<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE root>
<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">23420</article-id><article-id pub-id-type="doi">10.22363/2312-8143-2019-20-4-276-284</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Aviation and rocket and space technology</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Авиационная и ракетно-космическая техника</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">Design of the structural arrangement for a space reflector via parametric and topology optimization</article-title><trans-title-group xml:lang="ru"><trans-title>Разработка схемы подкрепления отражающей обшивки рефлектора методами параметрической и топологической оптимизации</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Filina</surname><given-names>Elena K.</given-names></name><name xml:lang="ru"><surname>Филина</surname><given-names>Елена Константиновна</given-names></name></name-alternatives><bio xml:lang="en"><p>post-graduate student of the Rocket-Space Composite Structures Department (SM13) at BMSTU, engineer at Astro Space Center of LPI RAS.</p></bio><bio xml:lang="ru"><p>аспирант кафедры СМ13 «Ракетно-космические композитные конструкции» МГТУ имени Н.Э. Баумана, инженер Астрокосмического центра ФИАН</p></bio><email>konst_mi@mail.ru</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Golubev</surname><given-names>Evgenii S.</given-names></name><name xml:lang="ru"><surname>Голубев</surname><given-names>Евгений Сергеевич</given-names></name></name-alternatives><bio xml:lang="en"><p>post-graduate student of the Technologies of Space-Rocket Mechanical Engineering Department (SM12) at BMSTU, lead engineer at Astro Space Center of LPI RAS.</p></bio><bio xml:lang="ru"><p>аспирант кафедры СМ12 «Технологии ракетно-космического машиностроения» МГТУ имени Н.Э. Баумана, ведущий инженер Астрокосмического центра ФИАН</p></bio><email>konst_mi@mail.ru</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Mikhailovskiy</surname><given-names>Konstantin V.</given-names></name><name xml:lang="ru"><surname>Михайловский</surname><given-names>Константин Валерьевич</given-names></name></name-alternatives><bio xml:lang="en"><p>Associate Professor of the Rocket-Space Composite Structures Department (SM13) at BMSTU, PhD in Engineering Sciences</p></bio><bio xml:lang="ru"><p>доцент кафедры СМ13 «Ракетно-космические композитные конструкции» МГТУ имени Н.Э. Баумана, кандидат технических наук</p></bio><email>konst_mi@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Arkhipov</surname><given-names>Mikhail Yu.</given-names></name><name xml:lang="ru"><surname>Архипов</surname><given-names>Михаил Юрьевич</given-names></name></name-alternatives><bio xml:lang="en"><p>senior researcher at Astro Space Center of LPI RAS, PhD in Engineering Sciences</p></bio><bio xml:lang="ru"><p>старший научный сотрудник Астрокосмического центра ФИАН, кандидат технических наук</p></bio><email>konst_mi@mail.ru</email><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Bauman Moscow State Technical University</institution></aff><aff><institution xml:lang="ru">Московский государственный технический университет имени Н.Э. Баумана</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Lebedev Physical Institute of Russian Academy of Sciences</institution></aff><aff><institution xml:lang="ru">Физический институт имени П.Н. Лебедева Российской академии наук</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2019-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2019</year></pub-date><volume>20</volume><issue>4</issue><issue-title xml:lang="en">VOL 20, NO4 (2019)</issue-title><issue-title xml:lang="ru">ТОМ 20, №4 (2019)</issue-title><fpage>276</fpage><lpage>284</lpage><history><date date-type="received" iso-8601-date="2020-04-09"><day>09</day><month>04</month><year>2020</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2019, Filina E.K., Golubev E.S., Mikhailovskiy K.V., Arkhipov M.Y.