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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">mgssuvest</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник МГСУ</journal-title><trans-title-group xml:lang="en"><trans-title>Vestnik MGSU</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1997-0935</issn><issn pub-type="epub">2304-6600</issn><publisher><publisher-name>Moscow State University of Civil Engineering (National Research University) (MGSU)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22227/1997-0935.2024.5.729-739</article-id><article-id custom-type="elpub" pub-id-type="custom">mgssuvest-266</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Проектирование и конструирование строительных систем. Строительная механика. Основания и фундаменты, подземные сооружения</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Construction system design and layout planning. Construction mechanics. Bases and foundations, underground structures</subject></subj-group></article-categories><title-group><article-title>Численное и экспериментальное исследование поведения защитного сооружения при ударном воздействии</article-title><trans-title-group xml:lang="en"><trans-title>Numerical and experimental study of the behavior of a protective structure under impact</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7685-0325</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тарасов</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Tarasov</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Денис Александрович Тарасов — кандидат технических наук, доцент кафедры автоматизированных систем безопасности</p><p>440026, г. Пенза, ул. Красная, д. 40</p><p>Scopus: 57204116511</p></bio><bio xml:lang="en"><p>Denis A. Tarasov — Candidate of Technical Sciences, Associate Professor of the Department of Automated Security Systems</p><p>40 Krasnaya st., Penza, 440026</p><p>Scopus: 57204116511</p></bio><email xlink:type="simple">tda82@list.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Пензенский государственный университет (ПГУ)<country>Россия</country></aff><aff xml:lang="en">Penza State University (PSU)<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>29</day><month>05</month><year>2024</year></pub-date><volume>19</volume><issue>5</issue><fpage>729</fpage><lpage>739</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Тарасов Д.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Тарасов Д.А.</copyright-holder><copyright-holder xml:lang="en">Tarasov D.A.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.vestnikmgsu.ru/jour/article/view/266">https://www.vestnikmgsu.ru/jour/article/view/266</self-uri><abstract><sec><title>Введение</title><p>Введение. В связи с постоянно существующими угрозами умышленного повреждения инфраструктуры критически важных объектов с применением автотранспортных средств становится актуальной и представляет практический интерес задача по разработке и исследованию защитных сооружений, направленных на предотвращение такого рода ущерба. Обосновано применение стальных канатов в качестве основных несущих элементов подобных сооружений.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Проведено с помощью предложенного численного алгоритма определение минимально допустимой площади поперечного сечения стальных канатов исходя из требований, предъявляемых к защитному сооружению по стойкости к ударному воздействию, вызванному наездом автомобиля с заданной массой и скоростью движения. В основу разработанного метода положено математическое моделирование задачи условной оптимизации. В качестве целевой функции выступала функция продольного усилия, возникающего в стальных канатах. Вместе с тем предъявлялись требования по соблюдению условий сохранения энергии и неразрывности деформаций, а также ограничения прочности. Выполнен поверочный расчет проектируемого защитного сооружения в коммерческом программном комплексе, реализованном на общепризнанном методе конечных элементов. Представлена методика осуществления натурного эксперимента. Проведен полномасштабный натурный эксперимент с целью определения истинного распределения деформаций по конструктивным элементам объекта испытания при ударном воздействии.</p></sec><sec><title>Результаты</title><p>Результаты. Представлены результаты экспериментального исследования. Выполнен сравнительный анализ данных, полученных в процессе численного и компьютерного моделирования, а также в ходе проведения натурного испытания. Установлено незначительное расхождение в значениях контролируемых параметров, полученных разными методами.