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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Structural Mechanics of Engineering Constructions and Buildings</journal-id><journal-title-group><journal-title xml:lang="en">Structural Mechanics of Engineering Constructions and Buildings</journal-title><trans-title-group xml:lang="ru"><trans-title>Строительная механика инженерных конструкций и сооружений</trans-title></trans-title-group></journal-title-group><issn publication-format="print">1815-5235</issn><issn publication-format="electronic">2587-8700</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">50717</article-id><article-id pub-id-type="doi">10.22363/1815-5235-2025-22-1-3-15</article-id><article-id pub-id-type="edn">ICIGST</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Analytical and numerical methods of analysis of structures</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Аналитические и численные методы расчета конструкций</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Analysis of Viscoelastic Behavior of Antifriction Layer Materials in Bridge Spherical Bearings under Thermomechanical Loading</article-title><trans-title-group xml:lang="ru"><trans-title>Анализ вязкоупругого поведения материалов антифрикционной прослойки сферической опорной части моста при термосиловом нагружении</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3012-2418</contrib-id><contrib-id contrib-id-type="spin">4748-1891</contrib-id><name-alternatives><name xml:lang="en"><surname>Kamenskikh</surname><given-names>Anna A.</given-names></name><name xml:lang="ru"><surname>Каменских</surname><given-names>Анна Александровна</given-names></name></name-alternatives><bio xml:lang="en"><p>Candidate of Technical Sciences, Associate Professor of the Department of Computational Mathematics, Mechanics and Biomechanics</p></bio><bio xml:lang="ru"><p>кандидат технических наук, доцент кафедры вычислительной математики, механики и биомеханики</p></bio><email>anna_kamenskih@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7426-1287</contrib-id><contrib-id contrib-id-type="spin">5496-7620</contrib-id><name-alternatives><name xml:lang="en"><surname>Bogdanova</surname><given-names>Anastasia P.</given-names></name><name xml:lang="ru"><surname>Богданова</surname><given-names>Анастасия Петровна</given-names></name></name-alternatives><bio xml:lang="en"><p>postgraduate student, Researcher of the Digital Engineering of Mechanical Engineering Processes and Production</p></bio><bio xml:lang="ru"><p>аспирант, научный сотрудник лаборатории цифрового инжиниринга машиностроительных процессов и производств</p></bio><email>anstasia_pankova@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5736-8645</contrib-id><contrib-id contrib-id-type="spin">4209-2760</contrib-id><name-alternatives><name xml:lang="en"><surname>Nosov</surname><given-names>Yuriy O.</given-names></name><name xml:lang="ru"><surname>Носов</surname><given-names>Юрий Олегович</given-names></name></name-alternatives><bio xml:lang="en"><p>Researcher of the Digital Engineering of Mechanical Engineering Processes and Production</p></bio><bio xml:lang="ru"><p>научный сотрудник лаборатории цифрового инжиниринга машиностроительных процессов и производств</p></bio><email>ura.4132@yandex.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0001-6608-8987</contrib-id><contrib-id contrib-id-type="spin">2878-0214</contrib-id><name-alternatives><name xml:lang="en"><surname>Kuznetsova</surname><given-names>Yulia S.</given-names></name><name xml:lang="ru"><surname>Кузнецова</surname><given-names>Юлия Сергеевна</given-names></name></name-alternatives><bio xml:lang="en"><p>Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Computational Mathematics, Mechanics and Biomechanics</p></bio><bio xml:lang="ru"><p>кандидат физико-математических наук, доцент кафедры вычислительной математики, механики и биомеханики</p></bio><email>suhodolchik@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Perm National Research Polytechnic University</institution></aff><aff><institution xml:lang="ru">Пермский национальный исследовательский политехнический университет</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2026-06-16" publication-format="electronic"><day>16</day><month>06</month><year>2026</year></pub-date><volume>22</volume><issue>1</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>3</fpage><lpage>15</lpage><history><date date-type="received" iso-8601-date="2026-06-19"><day>19</day><month>06</month><year>2026</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2026, Kamenskikh A.A., Bogdanova A.P., Nosov Y.O., Kuznetsova Y.S.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2026, Каменских А.А., Богданова А.П., Носов Ю.О., Кузнецова Ю.С.</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="en">Kamenskikh A.A., Bogdanova A.P., Nosov Y.O., Kuznetsova Y.S.</copyright-holder><copyright-holder xml:lang="ru">Каменских А.А., Богданова А.П., Носов Ю.О., Кузнецова Ю.С.