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2019, Филина Е.К., Голубев Е.С., Михайловский К.В., Архипов М.Ю.</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="en">Filina E.K., Golubev E.S., Mikhailovskiy K.V., Arkhipov M.Y.</copyright-holder><copyright-holder xml:lang="ru">Филина Е.К., Голубев Е.С., Михайловский К.В., Архипов М.Ю.</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/23420">https://journals.rudn.ru/engineering-researches/article/view/23420</self-uri><abstract xml:lang="en"><p>Development of the optimal structural arrangement for a reflector with the aim to improve its mass and design is of importance due to the necessity to increase areal density and decrease rigidity of the modern space antennas vehicles. Currently, CAE-systems allow to design reflectors using both traditional methods, for example, parametric optimization, and methods which are innovative in this field, such as topology optimization. The paper compares two methods of the structural arrangement design for a thin dimensionally stable reflector operating as part of a geostationary spacecraft: parametric and topology optimization. The algorithms of the structural arrangement development which include the statement of the optimization problem, geometry design and a number of check analyses are presented. A number of structural of a space reflector design under the action of loads at the stage of launch, temperature gradients at the exploitation conditions and modal analysis is performed. The designed reflectors are compared. The studies performed allowed us to develop the optimal structural arrangement for a space reflector using the parametric and topology optimization. The optimal structural arrangement for a space reflector using the optimization could be produced surface figure error (estimated in RMS) with respect to the theoretical paraboloid.</p></abstract><trans-abstract xml:lang="ru"><p>Проектирование оптимальной схемы подкрепления обшивки размеростабильного рефлектора для достижения конструктивно-массового совершенства представляет интерес вследствие необходимости снижения поверхностной плотности и увеличения жесткости современных зеркальных космических антенн космических аппаратов. На сегодняшний день системы численного инженерного анализа позволяют разрабатывать такие конструкции как традиционными способами, например параметрической оптимизацией, так и способами, новыми в области создания рефлекторов, - топологической оптимизацией. В работе для проектирования схемы подкрепления размеростабильного рефлектора зеркальной космической антенны, функционирующего в составе космического аппарата на геостационарной орбите, используется параметрическая и топологическая оптимизация. Представлены алгоритмы создания схемы подкрепления, включающие в себя этапы постановки задачи оптимизации, разработки геометрии и проведения серии поверочных расчетов. Рассмотрен ряд вариантов конструкции рефлектора зеркальной космической антенны при действии нагрузок на этапе выведения, температурных перепадов в условиях близких к эксплуатационным, а также выполнен модальный анализ. Произведено сравнение разработанных схем подкрепления разными методами. Выполненные исследования позволили разработать оптимальную схему подкрепления обшивки зеркальной космической антенны с помощью методов параметрической и топологической оптимизации. Установлено, что разработанная с помощью оптимизации схема подкрепления отражающей обшивки рефлектора зеркальной космической антенны позволяет обеспечить в условиях эксплуатации необходимое среднеквадратичное отклонение поверхности относительно теоретического параболоида.