</p></sec><sec><title>Выводы</title><p>Выводы. Предложенный численный алгоритм по поиску минимально допустимой площади поперечного сечения стальных канатов, исходя из требования заданной прочности, подтвердил свою надежность, а принятые конструктивные решения разработанного защитного сооружения свою обоснованность. Результаты исследования могут найти применение при проектировании подобных инженерных сооружений, предназначенных для физической защиты особо важных объектов.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. In connection with the constantly existing threats of deliberate damage to the infrastructure of critical facilities using vehicles, the task of development and research of protective structures aimed at preventing this kind of damage becomes relevant and of practical interest. The application of steel ropes as the main load-bearing elements of such structures is substantiated.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. The proposed numerical algorithm was used to determine the minimum permissible cross-sectional area of steel ropes based on the requirements for a protective structure in terms of resistance to impact caused by the collision of a car with a given mass and speed. The developed method is based on mathematical modelling of the conditional optimization problem. The objective function was the function of the longitudinal force arising in the steel ropes. At the same time, requirements were made to comply with the conditions of energy conservation and continuity of deformations, as well as strength limitations. A verification calculation of the designed protective structure was carried out in a commercial software package implemented on the generally recognized finite element method. The methodology of the full-scale experiment is presented. A full-scale experiment was carried out in order to determine the true distribution of deformations over the structural elements of the test object under impact.</p></sec><sec><title>Results</title><p>Results. The results of the experimental study are presented. A comparative analysis of the data obtained in the process of numerical and computer simulation, as well as in the course of a full-scale test, was carried out. A slight discrepancy in the values of the controlled parameters obtained by different methods was found.</p></sec><sec><title>Conclusions</title><p>Conclusions. The proposed numerical algorithm for searching the minimum permissible cross-sectional area of steel ropes, based on the requirement of a given strength, confirmed its reliability, and the adopted design solutions of the developed protective structure proved their validity. The results of the research can be used in the design of such engineering structures designed for the physical protection of critical facilities.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>защитное сооружение</kwd><kwd>противотаранное устройство</kwd><kwd>стальной канат</kwd><kwd>гибкая нить</kwd><kwd>удар</kwd><kwd>экспериментальное исследование</kwd><kwd>динамическая нагрузка</kwd><kwd>напряжения</kwd><kwd>деформации</kwd></kwd-group><kwd-group xml:lang="en"><kwd>protective structure</kwd><kwd>anti-ram device</kwd><kwd>steel rope</kwd><kwd>flexible thread</kwd><kwd>impact</kwd><kwd>experimental study</kwd><kwd>dynamic load</kwd><kwd>stresses</kwd><kwd>deformations</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Минаев В.А., Сычев М.П., Севрюков Д.В., Дудоладов В.А. Некоторые аспекты оценки характеристик и применения противотаранных устройств // Вопросы оборонной техники. Серия 16: Технические средства противодействия терроризму. 2018. № 7-8(121-122). С. 45–51. EDN XWCDLV.</mixed-citation><mixed-citation xml:lang="en">Minaev V.A., Sychev M.P., Sevryukov D.V., Dudoladov V.A. Some aspects of performance evaluation and application of anti-vehicle devices. Questions of Defense Technology. Series 16: Technical Means of Countering Terrorism. 2018; 7-8(121-122):45-51. EDN XWCDLV.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Tran P., Linforth S., Ngo T., Lumantarna R., Nguyen T. Design analysis of hybrid composite anti-ram bollard subjected to impulsive loadings // Composite Structures. 