<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">blackmet</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений. Черная Металлургия</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestiya. Ferrous Metallurgy</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0368-0797</issn><issn pub-type="epub">2410-2091</issn><publisher><publisher-name>National University of Science and Technology "MISIS"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17073/0368-0797-2022-4-285-293</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-2300</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>ИННОВАЦИИ В МЕТАЛЛУРГИЧЕСКОМ ПРОМЫШЛЕННОМ И ЛАБОРАТОРНОМ ОБОРУДОВАНИИ, ТЕХНОЛОГИЯХ И МАТЕРИАЛАХ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>INNOVATIONS IN METALLURGICAL INDUSTRIAL AND LABORATORY EQUIPMENT, TECHNOLOGIES AND MATERIALS</subject></subj-group></article-categories><title-group><article-title>Влияние опорного наполнителя и структуры оболочковой формы на ее трещиностойкость</article-title><trans-title-group xml:lang="en"><trans-title>Influence of support filler and structure of shell mold on its crack resistance</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0200-1675</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Одиноков</surname><given-names>В. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Odinokov</surname><given-names>V. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Валерий Иванович Одиноков, д.т.н., профессор, главный научный сотрудник Управления научно-исследовательской деятель­ностью</p><p>Россия, 681013, Хабаровский край, Комсомольск-на-Амуре, пр.  Ленина, 27</p></bio><bio xml:lang="en"><p>Valerii I. Odinokov, Dr. Sci. (Eng.), Prof., Chief Researcher of the Department of Research Activities</p><p>27 Lenina Ave., Komsomolsk-on-Amur, Khabarovsk Territory 681013, Russian Federation</p></bio><email xlink:type="simple">79122718858@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0200-1675</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Евстигнеев</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Evstigneev</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Иванович Евстигнеев, д.т.н., профессор, главный научный сотрудник Управления научно-исследовательской деятельностью</p><p>Россия, 681013, Хабаровский край, Комсомольск-на-Амуре, пр.  Ленина, 27</p></bio><bio xml:lang="en"><p>Aleksei I. Evstigneev, Dr. Sci. (Eng.), Prof., Chief Researcher of the Department of Research Activities</p><p>27 Lenina Ave., Komsomolsk-on-Amur, Khabarovsk Territory 681013, Russian Federation</p></bio><email xlink:type="simple">diss@knastu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8023-316X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дмитриев</surname><given-names>Э. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Dmitriev</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Эдуард Анатольевич Дмитриев, д.т.н., доцент, ректор</p><p>Россия, 681013, Хабаровский край, Комсомольск-на-Амуре, пр.  Ленина, 27</p></bio><bio xml:lang="en"><p>Eduard A. Dmitriev, Dr. Sci. (Eng.), Assist. Prof., Rector</p><p>27 Lenina Ave., Komsomolsk-on-Amur, Khabarovsk Territory 681013, Russian Federation</p></bio><email xlink:type="simple">rector@knastu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5142-2455</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чернышова</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Chernyshova</surname><given-names>D. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Дарья Витальевна Чернышова, аспирант</p><p>Россия, 681013, Хабаровский край, Комсомольск-на-Амуре, пр.  Ленина, 27</p></bio><bio xml:lang="en"><p>Dar’ya V. Chernyshova, Postgraduate</p><p>27 Lenina Ave., Komsomolsk-on-Amur, Khabarovsk Territory 681013, Russian Federation</p></bio><email xlink:type="simple">daracernysova744@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0667-2468</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Евстигнеева</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>EvstigneevaAnna A. Evstigneeva, Student</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Анна Алексеевна Евстигнеева, студент</p><p>Россия, 681013, Хабаровский край, Комсомольск-на-Амуре, пр.  Ленина, 27</p></bio><bio xml:lang="en"><p>Anna A. Evstigneeva, Student</p><p>27 Lenina Ave., Komsomolsk-on-Amur, Khabarovsk Territory 681013, Russian Federation</p></bio><email xlink:type="simple">annka.ewstic@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Комсомольский-на-Амуре государственный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Komsomolsk-on-Amur State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>05</day><month>05</month><year>2022</year></pub-date><volume>65</volume><issue>4</issue><fpage>285</fpage><lpage>293</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Одиноков В.