<?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">alternative</journal-id><journal-title-group><journal-title xml:lang="ru">Альтернативная энергетика и экология (ISJAEE)</journal-title><trans-title-group xml:lang="en"><trans-title>Alternative Energy and Ecology (ISJAEE)</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1608-8298</issn><publisher><publisher-name>Международный издательский дом научной периодики "Спейс</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.15518/isjaee.2024.12.143-157</article-id><article-id custom-type="elpub" pub-id-type="custom">alternative-2592</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>X. ЭКОНОМИЧЕСКИЕ АСПЕКТЫ АЭЭ 24. Экономические аспекты 24-6-0-0 Экономика технологий энергетического перехода</subject></subj-group></article-categories><title-group><article-title>Анализ напряжённо деформированного состояния корпуса ресивера водорода</article-title><trans-title-group xml:lang="en"><trans-title>Analysis of the stress-strain state of the hydrogen receiver housing</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7229-412X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Марьин</surname><given-names>Г. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Marin</surname><given-names>G. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Марьин Георгий Евгеньевич, канд. техн. наук., доцент</p><p>420066, г. Казань, ул. Красносельская, 51;</p><p>Scopus Author ID: 57213835443;</p><p>Research ID: AGS-9168-2022</p></bio><bio xml:lang="en"><p>Marin George Evgenievich, PhD in Engineering, Associate Professor</p><p>420066, Kazan, Krasnoselskaya st., 51;</p><p>Scopus Author ID: 57213835443;</p><p>Research ID: AGS-9168-2022</p></bio><email xlink:type="simple">george64199@mail.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/0009-0003-0434-4134</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Клейдман</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kleidman</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Клейдман Ольга Владимировна, канд. физ.-мат. наук, доцент</p><p>420066, г. Казань, ул. Красносельская, 51;</p><p>Research ID: JXL-2599-2024</p></bio><bio xml:lang="en"><p>Kleidman Olga Vladimirovna, Candidate of Physical and Mathematical Sciences, Associate Professor</p><p>420066, Kazan, Krasnoselskaya st., 51;</p><p>Research ID: JXL-2599-2024</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5183-3040</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Илюшин</surname><given-names>П. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Ilyushin</surname><given-names>P. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Илюшин Павел Владимирович, доктор техн. наук,руководитель Центра интеллектуальных электроэнергетических систем и распределенной энергетики</p><p>117186, Москва, ул. Нагорная 31/2;</p><p>Scopus Author ID: 55455903000;</p><p>Research ID: P-3799-2017</p></bio><bio xml:lang="en"><p>Ilyushin Pavel Vladimirovich, Doctor of Technical Sciences, Head of the Center for Intelligent Electric Power Systems and Distributed Energy</p><p>31/2 Nagornaya St., Moscow, 117186;</p><p>Scopus Author ID: 55455903000;</p><p>Research ID: P-3799-2017</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4424-7761</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ахметшин</surname><given-names>А. Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Akhmetshin</surname><given-names>A. R.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ахметшин Азат Ринатович, канд. техн. наук, доцент</p><p>420066, г. Казань, ул. Красносельская, 51;</p><p>Scopus Author ID: 57211796456;</p><p>Research ID: AGM-7165-2022</p></bio><bio xml:lang="en"><p>Akhmetshin Azat Rinatovich, PhD in Engineering, Associate Professor</p><p>420066, Kazan, Krasnoselskaya st., 51;</p><p>Scopus Author ID: 57211796456;</p><p>Research ID: AGM-7165-2022</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Казанский государственный энергетический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Kazan State Energy University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт энергетических исследований Российской академии наук</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Institute of Energy Research of the Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>15</day><month>03</month><year>2025</year></pub-date><volume>0</volume><issue>12</issue><fpage>143</fpage><lpage>157</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Международный издательский дом научной