2018. Vol. 189. Pp. 598–613. DOI: 10.1016/j.compstruct.2018.01.093</mixed-citation><mixed-citation xml:lang="en">Tran P., Linforth S., Ngo T., Lumantarna R., Nguyen T. Design analysis of hybrid composite anti-ram bollard subjected to impulsive loadings. Composite Structures. 2018; 189:598-613. DOI: 10.1016/j.compstruct.2018.01.093</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Шнякина Е.А. Имитационная модель оценки эффективности систем физической защиты объектов // Автоматизация. Современные технологии. 2023. Т. 77. № 6. С. 263–268. DOI: 10.36652/0869-4931-2023-77-6-263-268 EDN LVJLXB.</mixed-citation><mixed-citation xml:lang="en">Shnyakina E.A. Simulation model for efficiency evaluation of the objects physical protection systems. Automation. Modern Technologies. 2023; 77(6):263-268. DOI: 10.36652/0869-4931-2023-77-6-263-268. EDN LVJLXB.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Костин В.Н. Методика формирования элементов структуры организационного управления систем физической защиты на основе информационного подхода // Труды Института системного анализа Российской академии наук. 2020. Т. 70. № 1. С. 30–39. DOI: 10.14357/20790279200104 EDN DMVROZ.</mixed-citation><mixed-citation xml:lang="en">Kostin V.N. Formation technique of elements of the structure of organizational management of physical protection systems based on the information approach. Proceedings of the Instittute for Systems Analysis Russian Academy of Sciences (ISA RAS). 2020; 70(1):30-39. DOI: 10.14357/20790279200104. EDN DMVROZ.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Костин В.Н. Задачи концептуального проектирования физической защиты критически важных объектов // Проблемы информационной безопасности. Компьютерные системы. 2020. № 1. С. 58–67. EDN UPNQEB.</mixed-citation><mixed-citation xml:lang="en">Kostin V.N. Tasks of conceptual design of physical protection of critically important objects. Tasks of Conceptual Design of Physical Protection of Critically Important Objects. 2020; 1:58-67. EDN UPNQEB.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Демьянушко И.В., Михеев П.С., Медведев М.М. Особенности конструкций дорожных мобильных фронтальных ограждений и расчеты при проектировочном анализе // Автомобиль. Дорога. Инфраструктура. 2022. № 2 (32). EDN WUGDLP.</mixed-citation><mixed-citation xml:lang="en">Demyanushko I.V., Mikheev P.S., Medvedev M.M. Features of structures of road mobile frontal barriers and calculations in design analysis. Avtomobil. Road. Infrastructure. 2022; 2(32). EDN WUGDLP.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang Y., Li R., Heng K., Hu F. Dynamic behaviors of optimized K12 anti-ram bollards // Symmetry. 2022. Vol. 14. Issue 8. P. 1703. DOI: 10.3390/sym14081703</mixed-citation><mixed-citation xml:lang="en">Zhang Y., Li R., Heng K., Hu F. Dynamic behaviors of optimized K12 anti-ram bollards. Symmetry. 2022; 14(8):1703. DOI: 10.3390/sym14081703</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Bruski D., Burzyński S., Witkowski W. Analysis of passenger car crash with a cable barrier installed with anti-glare screens on a horizontal convex road curve with 400 m radius // International Journal of Impact Engineering. 2023. Vol. 173. P. 104486. DOI: 10.1016/j.ijimpeng.2022.104486</mixed-citation><mixed-citation xml:lang="en">Bruski D., Burzyński S., Witkowski W. Analysis of passenger car crash with a cable barrier installed with anti-glare screens on a horizontal convex road curve with 400 m radius. International Journal of Impact Engineering. 2023; 173:104486. DOI: 10.1016/j.ijimpeng.2022.104486</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Carter S.D., Rilett L.R. Evaluation of department of defense installation entry control facilities using microsimulation // Transportation Research Record. 2023. Vol. 2677. Issue 3. Pp. 128–144. DOI: 10.1177/03611981221114116</mixed-citation><mixed-citation xml:lang="en">Carter S.D., Rilett L.R. Evaluation of department of defense installation entry control facilities using microsimulation. Transportation Research Record. 2023; 2677(3):128-144. DOI: 10.1177/03611981221114116</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Salem S., Campidelli M., El-Dakhakhni W., Tait M. Resilience-based design for blast risk mitigation: Learning from natural disasters // Resilient structures and infrastructure. 2019. Pp. 177–194. DOI: 10.1007/978-981-13-7446-3_7</mixed-citation><mixed-citation xml:lang="en">Salem S., Campidelli M., El-Dakhakhni W., Tait M. Resilience-based design for blast risk mitigation: Learning from natural disasters. Resilient Structures and Infrastructure. 