3. Pp. 58-67. (In Ukrainian). https://doi.org/10.15407/itm2023.03.058 14. Marchenko V. T., Sazinа N. P. Methodological features of assessing the level of competence of experts in a group when determining the effectiveness of rocket and space systems. Teh. Meh. 2024. No. 1. Pp. 93-104. (In Ukrainian). https://doi.org/10.15407/itm2024.01.093 15. Zhukova L. G. 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FEATURES OF THE MATHEMATICAL SIMULATION OF DYNAMIC PROCESSES IN THE RECONFIGURABLE PROPELLANT FEED HYDRAULIC SYSTEM OF LIQUID-PROPELLANT ROCKET ENGINES
DOI: https://doi.org/10.15407/itm2026.01.023 Hydraulic pipeline systems in liquid-propellant rocket engines (LPREs) are numerous and diverse. In staged-combustion LPREs, use is made of reconfigurable hydraulic systems, in which the propellant component flow directions change during an engine start-up. A reliable engine start-up requires a smooth transition from the start-up propellant supply to the main propellant supply. The objective of this study is to develop an approach to the mathematical simulation of dynamic processes in a branched reconfigurable hydraulic feed system. A methodological framework for modeling dynamic processes in such systems is proposed. It involves determining the frequency responses of several configurations of a hydraulic system realized at different stages of its operation as a distributed-parameter system. The next step is the construction of a lumped-parameter mathematical model with fluid motion and continuity equations in lumped parameters. Lumped compliances are typically introduced in the hydraulic network model at pipeline junctions. Their number and values are selected so that the frequency responses of the distributed- and lumped-parameter models for each hydraulic system configuration may be in agreement within a prescribed accuracy. To demonstrate the proposed approach, a test reconfigurable hydraulic system is considered. Two configurations of the hydraulic system are set off: from the start-up tank to the gas generator and from the pump outlet to the gas generator. For both configurations, frequency responses of the corresponding distributed-parameter systems are determined. A lumped-parameter mathematical model of dynamic processes in the hydraulic system under analysis is developed. The values of the lumped compliances at the network nodes are identified such that the frequency responses of the distributed- and lumped-parameter models are in satisfactory agreement. 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EXPERIMENTAL METHODS OF SOLID ROCKET PROPELLANT CHARACTERIZATION
DOI: https://doi.org/10.15407/itm2026.01.034 The process of designing a solid-propellant rocket engine is a complex problem. Usually, it is solved by an iterative method, in which the initial data are gradually refined using experimental studies. With a sufficient statistical database, the problem is somewhat simplified because use can be made of the results for a similar engine close to that under development. In any case, the design is completed by engine testing. The cost of each stage depends on the complexity of the engine as a whole, but the most expensive stage is always the engine testing. Because of this, in order to minimize resources, rocket engine developers try to reduce the extent of experimental tryout. In addition to energy characteristics, an important parameter necessary for engine design is the propellant combustion characteristics. The solid rocket propellant burning rate depends on many factors: the propellant type and initial temperature, the combustion chamber pressure, the component particle size, the flight acceleration, the gas speed near the charge surface, etc. Accordingly, these properties are used to regulate the burning rate. Since it is now mathematically very difficult to predict the solid rocket propellant burning rate, various experimental methods are used for these purposes. The goal of the work is to analyze experimental methods of solid rocket propellant characterization at the research