И., Евстигнеев А.И., Дмитриев Э.А., Чернышова Д.В., Евстигнеева А.А., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Одиноков В.И., Евстигнеев А.И., Дмитриев Э.А., Чернышова Д.В., Евстигнеева А.А.</copyright-holder><copyright-holder xml:lang="en">Odinokov V.I., Evstigneev A.I., Dmitriev E.A., Chernyshova D.V., EvstigneevaAnna A. Evstigneeva, Student A.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" 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://fermet.misis.ru/jour/article/view/2300">https://fermet.misis.ru/jour/article/view/2300</self-uri><abstract><p>В последнее время большое внимание исследователи уделяют вопросу влияния внутренних и внешних факторов на напря­женное состояние оболочковой формы (ОФ). К внутренним факторам следует отнести ее морфологическое строение, виды, связи между контактирующими слоями. К внешним факторам следует отнести все виды силового и температурного воздействий на внешнюю поверхность оболочковой формы. В работе установлено влияние эффекта скольжения контактируемых между собой внутренних слоев на уровень напряженного состояния ОФ. Представлена математическая модель по определению напряженно-деформированного состоя­ния  (НДС) в многослойной ОФ при ее заливке жидким металлом. Оболочковая форма выполнена таким образом, что ее слои могут скользить друг относительно друга с наличием трения. Рассматриваемые вопросы являются продолжением последних работ авторов, в которых дана оценка влияния опорного наполнителя (ОН) и макроструктуры ОФ на ее НДС. При этом слои ОФ имеют одинаковые физико-механические свойства. В работе ставилась задача определить силовое влияние ОН и нагрузки в верхней части ОФ на НДС в ее сечениях. Влияние ОН оценивалось по величине трения между наружными поверхностями ОФ и ОН. Для решения задачи использовалась линейная теория упругости, уравнения теплопроводности, численные методы. На контакте наружной поверхности ОФ с поверхностью ОН решалась контактная задача. Твердая фаза в жидком металле при остывании определялась из уравнения межфазового перехода. Результаты расчетов представлены в виде графиков и эпюр. Отсутствие трения между слоями понижает трещиностойкость многослойной  ОФ.</p></abstract><trans-abstract xml:lang="en"><p>Recently, researchers have been paying more and more attention to the influence of internal and external factors on stress state of shell mold (SM). Internal factors should include morphological structure of SM, its types and connections between the contacting layers. External factors should include all types of force and temperature effects on SM external surface. The purpose of this work was to establish the sliding effect of SM internal layers in contact with each other on the level of SM stress state. The mathematical model for determining the stress-strain state (SSS) in the multilayer SM when it is filled with a liquid metal is presented. Moreover, the SM is made in such a way that its layers can slide relative to each other with the presence of friction. This work is a continuation of the recent works of the authors, where the influence of the temperature factor on the studied SM was estimated. At the same time, SM layers have the same physical and mechanical properties. The problem was solved in the same formulation as in the previous works of the authors. The task was set to determine the influence of the support filler (SF) and the clamp in the upper part of SM on SSS in its sections. The influence of SF was estimated by the amount of friction between the outer surfaces of SM and SF. Just as in the previous works of the authors, the linear theory of elasticity, heat conduction equations, and numerical methods were used to solve the problem. On the contact of  SM outer surface with SF surface, the contact problem was solved. Solid phase in the liquid metal during cooling was determined from the equation of interphase transition. Results of the calculations are presented in the form of graphs and plots. It is shown that the absence of friction between the layers reduces the crack resistance of SM multilayer.