2019; 177-194. DOI: 10.1007/978-981-13-7446-3_7</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Ивченко В.И., Шмелёв А.В., Талалуев А.В., Омелюсик А.В. Методические рекомендации по топологической оптимизации силовых конструкций с применением средств численного моделирования // Механика машин, механизмов и материалов. 2022. Vol. 4 (61). Pp. 68–79. DOI: 10.46864/1995-0470-2022-4-61-68-79. EDN FIHNIA.</mixed-citation><mixed-citation xml:lang="en">Ivchenko V.I., Shmialiou A.V., Talaluev A.V., Omeliusik A.V. Methodological recommendations on topological optimization of power structures using numerical modeling tools. Mechanics of Machines, Mechanisms and Materials. 2022; 4(61):68-79. DOI: 10.46864/1995-0470-2022-4-61-68-79 EDN FIHNIA</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Chen X., Agrawal A., El-Tawil S., Xu X., Cao R., Wong W. Inelastic behavior of a bridge bent subjected to truck impact: Experimental and computational study // Engineering Structures. 2019. Vol. 199. Issue 6. P. 109543. DOI: 10.1016/j.engstruct.2019.109543</mixed-citation><mixed-citation xml:lang="en">Chen X., Agrawal A., El-Tawil S., Xu X., Cao R., Wong W. Inelastic behavior of a bridge bent subjected to truck impact: Experimental and computational study. Engineering Structures. 2019; 199(6):109543. DOI: 10.1016/j.engstruct.2019.109543</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Chen L., Wu H., Liu T. Vehicle collision with bridge piers: A state-of-the-art review // Advances in Structural Engineering. 2021. Vol. 24. Issue 2. Pp. 385–400. DOI: 10.1177/1369433220953510</mixed-citation><mixed-citation xml:lang="en">Chen L., Wu H., Liu T. Vehicle collision with bridge piers: A state-of-the-art review. Advances in Structural Engineering. 2021; 24(2):385-400. DOI: 10.1177/1369433220953510</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Jalaluddin N.F.M., Said C.S. Sorotan Literatur Kajian kes penggunaan metod TRIZ dalam menyelesaikan masalah // Rumpun Jurnal Persuratan Melayu. 2021. Vol. 9. Issue 2. Pp. 48–57. URL: https://rumpunjurnal.com/jurnal/index.php/rumpun/article/view/145</mixed-citation><mixed-citation xml:lang="en">Jalaluddin N.F.M., Said C.S. Sorotan Literatur Kajian kes penggunaan metod TRIZ dalam menyelesaikan masalah. Rumpun Jurnal Persuratan Melayu. 2021; 9(2):48-57. URL: https://rumpunjurnal.com/jurnal/index.php/rumpun/article/view/145</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Kamel H. Review of design techniques of armored vehicles for protection against blast from improvised explosive devices // ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers. 2019. Vol. 83501. P. V013T13A001. DOI: 10.1115/IMECE2019-10227</mixed-citation><mixed-citation xml:lang="en">Kamel H. Review of design techniques of armored vehicles for protection against blast from Improvised Explosive Devices. ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers. 2019; 83501:V013T13A001. DOI: 10.1115/IMECE2019-10227</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Ma J., Guo Y. Stress analysis of steel wire in strand based on optical lever principle and finite element calculation // Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2020. Vol. 42. Pp. 1–10. DOI: 10.1007/s40430-019-2120-1</mixed-citation><mixed-citation xml:lang="en">Ma J., Guo Y. Stress analysis of steel wire in strand based on optical lever principle and finite element calculation. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2020; 42:1-10. DOI: 10.1007/s40430-019-2120-1</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Gurevich L., Danenko V., Bogdanov A., Kulevich V. Analysis of the stress-strain state of steel closed ropes under tension and torsion // The International Journal of Advanced Manufacturing Technology. 2022. Vol. 118. Issue 1–2. Pp. 15–22. DOI: 10.1007/s00170-021-07128-w</mixed-citation><mixed-citation xml:lang="en">Gurevich L., Danenko V., Bogdanov A., Kulevich V. Analysis of the stress-strain state of steel closed ropes under tension and torsion. The International Journal of Advanced Manufacturing Technology. 2022; 118(1-2):15-22. DOI: 10.1007/s00170-021-07128-w</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Palit P., Kushwaha S., Mathur J., Chaturvadi A. Life cycle assessment of wire rope used in crane application in a steel plant // Journal of failure analysis and prevention. 