stage. Research tests are carried out to study working processes occurring in the engine and its systems. Their study is necessary for the development and use of new propellants, radically new design ideas, and advanced materials and technologies. Research test programs are diverse and usually require new test and measurement methods and means. Therefore, this stage of rocket engine development is more often carried out using not standard equipment, but unique experimental installations or models, which allow one to obtain information on the object of research with a certain degree of reliability. The primary objectives of experimental studies at the research stage are to characterize the propellant and its combustion process to a required accuracy. This article overviews the most widely used methods for solid rocket propellant characterization. REFERENCES 1. Garbinets V. O., Gorbenko G. A., Gumnytsky B. P., Dzhur O. Ye., Kuchma L. D., Pron L. V. Fundamen-tals of Solid-Propellant Rocket Engine Theory and Design. Art-Press, 2005. 200 pp. (In Ukrainian). 2. Rogov N. G., Ishchenko M. A. Mixed Solid Rocket Propellants: Components. Requirements. Proper-ties. St. Petersburg: St. Petersburg State University of Technology, 2005. 195 pp. (In Russian). 3. Suprunenko V. A. Experimental Tryout Organization of Large-Sized Sustainer Solid-Propellant Rocket Engines. Dnipropetrovsk: Yuzhnoye State Design Office, 2000. 38 pp. (In Russian). 4. Gladkov I. M., Ermakov Yu. P., Malkin B. Ya. Mukhamedov V. S., Nalivaiko V. A., Soloukhin A. S. Solid-Propellant Pulse-Type Special-Purpose Engines. Design Fundamentals, Design, and Tryout Experience. Moscow: Central Research Institute of Information, 1990. 116 pp. (In Russian). 5. G. Gupta, L. Jawale, Mehilal, B. Bhattacharyа. Various methods for the determination of the burning rates of solid propellants - An overview. Central European Journal of Energetic Materials. 2015. V. 12. No. 3. Pp. 593-620. 6. Wei W., Yan X., Cui J., Wang R., Zheng Y., Xue C. Ultrasonic signal processing method for dynamic burning rate measurement based on improved wavelet thresholding and extreme value feature fitting. Micromachines. 2025. V. 16. 290. https://doi.org/10.3390/mi16030290 7. Oatman S. A., Caito A. A., Klinger D. J., Cooper J. N., Manship T. D., Son S. F. Closed vessel burning rate measurements of composite propellants using microwave interferometry. Propellants, Explosives, Pyrotechnics. 2024. V. 49. Iss.8. e202400072. https://doi.org/10.1002/prep.202400072 8. Trebinski R., Leciejewski Z. Surma Z. determining the burning rate of fine-grained propellants in closed vessel tests. Energies. 2022. V. 15. Iss. 7. 2680. https://doi.org/10.3390/en15072680 9. Razdan M.K., Kuo K. K. Erosive Burning Studies of Composite Solid Propellants by the Reacting Tur-bulent Boundary-Layer Approach. The Pennsylvania State University. 1976. 82 рp. 10. Liu J., Wang Y., Li X., Cong J. Using the impulse method to determine high-pressure dynamic burn-ing rate of solid propellants. Aerospace. 2023. V. 10. 818. https://doi.org/10.3390/aerospace10090818 11. Proroka V. A., Solntsev V. A., Kulyk O. V., Dobrodomov O. O., Shvets A. S., Lukianenko I. H., Dron M. M. Verification of methodological approaches to evaluating the characteristics of composite solid rocket propellants. Journal of Rocket-Space Technology. 2024. V. 33. No. 4-29. Pp. 11-22. (In Ukrainian). https://doi.org/10.15421/452446 12. DeLuca L. T., Annovazzi A. Survey of burning rate measurements in small solid rocket motors. Fire-PhysChem. 2024. V. 4. Iss. 2. Pp. 146-165. https://doi.org/10.1016/j.fpc.2023.11.004
FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING
DOI: https://doi.org/10.15407/itm2026.01.045 Thin-walled plate-shell structural elements are widely used in various sectors of engineering and the national economy, particularly in the aerospace, oil and gas, and power industries, mechanical engineering, construction, etc. The presence of holes in structures of this type leads to a sharp increase in local stresses, which under certain conditions may lead to destructive processes. This is especially true if they are used under extreme conditions, which is common in various sectors of engineering. Reducing stress concentration near holes in thin-walled structures is a pressing problem in solid mechanics. One way to do this is to use advanced functionally graded materials (FGMs) with specific mechanical properties. A gradient in mechanical properties allows one to control the stress and strain field of structural elements and may contribute to stress reduction near local stress concentrators. This FGM feature significantly increases the strength and reliability of structures as a whole. This paper presents the results of a computer simulation and finite-element analysis of the stress and strain field of thin rectangular FGM plates under various types of loading. The effect of the FGM plate elastic modulus variation law on stress and strain concentration in the vicinity of a hole is investigated. The stress and strain intensity distribution in local stress concentration zones is obtained. Cases of elastic modulus variation in a horizontal and a vertical direction for each of the loading types under consideration are studied. FGM plate heterogeneity parameters are found such that the stress concentration factor can be reduced down to ~19 %. At the same time, a proportional decrease in the strain intensity in the vicinity of the hole is also observed. The FGM plate elastic modulus variation law has a significant effect not only on the magnitude of the stress and strain concentration parameters, but also on the pattern of the stress distribution over the plate. The results of the series of computational experiments show that the use of FGMs in plates is advisable because it allows one to reduce both the stress and the strain intensity around a hole under various types of loading. REFERENCES 1. Birman V., Byrd L. W. Modeling and analysis of functionally graded materials and structures. Trans. ASME. Appl. Mech. Rev. 2007. V. 60. No. 5. Pp. 195-216. https://doi.org/10.1115/1.2777164 2. Kawasaki A., Watanabe R. Concept and P/M fabrication of functionally gradient materials. Ceramics International. 1997. V. 23, No. 1. Pp. 73-83. https://doi.org/10.1016/0272-8842(95)00143-3 3. Vasiliev V., Morozov E. Advanced Mechanics of Composite Materials and Structures. 4th ed. Amster-dam: Elsevier, 2018. 864 pp. https://doi.org/10.1016/B978-0-08-102209-2.00002-5 4. Helal W. M. K., Shi D. Y. Analysis of functionally graded rectangular plate by ANSYS. Key Engineer-ing Materials. 2013. V. 572. Pp. 505-508. https://doi.org/10.4028/www.scientific.net/KEM.572.505 5. Pidstyhach Ya. S. Selected Works. Kyiv: Naukova Dumka, 1995. 460 pp. (in Ukrainian). 6. Pilkey W. D., Pilkey D. F., Bi Z. Peterson's Stress Concentration Factors. 4th ed. Hoboken: Wiley, 2020. 640 pp. https://doi.org/10.1002/9781119532552 7. Savin G. N. Stress Distribution around Holes. Kiev: Naukova Dumka, 1968. 888 pp. (In Russian). 8. Hudramovich V. S., Hart E. L., Terokhin B. I. Stress concentration around a circular hole in thin plates and cylindrical shells with a radially inhomogeneous inclusion. Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials: Collected work. Springer Cham, 2024. Vol. 204. Chapter 18. Pp. 249-264. https://doi.org/10.1007/978-3-031-54063-9_18 9. Hart E. L., Terokhin B. I. Effect of functionally graded inclusion on stress conservation near a circu-lar hole in thin plates for different boundary conditions. Journal of Optimization, Differential Equa-tions and their Applications. 2025. V. 33. No. 1. Pp. 110-127. https://doi.org/10.15421/142506 10. Hart E. L., Terokhin B. I. Finite-element analysis of stress concentration in thin plates and cylindrical shells with a circular hole surrounded by an inclusion of functionally graded material. Journal of Mathematical Sciences. 2025. V. 291. No. 5. Pp. 703-715. https://doi.org/10.1007/s10958-025-07846-6 11. Hart E. L., Terokhin B. I. Methods for reducing stress concentration around holes in thin plates and cylindrical shells with annular radially inhomogeneous inclusions. International Applied Mechanics. 