</p></trans-abstract><kwd-group xml:lang="en"><kwd>space antenna</kwd><kwd>reflector</kwd><kwd>structural arran- gement</kwd><kwd>ribs</kwd><kwd>carbon fiber reinforced plastic</kwd><kwd>parametric optimization</kwd><kwd>topology optimization</kwd><kwd>static analysis</kwd><kwd>thermal deformations</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>зеркальная космическая антенна</kwd><kwd>рефлектор</kwd><kwd>схема подкрепления</kwd><kwd>ребра</kwd><kwd>углепластик</kwd><kwd>параметрическая оптимизация</kwd><kwd>топологическая оптимизация</kwd><kwd>статический анализ</kwd><kwd>термодеформации</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">Reznik S. Thermal regimes of space composite structures. Part I. MATEC Web of Conferences. EDP Sciences. 2018;194:01048. Available from: https://doi.org/ 10.1051/matecconf/201819401048</mixed-citation><mixed-citation xml:lang="ru">Reznik S. Thermal regimes of space composite structures. Part I // MATEC Web of Conferences. EDP Sciences. 2018. Vol. 194. P. 01048. DOI: 10.1051/ matecconf/201819401048.</mixed-citation></citation-alternatives></ref><ref id="B2"><label>2.</label><citation-alternatives><mixed-citation xml:lang="en">Pilipenko S, Smirnov A, Kardashev N. Current status of the space mission Millimetron. Frontier Research in Astrophysics. SISSA Medialab. 2016;237:037. Available from: https://doi.org/10.22323/1.237.0037.</mixed-citation><mixed-citation xml:lang="ru">Pilipenko S., Smirnov A., Kardashev N. Current status of the space mission Millimetron // Frontier Research in Astrophysics. SISSA Medialab. 2016. Vol. 237. P. 037. DOI: 10.22323/1.237.0037.</mixed-citation></citation-alternatives></ref><ref id="B3"><label>3.</label><citation-alternatives><mixed-citation xml:lang="en">Clampin M. Status of the James WEBB space telescope (JWST). Space Telescopes and Instrumentation 2008: Optical, Infrared, and Millimeter. International Society for Optics and Photonics. 2008;7010:70100L. Available from: https://doi.org/10.1117/12.790388.</mixed-citation><mixed-citation xml:lang="ru">Clampin M. Status of the James WEBB space telescope (JWST) // Space Telescopes and Instrumentation 2008: Optical, Infrared, and Millimeter. International Society for Optics and Photonics. 2008. Vol. 7010. P. 70100L. DOI: 10.1117/12.790388</mixed-citation></citation-alternatives></ref><ref id="B4"><label>4.</label><citation-alternatives><mixed-citation xml:lang="en">Babkina LA., Sorokin DV. Parametric Analysis of the Spacecraft Parabolic Antenna with a Multivariate Reinforcement Scheme. Engineering Journal: Science and Innovation. 2017;64(4):1–9. DOI: 10.18698/2308-6033-2017-4-1611. (In Russ.)</mixed-citation><mixed-citation xml:lang="ru">Бабкина Л.А., Сорокин Д.В. Параметрический анализ параболической антенны космического аппарата с многовариантной схемой подкрепления // Инженерный журнал: наука и инновации. 2017. Т. 64. № 4. С. 1-9. DOI: 10.18698/2308-6033-2017-4-1611.</mixed-citation></citation-alternatives></ref><ref id="B5"><label>5.</label><citation-alternatives><mixed-citation xml:lang="en">Yoder PJr, Vukobratovich D. Opto-Mechanical Systems Design. Design and Analysis of Opto-Mechanical Assemblies. 4th ed. Boca Raton: CRC Press; 2015. vol. 2. p. 97–101.</mixed-citation><mixed-citation xml:lang="ru">Yoder P., Jr., Vukobratovich D. Opto-Mechanical Systems Design. Design and Analysis of Opto-Mechanical Assemblies. 4th ed. Boca Raton: CRC Press, 2015. Vol. 2. P. 97-101.</mixed-citation></citation-alternatives></ref><ref id="B6"><label>6.</label><citation-alternatives><mixed-citation xml:lang="en">Reznik SV, Prosuntsov PV, Novikov AD. Comparison of space antennas mirror reflectors parameters made of composite materials. MATEC Web of Conferences. EDP Sciences. 