периодики "Спейс, 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Международный издательский дом научной периодики "Спейс</copyright-holder><copyright-holder xml:lang="en">Международный издательский дом научной периодики "Спейс</copyright-holder><license xlink:href="https://www.isjaee.com/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://www.isjaee.com/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://www.isjaee.com/jour/article/view/2592">https://www.isjaee.com/jour/article/view/2592</self-uri><abstract><p>В данной статье рассматривается работа вспомогательного оборудования при напряженно-деформируемом состоянии. При использовании водорода в энергетике необходимо учитывать и оценивать не только высокие энергетические свойства водородного топлива при использовании, но и его влияние на вспомогательное оборудование. Водород необходимо хранить при высоком давлении (на заправочных станциях давление может достигать 70 МПа). Особое внимание необходимо обратить на целостное состояние ресивера хранения водородного топлива – наиболее подвержены повреждениям точки приварки, сварные швы. Одним из способов анализа работы и последующего прогнозирования состояния вспомогательного оборудования может быть метод конечных элементов. На основе метода конечных элементов построена расчетная схема, которая позволила прогнозировать изменение конструкции во времени под воздействием внутренних сил. Проведенное исследование позволит выявлять дефекты на более ранних сроках работы, получать результаты численного анализа напряженно-деформируемого состояния. В настоящий момент основным стандартом в Российской Федерации, определяющим нормы и методы расчета на прочность, является ГОСТ 24755-89. Настоящий стандарт устанавливает нормы и методы расчета на прочность укрепления отверстий в обечайках, переходах и выпуклых днищах сосудов и аппаратов, применяемых в химической нефтеперерабатывающей и смежных отраслях промышленности, работающих под действием внутреннего или наружного давления. В результате исследований определены допустимые значения геометрических параметров для обеспечения жизнедеятельности и прочности корпуса ресивера водорода для расчетных давлений и возможных колебаний, температуры стенки, допустимого продления срока службы, времени эксплуатации.</p></abstract><trans-abstract xml:lang="en"><p>This article discusses the operation of auxiliary equipment in a stress-strain state. When using hydrogen in the energy industry, it is necessary to take into account and evaluate not only the high energy properties of hydrogen fuel during use, but also its effect on auxiliary equipment. Hydrogen must be stored at high pressure (at gas stations, the pressure can reach 70 MPa). Special attention should be paid to the complete condition of the hydrogen fuel storage receiver – welding points and welds are most susceptible to damage. The finite element method can be one of the ways to analyze the operation and then predict the condition of auxiliary equipment. Based on the finite element method, a calculation scheme was constructed that made it possible to predict the design change over time under the influence of internal forces. The conducted research will make it possible to identify defects at an earlier stage of operation and obtain the results of a numerical analysis of the stress-strain state. At the moment, GOST 24755-89 is the main standard in the Russian Federation that defines the norms and methods of strength calculation. This standard establishes norms and methods for calculating the strength of strengthening holes in shells, transitions and convex bottoms of vessels and apparatuses used in chemical oil refining and related industries operating under the influence of internal or external pressure. As a result of the research, the permissible values of geometric parameters have been determined to ensure the vital activity and strength of the hydrogen receiver housing for design pressures and possible fluctuations, wall temperature, permissible prolongation of service life, and operating time.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>водород</kwd><kwd>топливо</kwd><kwd>зеленая энергетика</kwd><kwd>водородная энергетика</kwd><kwd>напряженно-деформируемое состояние</kwd><kwd>метод конечных элементов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>hydrogen</kwd><kwd>fuel</kwd><kwd>green energy</kwd><kwd>hydrogen energy</kwd><kwd>stress-strain state</kwd><kwd>finite element method</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">Hewu Kuang. Impact of natural resources and technology on economic development and sustainable environment Yiyan Liang, Wenjia Zhao, Jiahong Cai. – Analysis of resources-energy-growth-environment linkages in BRICS // Resources Policy. – Volume 85. – Part B. – 2023, р. 103865.