2025. V. 61. No. 3. Pp. 359-368. https://doi.org/10.1007/s10778-025-01359-0 12. Hart E. L., Hudramovich V. S., Terokhin B. I. Effect of a functionally graded material inclusion on the stress concentration in thin plates and cylindrical shells with a circular opening. Teh. Meh. 2022. No. 4. Pp. 67-78. (in Ukrainian). https://doi.org/10.15407/itm2022.04.067 13. Hudramovich V. S., Hart E. L., Strunin K. A. Modeling of deformation process of a plate with elastic elongated inclusions based on the finite element method. Teh. Meh. 2014. No. 2. Pp. 12-23. (in Russian) 14. Hart E. L., Hudramovich V. S. Computer simulation of the stress-strain state of plates with reinforced elongate rectangular holes of various orientations. Strength of Materials and Theory of Structures. Kyiv, KNUBA, 2022. Iss. 108. Pp. 77-86. https://doi.org/10.32347/2410-2547.2022.108.77-86 15. Haque A., Ahmed L., Ramasetty A. Stress concentrations and notch sensitivity in woven ceramic ma-trix composites containing a circular hole. J. Amer. Ceramic Soc. 2005. V. 88. No. 8. Pp. 2195-2201. https://doi.org/10.1111/j.1551-2916.2005.00404.x 16. Sharma D. S. Stress distribution around polygonal holes. Intern. J. Mechanical Sciences. 2012. V. 65. No. 1. Pp. 115-124. https://doi.org/10.1016/j.ijmecsci.2012.09.009 17. Yang Q. Q., Gao C. F., Chen W. T. Stress concentration in a finite functionally graded material plate. Sci. China Phys. Mech. Astron. 2012. V. 55. Pp. 1263-1271. https://doi.org/10.1007/s11433-012-4774-x 18. Sburlati R. Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate. Int. J. Solids Struct. 2013. V. 50. No. 22-23. Pp. 3649-3658. https://doi.org/10.1016/j.ijsolstr.2013.07.007 19. Jana K., Pal S., Haldar S. Modal analysis of power law functionally graded material plates with rec-tangular cutouts. Mechanics Based Design of Structures and Machines. 2024. V. 52. No. 5. Pp. 2411-2439. https://doi.org/10.1080/15397734.2023.2180033 20. Kubair D. V., Bhanu-Chandar B. Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension. Intern. J. Mech. Sci. 2008. V. 50. No. 4. Pp. 732-742. https://doi.org/10.1016/j.ijmecsci.2007.11.009 21. Mohammadi M., Dryden J. R., Jiang L. Stress concentration around a hole in a radially inhomogene-ous plate. Intern. J. Solids Struct. 2011. V. 48. No. 3-4. Pp. 483-491. https://doi.org/10.1016/j.ijsolstr.2010.10.013 22. Enab T. A. Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings. Ain Shams Eng. Journal. 2014. V. 5. No. 3. Pp. 839-850. https://doi.org/10.1016/j.asej.2014.03.002 23. Rani P., Verma D., Ghangas G. Stress concentration analysis of functionally graded material coated elliptical inclusion under uniaxial tension. Materials Today: Proceedings, 2023. V. 78. Pt. 3. P. 351-358. https://doi.org/10.1016/j.matpr.2022.09.602 24. Abdalla H. M. A., De Bona F., Casagrande D. Optimization of functionally graded materials to make stress concentration vanish in a plate with circular hole. Composites. Part C. 2024. V. 15. Art. 100512. https://doi.org/10.1016/j.jcomc.2024.100512 25. Yang Q., Cao H., Tang Y., Li Y., Chen X. Experimental investigation of stress distributions in 3D printed graded plates with a circular hole. Materials. 2021. V. 14, No. 24. Pp. 1-13. https://doi.org/10.3390/ma14247845 26. Bobbio L. D., Bocklund B., Liu Z.-K., Beese A. M. Tensile behavior of stainless steel 304L to Ni-20Cr functionally graded material. Materialia. 2021. V. 18. Art. 101151. https://doi.org/10.1016/j.mtla.2021.101151 27. Zienkiewicz O. C., Taylor R. L., Fox D. D. The Finite Element Method for Solid and Structural Me-chanics. 7th ed. New York: Elsevier, 2014. 624 pp. 28. Timoshenko S. P., Gere J. M. Mechanics of Materials. New York: Van Nostrand Reinhold Company, 1972. 552 pp. 29. Lurie A.I. Theory of Elasticity. Foundations of Engineering Mechanics. Berlin-Heidelberg: Springer, 2005. 1050 рp. https://doi.org/10.1007/978-3-540-26455-2 30. Washizu K. Variational Methods in Elasticity and Plasticity. 2nd ed. Oxford: Pergamon Press, 1975. 412 pp.