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>литье по выплавляемым моделям</kwd><kwd>оболочковая форма</kwd><kwd>напряженное состояние</kwd><kwd>моделирование</kwd><kwd>трещинообразование</kwd><kwd>трение между контактирующими поверхностями</kwd><kwd>напряжение</kwd><kwd>перемещение</kwd></kwd-group><kwd-group xml:lang="en"><kwd>casting by investment models</kwd><kwd>shell mold</kwd><kwd>stress state</kwd><kwd>modeling</kwd><kwd>cracking</kwd><kwd>friction between contacting surfaces</kwd><kwd>stress</kwd><kwd>displacemen</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">Математическое моделирование процессов получения отливок в керамические оболочковые формы / В.И. Одиноков, Э.А. Дмитриев, А.И. Евстигнеев, А.В. Свиридов. М.: Инновационное машиностроение, 2020. 224 с.</mixed-citation><mixed-citation xml:lang="en">Odinokov V.I., Dmitriev E.A., Evstigneev A.I., Sviridov A.V. Mathe­matical Modeling of Processes of Castings Production into Cera­mic Shell Molds. Moscow: Innovatsionnoe mashinostroenie, 2020, 224 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Одиноков В.И., Дмитриев Э.А., Евстигнеев А.И., Свиридов А.В., Иванкова Е.П. Моделирование и оптимизация выбора свойств материалов и морфологического строения структуры оболочковых форм по выплавляемым моделям // Известия вузов. Черная металлургия. 2020. Т. 63. № 9. С. 742–754. https://doi.org/10.17073/0368-0797-2020-9-742-754</mixed-citation><mixed-citation xml:lang="en">Odinokov V.I., Dmitriev E.A., Evstigneev A.I., Sviridov A.V., Ivankova E.P. Choice of materials properties and structure of shell molds by investment models. Izvestiya. Ferrous Metallurgy. 2020, vol. 63, no. 9, pp. 742–754. (In Russ.) https://doi.org/10.17073/0368-0797-2020-9-742-754</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Одиноков В.И., Евстигнеев А.И., Дмитриев Э.А., Чернышова Д.В., Евстигнеева А.А. Влияние внутреннего фактора на трещиностойкость оболочковой формы по выплавляемым моделям // Известия вузов. Черная металлургия. 2022. Т. 65. № 2. С. 137–144. https://doi.org/10.17073/0368-0797-2022-2-137-144</mixed-citation><mixed-citation xml:lang="en">Odinokov V.I., Evstigneev A.I., Dmitriev E.A., Chernyshova D.V., Evstigneeva A.A. Influence of internal factor on crack resistance of shell mold by investment models. Izvestiya. Ferrous Metallurgy. 2022, vol. 65, no. 2, pp. 137–144. (In Russ.). https://doi.org/10.17073/0368-0797-2022-2-137-144</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Kulikov G.M. Influence of anisotropy on the stress state of multilayer reinforced shells // Soviet Applied Mechanics. 1987. Vol. 22. No. 12. P. 1166–1170.</mixed-citation><mixed-citation xml:lang="en">Kulikov G.M. Influence of anisotropy on the stress state of multi­layer reinforced shells. Soviet Applied Mechanics. 1987, vol. 22, no.  12, pp. 1166–1170.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Zveryaev E.M., Berlinov M.V., Berlinova M.N. The integral method of definition of basic tension condition anisotropic shell // International Journal of Applied Engineering Research. 2016. Vol. 11. No. 8. P. 5811–5816.</mixed-citation><mixed-citation xml:lang="en">Zveryaev E.M., Berlinov M.V., Berlinova M.N. The integral method of definition of basic tension condition anisotropic shell. International Journal of Applied Engineering Research. 2016, vol. 11, no.  8, pp. 5811–5816.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Maximyuk V.A., Storozhuk E.A., Chernyshenko I.S. Stress state of flexible composite shells with reinforced holes // International App­lied Mechanics. 2014. Vol. 50. No. 5. P. 558–565. https://doi.org/10.1007/s10778-014-0654-6</mixed-citation><mixed-citation xml:lang="en">Maximyuk V.A., Storozhuk E.A., Chernyshenko I.S. Stress state of flexible composite shells with reinforced holes. International App­lied Mechanics. 2014, vol. 50, no. 5, pp. 558–565. https://doi.org/10.1007/s10778-014-0654-6</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Vetrov O.S., Shevchenko V.P. Study of the stress-strain state of orthotropic shells under the action of dynamical impulse loads // Journal of Mathematical Sciences. 2012. Vol. 183. No. 2. P. 231–240. https://doi.org/10.1007/s10958-012-0809-0</mixed-citation><mixed-citation xml:lang="en">Vetrov O.S., Shevchenko V.P. Study of the stress-strain state of orthotropic shells under the action of dynamical impulse loads. Journal of Mathematical Sciences. 2012, vol. 183, no. 2, pp. 231–240. https://doi.org/10.1007/s10958-012-0809-0</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Vasilenko A.T., Urusova G.P. The stress state of anisotropic co­nic shells with thickness varying in two directions // International Applied Mechanics. 