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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">RUDN Journal of Engineering Research</journal-id><journal-title-group><journal-title xml:lang="en">RUDN Journal of Engineering Research</journal-title><trans-title-group xml:lang="ru"><trans-title>Вестник Российского университета дружбы народов. Серия: Инженерные исследования</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2312-8143</issn><issn publication-format="electronic">2312-8151</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">25561</article-id><article-id pub-id-type="doi">10.22363/2312-8143-2020-21-3-208-214</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Civil Engineering (Construction)</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Строительство</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">Geometric nonlinear analysis of thin elastic paraboloid of revolution shaped shells with radial waves</article-title><trans-title-group xml:lang="ru"><trans-title>Геометрически нелинейный расчет тонких упругих оболочек в форме параболоида вращения с радиальными волнами</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Gil-oulbé</surname><given-names>Mathieu</given-names></name><name xml:lang="ru"><surname>Жиль-улбе</surname><given-names>Матье</given-names></name></name-alternatives><bio xml:lang="en"><p>Associate Professor of the Department of Civil Engineering of the Academy of Engineering of the RUDN University; PhD in Civil Engineering</p></bio><bio xml:lang="ru"><p>доцент департамента строительства Инженерной академии РУДН; кандидат технических наук</p></bio><email>markovich-as@rudn.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Markovich</surname><given-names>Aleksey S.</given-names></name><name xml:lang="ru"><surname>Маркович</surname><given-names>Алексей Семенович</given-names></name></name-alternatives><bio xml:lang="en"><p>Associate Professor of the Department of Civil Engineering of the Academy of Engineering of the RUDN University; PhD in Civil Engineering</p></bio><bio xml:lang="ru"><p>доцент департамента строительства Инженерной академии РУДН; кандидат технических наук</p></bio><email>markovich-as@rudn.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Ngandu</surname><given-names>Prosper</given-names></name><name xml:lang="ru"><surname>Нганду</surname><given-names>Проспер</given-names></name></name-alternatives><bio xml:lang="en"><p>undergraduate student of the Department of Civil Engineering of the Academy of Engineering of the RUDN University</p></bio><bio xml:lang="ru"><p>магистрант департамента строительства Инженерной академии РУДН</p></bio><email>markovich-as@rudn.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Anosova</surname><given-names>Svetlana V.</given-names></name><name xml:lang="ru"><surname>Аносова</surname><given-names>Светлана Вячеславовна</given-names></name></name-alternatives><bio xml:lang="en"><p>undergraduate student of the Department of Civil Engineering of the Academy of Engineering of the RUDN University</p></bio><bio xml:lang="ru"><p>магистрант департамента строительства Инженерной академии РУДН</p></bio><email>markovich-as@rudn.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Peoples’ Friendship University of Russia (RUDN University)</institution></aff><aff><institution xml:lang="ru">Российский университет дружбы народов</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2020-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2020</year></pub-date><volume>21</volume><issue>3</issue><issue-title xml:lang="en">VOL 21, NO3 (2020)</issue-title><issue-title xml:lang="ru">ТОМ 21, №3 (2020)</issue-title><fpage>208</fpage><lpage>214</lpage><history><date date-type="received" iso-8601-date="2021-01-29"><day>29</day><month>01</month><year>2021</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2020, Gil-oulbé M., Markovich A.S., Ngandu P., Anosova S.V.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2020, Жиль-улбе М., Маркович А.С., Нганду П., Аносова С.В.</copyright-statement><copyright-year>2020</copyright-year><copyright-holder xml:lang="en">Gil-oulbé M., Markovich A.S., Ngandu P., Anosova S.V.</copyright-holder><copyright-holder xml:lang="ru">Жиль-улбе М., Маркович А.С., Нганду П., Аносова С.В.</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/">http://creativecommons.org/licenses/by/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/engineering-researches/article/view/25561">https://journals.rudn.ru/engineering-researches/article/view/25561</self-uri><abstract xml:lang="en"><p>From the old ancient types of roof and dome construction, various forms of shells have been discovered which attract special attention. A shell is a structure composed of sheet material so that the curvature plays an important role in the structural behaviour, realizing its spatial form. There are different types of shells, namely thick and thin shells. G. Brankov, S.N. Krivoshapko, V.N. Ivanov, and V.A. Romanova made interesting researches of shells in the form of umbrella and umbrella-type surfaces. The term “nonlinear” refers to a given structure undergoing a change in stiffness in its loaded state. There are basically three different types of nonlinearities: geometric, physical and contact (boundary condition nonlinearity). For further analysis of the stress-strain state, a paraboloid with an inner radius of 4 m and an outer radius of 20 m and the number of waves equal to 6 was considered. The test shell is made of reinforced concrete. The minimum load parameter at which the shell loses stability indicates a more than three times the margin.</p></abstract><trans-abstract xml:lang="ru"><p>Древние крыши и купола привлекают особое внимание, благодаря разнообразию форм оболочек. Оболочка - это конструкция, состоящая из листового материала, ее кривизна играет важную роль в конструктивном поведении, реализуя пространственную форму. Существуют два типа оболочек: толстые и тонкие. Г. Бранков, С.Н. Кривошапко, В.Н. Иванов и В.А. Романова провели интересные исследования параболоидных оболочек в форме зонтичных и зонтичного типа поверхностей. К данной конструкции, подвергающейся изменению жесткости в ее нагруженном состоянии, применим термин «нелинейный». Существует три основных типа нелинейностей: геометрическая, материальная и контактная (нелинейность граничных условий). В качестве объекта исследования для определения напряженно-деформированного состояния был выбран параболоид с внутренним радиусом 4 м, внешним радиусом 20 м и числом волн, равным 6. Тестовая оболочка изготавливалась из железобетона. Параметр минимальной нагрузки, при котором оболочка теряет стабильность, показал запас более чем в три раза.</p></trans-abstract><kwd-group xml:lang="en"><kwd>paraboloid of revolution with radial waves</kwd><kwd>physical nonlinearity</kwd><kwd>contact nonlinearity</kwd><kwd>boundary condition nonlinearity</kwd><kwd>thin shell</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>параболоид вращения с радиальными волнами</kwd><kwd>материальная нелинейность</kwd><kwd>контактная нелинейность</kwd><kwd>нелинейность граничных условий</kwd><kwd>тонкая оболочка</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Krivoshapko SN, Mamieva IA. 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