MODAL ANALYSIS OF A HORIZONTAL SHELL STRUCTURE UNDER BLAST LOADING
DOI: https://doi.org/10.15407/itm2026.01.054 This article addresses the problem of modal analysis of a horizontal steel tank with a capacity of 50 m³ on concrete saddle supports. The structure is modeled as a cylindrical shell of length 8.15 m, radius 1.4 m, and wall thickness 5 mm. The geometric model of the tank is presented in a three-dimensional form. To model the horizontal shell, eight-node shell finite elements (SHELL281) are employed. The saddle supports are modeled using three-dimensional twenty-node second-order finite elements (SOLID186). The horizontal shell is reinforced with stiffening beams and a diaphragm. The bottom surfaces of the supports are fixed. Contact interaction between the shell and supports is modeled as well. We use a refined mesh in the contact zones. To model the stiffening beams, nonlinear three-node beam elements based on Timoshenko’s beam theory are utilized. The natural frequencies and mode shapes are computed using the finite-element method. The boundary conditions considered in the modal analysis include the assumption of no contact loss. The calculated modal participation factors show that the first mode plays a dominant role in evaluating dynamic behavior of the structure in the Y-axis direction. This mode is also a torsional one about the vertical Z-axis, thus indicating the possibility of resonance effects under seismic loading. From an energy standpoint, beam elements of the diaphragm exhibit an excessive concentration of specific strain energy; such elements require some reinforcement to prevent resonance-induced excitations. Under blast loading, the extent of structural damage depends on the response rate of the structure to the blast wave. Small, stiff structures respond significantly faster than large ones. When the duration of the blast wave exceeds the natural vibration period of the structure, the critical factor is the overpressure. Conversely, if the blast wave duration is short compared to the natural period, the impulse becomes the dominant factor. A dynamic analysis of the impact of a 100 kg TNT charge on the horizontal shell structure with account for the first natural frequency showed that at distances less than 52.6 m, the blast loading can be considered short and substituted with an instantaneous impulse. At larger distances, however, both the impulse action and the overpressure must be taken into account. REFERENCES 1. Dong X., Lian J., Wang H., Yu T., Zhao Y. Structural vibration monitoring and operational modal analysis of offshore wind turbine structure. Ocean Engineering. 2018. V. 150. Pp. 280-297. https://doi.org/10.1016/j.oceaneng.2017.12.052 2. Balageas D., Fritzen C.-P., Güemes A. Structural Health Monitoring. John Wiley & Sons. 2010. 496 pp. 3. Jana K., Pal S., Haldar S. Modal analysis of power law functionally graded material plates with rectangular cutouts. Mechanics Based Design of Structures and Machines. 2023. V. 52. No. 5. Pp. 2411-2439. https://doi.org/10.1080/15397734.2023.2180033 4. Ramu I., Mohanty S. C. Modal analysis of functionally graded material plates using finite element method. Procedia Materials Science. 2014. V. 6. Pp. 460-467. https://doi.org/10.1016/j.mspro.2014.07.059 5. Inaudi J. A. Rayleigh quotient algorithm for modal analysis of structural models. Mecánica Computacional. 2016. Vl. 34. Pp. 1459-1477. 6. Si X. H., Lu W. X., Chu F. L. Modal analysis of circular plates with radial side cracks and in contact with water on one side based on the Rayleigh-Ritz method. Journal of Sound and Vibration. 2012. V. 331. No. 1. Pp. 231-251. https://doi.org/10.1016/j.jsv.2011.08.026 7. Chapelle D., Bathe K. The Finite Element Analysis of Shells - Fundamentals. Heidelberg: Springer-Verlag, 2011. 410 pp. https://doi.org/10.1007/978-3-642-16408-8 8. Krivenko O. P., Vorona Yu. V., Kozak A. A. Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures. Strength of Materials and Theory of Structures. 2021. Iss. 107. Pp. 20-34. https://doi.org/10.32347/2410-2547.2021.107.20-34 9. Kucherenko O. Ye., Blazhko V. A. Verification of a finite-element model of a horizontal shell structure - support contact. Teh. Meh. 2025. No. 2. Pp. 63-71. (In Ukrainian). https://doi.org/10.15407/itm2025.02.063 10. Rabbat B. G., Russell H. G. Friction coefficient of steel on concrete or grout. Journal of Structural Engineering. 1985. V. 111. Iss. 3. P. 505-515. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:3(505) 11. Hauck B., Szekrenyes A. Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures. Mathematics and Mechanics of Solids. 2024. V. 29. No. 7. Pp. 1325-1363. https://doi.org/10.1177/10812865231221992 12. Birbraer A. N. Seismic Analysis of Structures. St. Petersburg: Nauka, 1998. 255 pp. 13. Crowl D.A. Understanding Explosions. New-York: American Institute of Chemical Engineers, 2003. 214 pp. https://doi.org/10.1002/9780470925287 14. Kobiiev V. H. Deformation features and determining the specificity of the effect of external factors on shell systems under high-power impulse loads. Opir Materialiv i Teoria Sporud. 2006. No. 78. Pp. 82-89. (In Ukrainian). 15. Clough R. W., Penzien J. Dynamics of Structures. New-York: McGrow-Hill Book Company, 1975. 320 pp. 16. Vorob'ev Yu. S., Kolodyazhny A. B., Sevryukov V. I., Yatyunin E. G. High-Rate Straining of Structural Elements. Kiev: Naukova Dumka, 1989. 192 pp. (In Russian).