2000. Vol. 35. No. 5. P. 631–638. https://doi.org/10.1007/BF02682077</mixed-citation><mixed-citation xml:lang="en">Vasilenko A.T., Urusova G.P. The stress state of anisotropic conic shells with thickness varying in two directions. International Applied Mechanics. 2000, vol. 35, no. 5, pp. 631–638. https://doi.org/10.1007/BF02682077</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Tovstik P.E., Tovstik T.P. Two-dimensional linear model of elastic shell accounting for general anisotropy of material // Acta Mechanica. 2014. Vol. 225. No. 3. P. 647–661. https://doi.org/10.1007/s00707-013-0986-z</mixed-citation><mixed-citation xml:lang="en">Tovstik P.E., Tovstik T.P. Two-dimensional linear model of elastic shell accounting for general anisotropy of material. Acta Mechanica. 2014, vol. 225, no. 3, pp. 647–661. https://doi.org/10.1007/s00707-013-0986-z</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Grigorenko Y.M., Vasilenko A.T, Pankratova N.D. Stress state and deformability of composite shells in the three-dimensional statement // Mechanics of Composite Materials. 1985. Vol. 20. No. 4. P. 468–474. https://doi.org/10.1007/BF00609648</mixed-citation><mixed-citation xml:lang="en">Grigorenko Y.M., Vasilenko A.T, Pankratova N.D. Stress state and deformability of composite shells in the three-dimensional statement. Mechanics of Composite Materials. 1985, vol. 20, no. 4, pp.  468–474. https://doi.org/10.1007/BF00609648</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Vasilenko A.T., Sudavtsova G.K. The stress state of stiffened shallow orthotropic shells // International Applied Mechanics. 2001. Vol. 37. No. 2. P. 251–262. https://doi.org/10.1023/A:1011393724113</mixed-citation><mixed-citation xml:lang="en">Vasilenko A.T., Sudavtsova G.K. The stress state of stiffened shallow orthotropic shells. International Applied Mechanics. 2001, vol.  37, no. 2, pp. 251–262. https://doi.org/10.1023/A:1011393724113</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Nemish Yu.N., Zirka A.I., Chernopiskii D.I. Theoretical and experimental investigations of the stress-strain state of nonthin cylindrical shells with rectangular holes // International Applied Mechanics. 2000. Vol. 36. No. 12. P. 1620–1625.</mixed-citation><mixed-citation xml:lang="en">Nemish Yu.N., Zirka A.I., Chernopiskii D.I. Theoretical and experimental investigations of the stress-strain state of nonthin cylindrical shells with rectangular holes. International Applied Mechanics. 2000, vol. 36, no. 12, pp. 1620–1625.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Rogacheva N.N. The effect of surface stresses on the stress-strain state of shells // Journal of Applied Mathematics and Mechanics. 2016. Vol. 80. No. 2. P. 173–181. https://doi.org/10.1016/j.jappmathmech.2016.06.011</mixed-citation><mixed-citation xml:lang="en">Rogacheva N.N. The effect of surface stresses on the stress-strain state of shells. Journal of Applied Mathematics and Mechanics. 2016, vol. 80, no. 2, pp. 173–181. https://doi.org/10.1016/j.jappmathmech.2016.06.011</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Banichuk N.V., Ivanova S.Yu., Makeev E.V. On the stress state of shells penetrating into a deformable solid // Mechanics of So­lids. 2015. Vol. 50. No. 6. P. 698–703. https://doi.org/10.3103/S0025654415060102</mixed-citation><mixed-citation xml:lang="en">Banichuk N.V., Ivanova S.Yu., Makeev E.V. On the stress state of shells penetrating into a deformable solid. Mechanics of Solids. 2015, vol. 50, no. 6, pp. 698–703. https://doi.org/10.3103/S0025654415060102</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Krasovsky V.L., Lykhachova O.V., Bessmertnyi Ya.O. Deformation and stability of thin-walled shallow shells in the case of periodically non-uniform stress-strain state. In: Proc. of the 11th Int. Conference «Shell Structures: Theory and Applications». 2018. Vol. 4. P. 251–254.</mixed-citation><mixed-citation xml:lang="en">Krasovsky V.L., Lykhachova O.V., Bessmertnyi Ya.O. Deformation and stability of thin-walled shallow shells in the case of periodically non-uniform stress-strain state. In: Proc. of the 11th Int. Conference “Shell Structures: Theory and Applications”. 2018, vol. 4, pp. 251–254.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Storozhuk E.A., Chernyshenko I.S., Kharenko S.B. Elastoplastic deformation of conical shells with two circular holes // International Applied Mechanics. 