</mixed-citation><mixed-citation xml:lang="en">Hewu Kuang. Impact of natural resources and technology on economic development and sustainable environment Yiyan Liang, Wenjia Zhao, Jiahong Cai. – Analysis of resources-energy-growth-environment linkages in BRICS // Resources Policy. – Volume 85. – Part B. – 2023, р. 103865.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Wei Jiang. Which is the more important factor of carbon emission, coal consumption or industrial structure. Wei Jiang, Yifei Sun // Energy Policy. – Volume 176. – 2023, р. 113508.</mixed-citation><mixed-citation xml:lang="en">Wei Jiang. Which is the more important factor of carbon emission, coal consumption or industrial structure. Wei Jiang, Yifei Sun // Energy Policy. – Volume 176. – 2023, р. 113508.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Dmitry Pashchenko. Combined methane reforming with a mixture of methane combustion products and steam over a Ni-based catalyst: An experimental and thermodynamic study. Dmitry Pashchenko // Energy. – Volume 185. – 2019. – Pр. 573-584.</mixed-citation><mixed-citation xml:lang="en">Dmitry Pashchenko. Combined methane reforming with a mixture of methane combustion products and steam over a Ni-based catalyst: An experimental and thermodynamic study. Dmitry Pashchenko // Energy. – Volume 185. – 2019. – Pр. 573-584.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Siu Hua Chang. An overview of pure hydrogen production via electrolysis and hydrolysis, Siu Hua Chang, Mohd Fariz Rajuli // International Journal of Hydrogen Energy. – Volume 84. – 2024. – Pр. 521-538.</mixed-citation><mixed-citation xml:lang="en">Siu Hua Chang. An overview of pure hydrogen production via electrolysis and hydrolysis, Siu Hua Chang, Mohd Fariz Rajuli // International Journal of Hydrogen Energy. – Volume 84. – 2024. – Pр. 521-538.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Jun Chi. Water electrolysis based on renewable energy for hydrogen production, Jun Chi, Hongmei Yu // Chinese Journal of Catalysis. – Volume 39. – Issue 3. – 2018. – Pр. 390-394.</mixed-citation><mixed-citation xml:lang="en">Jun Chi. Water electrolysis based on renewable energy for hydrogen production, Jun Chi, Hongmei Yu // Chinese Journal of Catalysis. – Volume 39. – Issue 3. – 2018. – Pр. 390-394.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Fang Wang. Enhancing biogas production of corn stover by fast pyrolysis pretreatment, Fang Wang, Deli Zhang, Houkai Wu, Weiming Yi, Peng Fu, Yongjun Li, Zhihe Li // Bioresource Technology. – Volume 218. – 2016. – Pр. 731-736.</mixed-citation><mixed-citation xml:lang="en">Fang Wang. Enhancing biogas production of corn stover by fast pyrolysis pretreatment, Fang Wang, Deli Zhang, Houkai Wu, Weiming Yi, Peng Fu, Yongjun Li, Zhihe Li // Bioresource Technology. – Volume 218. – 2016. – Pр. 731-736.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Karaeva J. Amaranth Inflorescence Wastes. Karaeva, J., Timofeeva, S., Islamova, S., Panchenko P., Bolshev V. // Bioenergy Potential, Biochar and Hydrocarbon Rich Bio-Oil Production Agriculture (Switzerland). – 2023, 13(2), 260.</mixed-citation><mixed-citation xml:lang="en">Karaeva J. Amaranth Inflorescence Wastes. Karaeva, J., Timofeeva, S., Islamova, S., Panchenko P., Bolshev V. // Bioenergy Potential, Biochar and Hydrocarbon Rich Bio-Oil Production Agriculture (Switzerland). – 2023, 13(2), 260.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Achitaev A. Life extension of AC-DC converters for hydrogen electrolysers operating as part of offshore wind turbines / Achitaev A., Suvorov A., Ilyushin P., Suslov K. // International Journal of Hydrogen Energy. – 2024, 51. – Pр. 137-159.</mixed-citation><mixed-citation xml:lang="en">Achitaev A. Life extension of AC-DC converters for hydrogen electrolysers operating as part of offshore wind turbines / Achitaev A., Suvorov A., Ilyushin P., Suslov K. // International Journal of Hydrogen Energy. – 2024, 51. – Pр. 137-159.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Marin G. E. Gas turbine operating as part of a thermal power plant with hydrogen storages / Marin G. E., Osipov B. M., Titov A. V., Akhmetshin A. R. // International Journal of Hydrogen Energy. – 2023, 48(86). – Pр. 33393-33400.