ANALYSIS OF THE ANTIPLANE DEFORMATION OF A CRACKED QUASICRYSTAL WITH CONSIDERATION FOR SURFACE EFFECTS
DOI: https://doi.org/10.15407/itm2026.01.062 The antiplane shear deformation (Mode III) of a linear hexagonal quasicrystal containing an isolated crack under remote uniform loading is investigated taking into account phonon–phason coupling and surface effects within the framework of the Gurtin–Murdoch surface elasticity model. The crack faces are modeled as elastic membranes possessing surface phonon, phason, and coupling constants of their own, which makes it possible to adequately describe size effects at the nano- and submicron scales. Based on the equations of quasicrystal elasticity theory incorporating both phonon and phason fields, a mathematical model of the problem is developed. The boundary conditions on the crack faces, modified by surface energy, lead to a system of singular integro-differential equations with a Cauchy-type kernel. To solve this system, the collocation method with Chebyshev polynomials is applied, thus ensuring a high accuracy and good convergence of the numerical procedure. The numerical analysis performed for a one-dimensional hexagonal quasicrystal shows that accounting for surface elasticity significantly alters the stress and strain field near the crack tip. In contrast to classical fracture mechanics, where a square-root stress singularity occurs, the proposed model predicts finite stresses and strains. Surface elasticity acts as a regularizing mechanism that “smooths” the singularity and introduces a size-dependent response. It is shown that as the crack length increases, the stresses at the crack tip and in its vicinity increase, while the normalized crack opening displacement changes only slightly. For small cracks, surface effects are dominant, whereas with increasing defect size the behavior gradually approaches the classical solution, although it does not coincide with it completely. The results can be used to assess the strength and fracture toughness of quasicrystalline materials taking into account nanoscale effects. The obtained results are important for the advancement of modern engineering mechanics, particularly fracture mechanics and the mechanics of nanostructured materials, as they extend classical approaches by incorporating surface and size-dependent effects and contribute to improving the reliability of strength predictions for structural components. REFERENCES 1. Gurtin M. E., Murdoch A. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 1975. V. 57. Pp. 291-323. https://doi.org/10.1007/BF00261375 2. Kim C. I., Schiavone P., Ru C. Q. The effects of surface elasticity on an elastic solid with mode-III crack: complete solution. ASME J. Appl. Mech. 2010. V. 77. 021011. https://doi.org/10.1115/1.3177000 3. Wang X., Zhou K. A crack with surface effects in a piezoelectric material. Math. Mech. Solids. 2015. V. 20. Pp. 1131-1146. 4. 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V. 110. 104305. https://doi.org/10.1063/1.3660431 9. Pan X., Yu S., Feng X. A continuum theory of surface piezoelectricity for nanodielectrics. Sci. China. 2011. V. 54. Pp. 564-573. https://doi.org/10.1007/s11433-011-4275-3 10. Ru C. Q. Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions. Sci. China. 2010. V. 53. Pp. 536-544. https://doi.org/10.1007/s11433-010-0144-8 11. Zhao X. F., Ma Y. Y., Lu S. N. Anti-plane problem of nano-cracks emanating from a regular triangular nano-hole in one dimensional hexagonal quasicrystals. Science Technology and Engineering. 2023. V. 23. No. 7. Pp. 2727-2733. 12. Xin Y. Y., Xiao J. H. Fracture mechanics of an arbitrary position crack emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals. Acta Mechanica. 2023. V. 234. No. 4. Pp. 1409-1420. https://doi.org/10.1007/s00707-022-03424-y 13. Xin Y. Y., Xiao J. H. 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FINITE-ELEMENT SIMULATION OF THE IN-SERVICE STRESS AND STRAIN FIELD OF HIP JOINT ELEMENTS BASED ON COMPUTER TOMOGRAPHY DATA
DOI: https://doi.org/10.15407/itm2026.01.073 The development of innovative human hip arthroplasty technologies and up-to-date designs of endoprostheses, in particular acetabularcomponents, and the improvement of methods to fix them in the acetabular component – hipbone system and surgical techniques made it possible to make extremities fully operable, restore freedom of motion without any pain or discomfort, improve life quality, and readapt patients to work. The current trends in hip arthroplasty are the improvement of existing hip joint endoprosthesis designs and the development of new ones based on the results of biomechanical studies of acetabular component fixation stability and the development of technologies for designing an individual endoprosthesis by constructing virtual 3D hipbone models using computer tomography data with the aim to extend the endoprosthesis service life. Important problems in orthopedy- and traumatology-related biomechanics are the mathematical simulation and the analysis of the behavior of variously designed acetabular components of a hip joint endoprosthesis in conditions of traumatic defects of the acetabulum. The goal of the studies presented in this paper is to develop a finite-element model based on computer tomography data to study