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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">45221</article-id><article-id pub-id-type="doi">10.22363/1815-5235-2025-21-2-155-166</article-id><article-id pub-id-type="edn">NRNOQA</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Analysis of thin elastic shells</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Расчет тонких упругих оболочек</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">Torses with Two Curves in Intersecting Planes and with Parallel Axes</article-title><trans-title-group xml:lang="ru"><trans-title>Торсы с двумя кривыми в пересекающихся плоскостях и с параллельными осями</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9385-3699</contrib-id><contrib-id contrib-id-type="spin">2021-6966</contrib-id><name-alternatives><name xml:lang="en"><surname>Krivoshapko</surname><given-names>Sergey N.</given-names></name><name xml:lang="ru"><surname>Кривошапко</surname><given-names>Сергей Николаевич</given-names></name></name-alternatives><bio xml:lang="en"><p>Doctor of Technical Sciences, Associate Professor of the Department of Construction Technology and Structural Materials, Academy of Engineering</p></bio><bio xml:lang="ru"><p>доктор технических наук, профессор кафедры технологий строительства и конструкционных материалов, инженерная академия</p></bio><email>sn_krivoshapko@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">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="2025-07-11" publication-format="electronic"><day>11</day><month>07</month><year>2025</year></pub-date><volume>21</volume><issue>2</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>155</fpage><lpage>166</lpage><history><date date-type="received" iso-8601-date="2025-07-23"><day>23</day><month>07</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Krivoshapko S.N.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Кривошапко С.Н.</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Krivoshapko S.N.</copyright-holder><copyright-holder xml:lang="ru">Кривошапко С.Н.</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/45221">https://journals.rudn.ru/structural-mechanics/article/view/45221</self-uri><abstract xml:lang="en"><p>Methods for designing torse surfaces with two specified plane directrix curves in intersecting planes, which are projected onto the opposite sides of an arbitrary plane quadrilateral base, are studied and implemented. The other two sides of the base coincide with the two genertrix lines. The theoretical construction techniques are illustrated and visualized using computer graphics for four torse surfaces. Parabolas of the second and fourth orders and a hyperbola are chosen as the directrix curves. The geometric and strength studies on torse surfaces and shells that have been conducted by scientists over the past 10 years are briefly described. They show that interest in their study is not fading, but is moving towards computer modeling and comparative strength calculations using the finite element method. The directions in research of various torses, that are desirable to extend to the torse surfaces proposed for implementation, are illustrated.</p></abstract><trans-abstract xml:lang="ru"><p>Исследованы и реализованы методики проектирования торсовой поверхности с двумя заданными направляющими плоскими кривыми на пересекающихся плоскостях, которые проецируются на противоположные стороны произвольного плоского четырехугольника. Две другие стороны плана совпадают с двумя образующими прямыми. Теоретические построения проиллюстрированы и визуализированы с помощью компьютерной графики на четырех торсовых поверхностях. В качестве направляющих кривых выбраны параболы второго и четвертого порядков и гипербола. Кратко описаны геометрические и прочностные исследования по торсовым поверхностям и оболочкам, которые проводились учеными за последние 10 лет. Они показывают, что интерес к их изучению не проходит, но перемещается в сторону компьютерного моделирования и сравнительных расчетов на прочность при помощи метода конечных элементов. Проиллюстрированы направления в исследованиях разнообразных торсов, которые желательно распространить на предлагаемые к внедрению торсовые поверхности.</p></trans-abstract><kwd-group xml:lang="en"><kwd>torse surface</kwd><kwd>arbitrary quadrilateral base</kwd><kwd>torse design</kwd><kwd>coplanarity of three vectors</kwd><kwd>torse implementation</kwd><kwd>developable helicoid</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>торсовая поверхность</kwd><kwd>произвольный четырехугольный план</kwd><kwd>конструирование торсов</kwd><kwd>компланарность трех векторов</kwd><kwd>использование торсов</kwd><kwd>развертывающийся геликоид</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Krivoshapko S.N., Gil-oulbé M. Tangential developable surfaces and their application in real structures. 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