2017;110:01072. Available from: https:// doi.org/10.1051/matecconf/201711001072</mixed-citation><mixed-citation xml:lang="ru">Reznik S.V., Prosuntsov P.V., Novikov A.D. Comparison of space antennas mirror reflectors parameters made of composite materials // MATEC Web of Conferences. EDP Sciences. 2017. Vol. 110. P. 01072. DOI: 10.1051/ matecconf/201711001072</mixed-citation></citation-alternatives></ref><ref id="B7"><label>7.</label><citation-alternatives><mixed-citation xml:lang="en">Qu Y, Wang W, Liu B, Li X. Topology Optimization Design of Space Rectangular Mirror. Proceedings of SPIE 10154, Advanced Optical Design and Manufacturing Technology and Astronomical Telescopes and Instrumentation, 1015421, 2016, Oct. 19, Beijing, China. DOI: 10.1117/12.2247396.</mixed-citation><mixed-citation xml:lang="ru">Qu Y., Wang W., Liu B., Li X. Topology Optimization Design of Space Rectangular Mirror // Proceedings SPIE 10154, Advanced Optical Design and Manufacturing Technology and Astronomical Telescopes and Instrumentation. 1015421. 2016, Oct. 19, Beijing, China. DOI: 10.1117/12.2247396.</mixed-citation></citation-alternatives></ref><ref id="B8"><label>8.</label><citation-alternatives><mixed-citation xml:lang="en">Liu J, Jiang B. Topology Optimization Design of a Space Mirror. Proceedings SPIE 9795, Selected Papers of the Photoelectronic Technology Committee Conferences, 97952Y, 2015, June – July, Hefei, Suzhou and Harbin, China. DOI: 10.1117/12.2209031.</mixed-citation><mixed-citation xml:lang="ru">Liu J., Jiang B. Topology Optimization Design of a Space Mirror // Proceedings SPIE 9795: Selected Papers of the Photoelectronic Technology Committee Conferences. 97952Y. 2015, June - July, Hefei, Suzhou and Harbin, China. DOI: 10.1117/12.2209031.</mixed-citation></citation-alternatives></ref><ref id="B9"><label>9.</label><citation-alternatives><mixed-citation xml:lang="en">Budinoff JG, Michels GJ. Design and Optimization of the Spherical Primary Optical Telescope (SPOT) Primary Mirror Segment. Proceedings SPIE 5877, Optomechanics 2005, 587711, 2005 Sept. 9, San Diego, US. DOI: 10.1117/12.626566.</mixed-citation><mixed-citation xml:lang="ru">Budinoff J.G., Michels G.J. Design and Optimization of the Spherical Primary Optical Telescope (SPOT) Primary Mirror Segment // Proceedings SPIE 5877. Optomechanics 2005. 587711. 2005, Sept. 9, San Diego, US. DOI: 10.1117/12.626566.</mixed-citation></citation-alternatives></ref><ref id="B10"><label>10.</label><citation-alternatives><mixed-citation xml:lang="en">Park K-S, Lee JH, Youn S-K. Lightweight mirror design method using topology optimization. Optical engineering. 2005;44(5):053002. DOI: 10.1117/1.1901685.</mixed-citation><mixed-citation xml:lang="ru">Park K.-S., Lee J.H., Youn S.-K. Lightweight mirror design method using topology optimization // Optical engineering. 2005. Vol. 44. No. 5. P. 053002. DOI: 10.1117/1.1901685.</mixed-citation></citation-alternatives></ref><ref id="B11"><label>11.</label><citation-alternatives><mixed-citation xml:lang="en">Liu G, Guo L, Wang X, Wu Q. Topology and parametric optimization based lightweight design of a space reflective mirror. Optical engineering. 2018;57(7):075101. DOI: 10.1117/1.OE.57.7.075101.</mixed-citation><mixed-citation xml:lang="ru">Liu G., Guo L., Wang X., Wu Q. Topology and parametric optimization based lightweight design of a space reflective mirror // Optical engineering. 2018. Vol. 57. No. 7. P. 075101. DOI: 10.1117/1.OE.57.7.075101.</mixed-citation></citation-alternatives></ref><ref id="B12"><label>12.