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/structural-mechanics/article/view/50717">https://journals.rudn.ru/structural-mechanics/article/view/50717</self-uri><abstract xml:lang="en"><p>Thermoplastic polymeric materials have found wide application as protective and antifriction coatings and interlayers of friction units. Spherical bearings include relatively thin sliding layers made of antifriction materials. Polytetrafluoroethylene (PTFE) is widely used as a material for sliding layers. However, at present, there are modern composite and modified materials with improved physical and mechanical properties that can be used as sliding layers. Antifriction materials are often modeled in terms of elasticity theory or elastoplasticity theory. However, it has been established that these materials exhibit viscoelastic properties. A series of experiments to determine the thermomechanical properties of the materials is performed in the current work. PTFE, a metal composite based on PTFE with bronze inclusions (MAK (F4BR40M2)) and structurally modified Arflon AR-200 PTFE were investigated using dynamic mechanical analysis. The temperature change range [-40; +80] °C was considered, it corresponds to the operating temperatures of bridge structures. Temperature dependencies of the storage modulus, loss modulus and loss tangent were obtained. Viscoelastic models of material behavior, such as Maxwell bodies using Prony series and temperature-time analogy, were constructed based on experimental data. Viscoelastic behavior of materials was analyzed in terms of deformation of a bridge spherical bearing under static and periodic loads, taking into account the ambient temperature. The relationships for the effect of temperature on the stress-strain response and contact parameters were obtained. The influence of the thermal expansion coefficient of materials on the structure behavior was considered. It was found that the sliding layer made of MAK allows for a more favorable stress-strain state compared to the structure including a sliding layer made of PTFE: the maximum stress intensity is less by ~ 3%; the maximum strain intensity is less by ~ 20%; displacements along the normal to the sliding layer are less by ~ 17.2%.</p></abstract><trans-abstract xml:lang="ru"><p>Термопластические полимерные материалы нашли широкое применение в качестве защитных и антифрикционных покрытий и прослоек узлов трения. Сферические опорные части включают относительно тонкие слои скольжения из антифрикционных материалов. Политетрафторэтилен (ПТФЭ) широко используется в качестве материала слоев скольжения. Однако существуют современные композиционные и модифицированные материалы с улучшенными физико-механическими свойствами, которые могут применяться в качестве слоев скольжения. Антифрикционные материалы часто моделируются в рамках теории упругости или теории упругопластичности. Но установлено, что данные материалы проявляют вязкоупругие свойства. В текущей работе выполнен цикл экспериментов для определения термомеханических свойств материалов. ПТФЭ, металлокомпозит на основе ПТФЭ с бронзовыми включениями (МАК (Ф4БР40М2)) и структурно-модифицированный ПТФЭ Арфлон AR-200 были исследованы в рамках динамического механического анализа. Рассматривался диапазон изменения температур [-40; +80] °С, он соответствует температурам эксплуатации мостовых сооружений. Получены температурные зависимости модуля накопления, модуля потерь и тангенса угла механических потерь. На основе экспериментальных данных построены вязкоупругие модели поведения материалов, такие как тела Максвелла, с использованием рядов Прони и температурно-временной аналогии. Вязкоупругое поведение материалов было проанализировано в рамках деформирования сферической опорной части мостовых сооружений при статической и периодической нагрузке с учетом температуры окружающей среды. Получены зависимости параметров напряженно-деформированного состояния и контакта от температуры. Рассмотрено влияние коэффициента термического расширения материалов на поведение конструкции. Установлено, что слой скольжения из МАК позволяет получить более благоприятное напряженно деформированное состояние по сравнению с конструкцией, включающей слой скольжения из ПТФЭ: максимальная интенсивность напряжений меньше ~ на 3 %; максимальная интенсивность деформаций меньше ~ на 20 %; перемещения по нормали слоя скольжения меньше ~ на 17,2 %.</p></trans-abstract><kwd-group xml:lang="en"><kwd>bridge structure</kwd><kwd>bearing</kwd><kwd>modeling</kwd><kwd>viscoelasticity</kwd><kwd>polymer</kwd><kwd>composite</kwd><kwd>Maxwell’s model</kwd><kwd>Prony</kwd><kwd>finite element method</kwd><kwd>contact</kwd><kwd>friction</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>мостовое сооружение</kwd><kwd>опорная часть</kwd><kwd>моделирование</kwd><kwd>вязкоупругость</kwd><kwd>полимер</kwd><kwd>композит</kwd><kwd>модель Максвелла</kwd><kwd>Прони</kwd><kwd>метод конечных элементов</kwd><kwd>контакт</kwd><kwd>трение</kwd></kwd-group><funding-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Исследование выполнено за счет гранта Российского научного фонда № 25-29-00638, https://rscf.ru/project/25-29-00638/</institution></institution-wrap><institution-wrap><institution xml:lang="en">he research was funded by the grant of the Russian Science Foundation No. 25-29-00638, https://rscf.ru/project/25-29-00638/</institution></institution-wrap></funding-source></award-group></funding-group></article-meta><fn-group/></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Liang X., Wu P., Lan L., Wang Y., Ning Y., Wang Y., Qin Y. 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