the stress and strain field of hip joint elements under service loads and thoroughly analyze the contact interaction of the femoral head with the acetabulum. The paper presents an algorithm for constructing a geometrical model based on computer tomography data to study the hip joint strength and a 3D geometrical model developed by that algorithm, which includes the sacrum, the ilium, the pubis, the acetabulum, and the femoral head. Based on that model, a finite-element model is developed to study the stress and strain field of hip joint elements under service loads and thoroughly analyze the contact interaction of the femoral head with the acetabulum. The proposed model may be used in the development of finite-element models to study the stress and strain field of the elements of a hip joint with a defective acetabulum and an endoprosthesis under service loads and make a comparative analysis of the operation of a hip joint and its endoprosthesis in biomechanical assessment of the fixation stability of variously designed acetabular components of a hip joint endoprosthesis. REFERENCES 1. Exploring recent trends and innovations in total hip arthroplasty. URL: https://orthospinenews.com/2025/06/23/exploring-recent-trends-and-innovations-in-total-hip-arthroplasty/ (Last accessed on July 24, 2025). 2. Hip arthroplasty (hip joint replacement). 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DARRIEUS ROTOR SPEED CONTROL BY SIMULTANEOUS CHANGES IN THE ROTOR CONFIGURATION AND THE GENERATOR BRAKING TORQUE
DOI: https://doi.org/10.15407/itm2026.01.086 In recent decades, the "green" power industry has been developing rapidly. The growing interest in generating "green" power has led to a sharp increase in the number of operating systems, among which vertical-axis wind turbines (WT) occupy a significant place. Along with a number of advantages, the most difficult issues when using vertical-axis WTs are ensuring their self-starting and increasing efficiency. Due to the rotation of the turbine about a vertical axis, the aerodynamics of the turbine is more complex than that of a comparable horizontal-axis wind turbine, and knowledge and understanding of these turbines remain far from complete. The introduction of any approaches to improving the properties of a WT as a whole requires an in-depth study and coordination of the operation of its elements to ensure the compatibility of the operation of individual components. The proposed work considers a system to control the rotation of the Darrieus rotor of vertical-axis wind turbines, which consists of three control loops: two loops for changing the length of the blades and traverses and a loop for controlling the braking torque of the permanent magnet generator. The use of a generator to control the rotation of the rotor of a wind turbine is a traditional means of ensuring small deviations in the rotation speed about the point of maximum power for the current wind flow speed. The use of permanent magnet synchronous generators for this purpose, which have a number of useful properties, is quite a new line in the design of control systems. The work considers the features of the dynamics and control of the rotor rotation speed of vertical-axis wind turbines as a control object, which is stabilized by a simultaneous change in the configuration of the wind turbine rotor and the braking torque of the permanent magnet generator. The simultaneous use of the three stabilization channels contributes to a greater adaptation of the turbine rotor to changes in wind speed, thus significantly reducing the load on the power transmission systems and the requirements for excess power dissipation systems, such as emergency braking systems, and allowing one to reduce power consumption to counteract significant changes in wind speed. The use of the adaptation principle to speed up turbine braking in emergencies seems to be very useful. In this regard, a continuation of the authors' previous work aimed at generalizing and extending the approach to controlling the rotor speed of vertical-axis wind turbines by simultaneously changing the rotor configuration and the braking torque of the permanent magnet generator becomes an important task of significant practical interest. The goal of this article is to synthesize algorithms for stabilizing the speed of the Darier rotor of vertical-axis wind turbines controlled by a simultaneous change in the rotor configuration and the braking torque of the permanent magnet generator and analyze their effectiveness. The methods of solving the problem are methods of the classical theory of automatic control and mathematical simulation. The novelty of the obtained results lies in accounting for control actions produced by changes in the rotor configuration and the braking torque of the permanent magnet generator, determining the stability conditions of the stabilization system, and extending the authors’ method of redistributing the load on the stabilization channels to ensure their operability. The proposed and analyzed stabilization algorithms and the approach to operability assurance may be used in the design of advanced vertical-axis wind turbines of various capacities. REFERENCES 1. Longhuan Du, Ingram G., Dominy R. 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