</label><citation-alternatives><mixed-citation xml:lang="en">Liu S, Hu R, Li Q, Zhou P, Dong Z, Kang R. Topology optimization-based lightweight primary mirror design of a large-aperture space telescope. Applied optics. 2014;53(35):8318–8325. Available from: https://doi.org/ 10.1364/AO.53.008318.</mixed-citation><mixed-citation xml:lang="ru">Liu S., Hu R., Li Q., Zhou P., Dong Z., Kang R. Topology optimization-based lightweight primary mirror design of a large-aperture space telescope // Applied optics. 2014. Vol. 53. No. 35. Pp. 8318-8325. URL: https:// doi.org/10.1364/AO.53.008318</mixed-citation></citation-alternatives></ref><ref id="B13"><label>13.</label><citation-alternatives><mixed-citation xml:lang="en">Leea Dong-Chan, Lee Jeong-Ick. Structural optimization design for large mirror. Optics and Lasers in Engineering. 2004;42:109–117. DOI: 10.1016/S0143-8166(03) 00079-4.</mixed-citation><mixed-citation xml:lang="ru">Leea Dong-Chan, Lee Jeong-Ick. Structural optimization design for large mirror // Optics and Lasers in Engineering. 2004. Vol. 42. Pp. 109-117. DOI: 10.1016/ S0143-8166(03)00079-4.</mixed-citation></citation-alternatives></ref><ref id="B14"><label>14.</label><citation-alternatives><mixed-citation xml:lang="en">Eschenauer HA, Olhoff N. Topology optimization of continuum structures: a review. Applied Mechanics Reviews. 2001;54(4):331–390. DOI: 10.1115/1.1388075.</mixed-citation><mixed-citation xml:lang="ru">Eschenauer H.A., Olhoff N. Topology optimization of continuum structures: a review // Applied Mechanics Reviews. 2001. Vol. 54. No. 4. Pp. 331-390. URL: https://doi.org/10.1115/1.1388075</mixed-citation></citation-alternatives></ref><ref id="B15"><label>15.</label><citation-alternatives><mixed-citation xml:lang="en">Denisova LV, Kalinin DYu, Reznik SV. Theoretical and Experimental Studies of Heat-Transfer Modes of Space Antenna Mesh Reflectors. Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering. 2011;1:92–105. (In Russ.)</mixed-citation><mixed-citation xml:lang="ru">Денисова Л.В., Калинин Д.Ю., Резник С.В. Теоретические и экспериментальные исследования тепловых режимов сетчатых рефлекторов космических антенн // Вестник Московского государственного технического университета имени Н.Э. Баумана. Серия: Машиностроение. 2011. №. 1. C. 92-105.</mixed-citation></citation-alternatives></ref><ref id="B16"><label>16.</label><citation-alternatives><mixed-citation xml:lang="en">Reznik SV, Denisov OV, Chudnov IV. Main Approaches to Formation of a Thermal Vacuum Test Program of Precision Mirror Reflectors of Space Antennas. Science and Education: Scientific Edition of Bauman MSTU. 2013;8:167–184. DOI: 10.7463/0813.0612062.</mixed-citation><mixed-citation xml:lang="ru">Резник С.В., Денисов О.В., Чуднов И.В. Основные подходы к формированию программы термовакуумных испытаний прецизионных рефлекторов зеркальных космических антенн // Наука и образование: научное издание МГТУ имени Н.Э. Баумана. 2013. №. 8. C. 167-184.</mixed-citation></citation-alternatives></ref><ref id="B17"><label>17.</label><citation-alternatives><mixed-citation xml:lang="en">Arkhipov MYu. Development of models for studies of the deformation state a large space telescope reflectors petal type (PhD in Engineering Sciences dissertation). Moscow; 2002.</mixed-citation><mixed-citation xml:lang="ru">Архипов М.Ю. Разработка моделей для исследования деформированного состояния рефлектора крупногабаритного космического радиотелескопа лепесткового типа: дис.. канд. техн. наук. М., 2002.</mixed-citation></citation-alternatives></ref><ref id="B18"><label>18.</label><citation-alternatives><mixed-citation xml:lang="en">ANSYS User's Manual. ANSYS Inc.; 2016.</mixed-citation><mixed-citation xml:lang="ru">ANSYS User's Manual. ANSYS Inc., 2016.</mixed-citation></citation-alternatives></ref></ref-list></back></article>