2012. Vol. 48. No. 3. P. 343–348. https://doi.org/10.1007/s10778-012-0525-y</mixed-citation><mixed-citation xml:lang="en">Storozhuk E.A., Chernyshenko I.S., Kharenko S.B. Elastoplastic deformation of conical shells with two circular holes. International Applied Mechanics. 2012, vol. 48, no. 3, pp. 343–348. https://doi.org/10.1007/s10778-012-0525-y</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Ivanov V.N., Imomnazarov T.S., Farhan I.T.F., Tiekolo D. Analysis of stress-strain state of multi-wave shell on parabolic trapezoidal plan // Advanced Structured Materials. 2020. Vol. 113. P. 257–262. https://doi.org/10.1007/978-3-030-20801-1_19</mixed-citation><mixed-citation xml:lang="en">Ivanov V.N., Imomnazarov T.S., Farhan I.T.F., Tiekolo D. Analysis of stress-strain state of multi-wave shell on parabolic trapezoidal plan. Advanced Structured Materials. 2020, vol. 113, pp. 257–262. https://doi.org/10.1007/978-3-030-20801-1_19</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Gerasimenko P.V., Khodakovskiy V.A. Numerical algorithm for investigating the stress-strain state of cylindrical shells of railway tanks // Vestnik of the St. Petersburg University: Mathematics. 2019. Vol. 52. No. 2. P. 207–213.</mixed-citation><mixed-citation xml:lang="en">Gerasimenko P.V., Khodakovskiy V.A. Numerical algorithm for investigating the stress-strain state of cylindrical shells of railway tanks. Vestnik of the St. Petersburg University: Mathematics. 2019, vol. 52, no. 2, pp. 207–213.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Meish V.F., Maiborodina N.V. Stress state of discretely stiffened ellipsoidal shells under a nonstationary normal load // International Applied Mechanics. 2018. Vol. 54. No. 6. P. 675–686. https://doi.org/10.1007/s10778-018-0922-y</mixed-citation><mixed-citation xml:lang="en">Meish V.F., Maiborodina N.V. Stress state of discretely stiffened ellipsoidal shells under a nonstationary normal load. International Applied Mechanics. 2018, vol. 54, no. 6, pp. 675–686. https://doi.org/10.1007/s10778-018-0922-y</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Marchuk A.V., Gnidash S.V. Analysis of the effect of local loads on thick-walled cylindrical shells with different boundary conditions // International Applied Mechanics. 2016. Vol. 52. No. 4. P. 368–377. https://doi.org/10.1007/s10778-016-0761-7</mixed-citation><mixed-citation xml:lang="en">Marchuk A.V., Gnidash S.V. Analysis of the effect of local loads on thick-walled cylindrical shells with different boundary conditions. International Applied Mechanics. 2016, vol. 52, no. 4, pp. 368–377. https://doi.org/10.1007/s10778-016-0761-7</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Grigorenko Ya.M., Grigorenko A.Ya., Zakhariichenko L.I. Analysis of influence of the geometrical parameters of elliptic cylindrical shells with variable thickness on their stress-strain state // International Applied Mechanics. 2018. Vol. 54. No. 2. P. 155–162. https://doi.org/10.1007/s10778-018-0867-1</mixed-citation><mixed-citation xml:lang="en">Grigorenko Ya.M., Grigorenko A.Ya., Zakhariichenko L.I. Analysis of influence of the geometrical parameters of elliptic cylindrical shells with variable thickness on their stress-strain state. International Applied Mechanics. 2018, vol. 54, no. 2, pp. 155–162. https://doi.org/10.1007/s10778-018-0867-1</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Репях С.И. Технологические основы литья по выплавляемым моделям. Днепропетровск: Лира, 2006. 1056 с.</mixed-citation><mixed-citation xml:lang="en">Repyakh S.I. Technological Basics of Casting by Investment Mo­dels. Dnepropetrovsk: Lira, 2008, 1056 p.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Математическое моделирование сложных технологичес­ких процессов / В.И. Одиноков, Б.Г. Каплунов, А.В. Песков, А.В. Баков. М.: Наука, 2008. 176 с.</mixed-citation><mixed-citation xml:lang="en">Odinokov V.I., Kaplunov B.G., Peskov A.V., Bakov A.V. Mathema­tic Modeling of Complex Technological Processes. Moscow: Nauka, 2008, 176 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Свидетельство о государственной регистрации программы для ЭВМ № 2012661389. / В.И. Одиноков, А.Н. Прокудин, А.М. Сергеева, Г.М. Севастьянов. ОДИССЕЙ. Зарегистрировано в Реестре программ для ЭВМ 13.12.2012.</mixed-citation><mixed-citation xml:lang="en">Odinokov V.I., Prokudin A.N., Sergeeva A.M., Sevast’yanov G.M. ODYSSEUS. Certificate of state registration of the computer prog­ram no. 2012661389. Registered in the Register of Computer Prog­rams on 13.12.2012. (In Russ.).</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>