2019. Vol. 19. Issue 3. Pp. 752–760. DOI: 10.1007/s11668-019-00655-5</mixed-citation><mixed-citation xml:lang="en">Palit P., Kushwaha S., Mathur J., Chaturvadi A. Life cycle assessment of wire rope used in crane application in a steel plant. Journal of failure Analysis and Prevention. 2019; 19(3):752-760. DOI: 10.1007/s11668-019-00655-5</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Eremeev P.G., Vedyakov I.I., Zvezdov A.I. Suspension large span roofs structures in Russia // International Journal for Computational Civil and Structural Engineering. 2021. Vol. 17. Issue 2. Pp. 34–42. DOI: 10.22337/2587-9618-2021-17-2-34-41. EDN NBSNNA.</mixed-citation><mixed-citation xml:lang="en">Eremeev P.G., Vedyakov I.I., Zvezdov A.I. Suspension large span roofs structures in Russia. International Journal for Computational Civil and Structural Engineering. 2021; 17(2):34-42. DOI: 10.22337/2587-9618-2021-17-2-34-41. EDN NBSNA.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Jiang Z., Liu X., Shi K., Lin Q., Zhang Z. Catenary equation-based approach for force finding of cable domes // International Journal of Steel Structures. 2019. Vol. 19. Pp. 283–292. DOI: 10.1007/s13296-018-0117-8</mixed-citation><mixed-citation xml:lang="en">Jiang Z., Liu X., Shi K., Lin Q., Zhang Z. Catenary equation-based approach for force finding of cable domes. International Journal of Steel Structures. 2019; 19:283-292. DOI: 10.1007/s13296-018-0117-8</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Jia L., Zhang C., Jiang Y.M., Cheng J., Xiao R. Simplified calculation methods for static behaviors of triple-tower suspension bridges and parametric study // International Journal of Steel Structures. 2018. Vol. 18. Issue 2. Pp. 685–698. DOI: 10.1007/s13296-018-0028-8</mixed-citation><mixed-citation xml:lang="en">Jia L., Zhang C., Jiang Y., Cheng J., Xiao R. Simplified calculation methods for static behaviors of triple-tower suspension bridges and parametric study. International Journal of Steel Structures. 2018; 18(2):685-698. DOI: 10.1007/s13296-018-0028-8</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Song T., Wang B., Song Y. A simplified calculation method for multi-tower self-anchored suspension bridges based on frame structure theory model // International Journal of Steel Structures. 2022. Vol. 22. Issue 1. Pp. 373–388. DOI: 10.1007/s13296-022-00581-7</mixed-citation><mixed-citation xml:lang="en">Song T., Wang B., Song Y. A simplified calculation method for multi-tower self-anchored suspension bridges based on frame structure theory model. International Journal of Steel Structures. 2022; 22(1):373-388. DOI: 10.1007/s13296-022-00581-7</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Сиянов А.И., Ярошевич Д.К. Расчет цилиндрических сетчатых покрытий с учетом уравнений движения // Вестник Томского государственного архитектурно-строительного университета. 2023. Т. 25. № 3. С. 112–119. DOI: 10.31675/1607-1859-2023-25-3-112-119. EDN JCAXAA.</mixed-citation><mixed-citation xml:lang="en">Siyanov A.I., Yaroshevich D.K. Calculation of cylindrical mesh coatings based on equations of motion. Bulletin of the Tomsk State University of Architecture and Civil Engineering. 2023; 25(3):112-119. DOI: 10.31675/1607-1859-2023-25-3-112-119. EDN JCAXAA.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Тарасов Д.А., Коновалов В.В., Данилов А.Л., Бобылев А.И. Определение области несущей способности гибкой нити при действии поперечного удара // XXI век: итоги прошлого и проблемы настоящего плюс. 2021. Т. 10. № 2 (54). С. 40–43. DOI: 10.46548/21vek-2021-1054-0007. EDN FKUILU.</mixed-citation><mixed-citation xml:lang="en">Tarasov D.A., Konovalov V.V., Danilov A.L., Bobylev A.I. Determination of the region of carrying capacity of a flexible thread during action cross impact. XXI Century: Results of the Past and Problems of the Present Plus. 2021; 10(2):40-43. DOI: 10.46548/21vek-2021-1054-0007. EDN FKUILU.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Тарасов Д.А. Параметрическая оптимизация стальных канатов при действии поперечного удара // XXI век: итоги прошлого и проблемы настоящего плюс. 2015. № 2 (24). С. 56–62. EDN TYVZHD.</mixed-citation><mixed-citation xml:lang="en">Tarasov D.A. Parametric optimization of steel ropes under lateral impact. XXI Century: Results of the Past and Problems of the Present Plus. 2015; 2(24):56-62. EDN TYVZHD.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