</mixed-citation><mixed-citation xml:lang="en">Marin G. E. Gas turbine operating as part of a thermal power plant with hydrogen storages / Marin G. E., Osipov B. M., Titov A. V., Akhmetshin A. R. // International Journal of Hydrogen Energy. – 2023, 48(86). – Pр. 33393-33400.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Marin G. Improving the Performance of Power Plants with Gas Turbine Units Proceedings. Marin G., Osipov B., Titov A., Shubina A., Novoselova M. 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2022, 2022, Pages 832-836.</mixed-citation><mixed-citation xml:lang="en">Marin G. Improving the Performance of Power Plants with Gas Turbine Units Proceedings. Marin G., Osipov B., Titov A., Shubina A., Novoselova M. 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2022, 2022, Pages 832-836.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Kolbantseva D. L. Prospects for hydrogen production by the method of gasification of MSW at operating TPPs. D. L. Kolbantseva, D. A. Treshchev, K. S. Kalmykov, I. D. Anikina, M. A. Treshcheva, A. A. Kalyutik, Ya. A. Vladimirov, K. A. Naypak // International Journal of Hydrogen Energy, Volume 51, Part D, 2024. – Pр. 96-106.</mixed-citation><mixed-citation xml:lang="en">Kolbantseva D. L. Prospects for hydrogen production by the method of gasification of MSW at operating TPPs. D. L. Kolbantseva, D. A. Treshchev, K. S. Kalmykov, I. D. Anikina, M. A. Treshcheva, A. A. Kalyutik, Ya. A. Vladimirov, K. A. Naypak // International Journal of Hydrogen Energy, Volume 51, Part D, 2024. – Pр. 96-106.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Marin G. E. Prospects for implementation of hydrogen filling stations in the Russian Federation Marin G. E., Titov A. V., Akhmetshin A. R. // International Journal of Hydrogen Energy, 2024, 78, Pages 901-906.</mixed-citation><mixed-citation xml:lang="en">Marin G. E. Prospects for implementation of hydrogen filling stations in the Russian Federation Marin G. E., Titov A. V., Akhmetshin A. R. // International Journal of Hydrogen Energy, 2024, 78, Pages 901-906.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Aminov R. Z. Estimating the system efficiency of the multifunctional hydrogen complex at nuclear power plants / R. Z. Aminov, A. N. Bairamov, M. V. Garievskii // International Journal of Hydrogen Energy, Volume 45, Issue 29, 2020, Pages 14614-14624.</mixed-citation><mixed-citation xml:lang="en">Aminov R. Z. Estimating the system efficiency of the multifunctional hydrogen complex at nuclear power plants / R. Z. Aminov, A. N. Bairamov, M. V. Garievskii // International Journal of Hydrogen Energy, Volume 45, Issue 29, 2020, Pages 14614-14624.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Aminov R. Z. Assessment of technical and economic efficiency of a closed hydrogen cycle at NPP. Aminov R. Z., Egorov A. N. // International Journal of Hydrogen Energy, 2020, 45(32), Pages 15744-15751.</mixed-citation><mixed-citation xml:lang="en">Aminov R. Z. Assessment of technical and economic efficiency of a closed hydrogen cycle at NPP. Aminov R. Z., Egorov A. N. // International Journal of Hydrogen Energy, 2020, 45(32), Pages 15744-15751.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Marin G. E. Simulation of the operation of a gas turbine installation of a thermal power plant with a hydrogen fuel production system / Marin G. E., Osipov B. M., Titov A. V., Akhmetshin A. R. // International Journal of Hydrogen Energy, 2023, 48(12), Pages 4543-4550.</mixed-citation><mixed-citation xml:lang="en">Marin G. E. Simulation of the operation of a gas turbine installation of a thermal power plant with a hydrogen fuel production system / Marin G. E., Osipov B. M., Titov A. V., Akhmetshin A. R. // International Journal of Hydrogen Energy, 2023, 48(12), Pages 4543-4550.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Xiafan Xu. A high-efficiency liquid hydrogen storage system cooled by a fuel-cell-driven refrigerator for hydrogen combustion heat recovery / Xiafan Xu, Hao Xu, Jianpeng Zheng, Liubiao Chen, Junjie Wang // Energy Conversion and Management. – Volume 226. – 2020, 113496. – ISSN 0196-8904.</mixed-citation><mixed-citation xml:lang="en">Xiafan Xu. A high-efficiency liquid hydrogen storage system cooled by a fuel-cell-driven refrigerator for hydrogen combustion heat recovery / Xiafan Xu, Hao Xu, Jianpeng Zheng, Liubiao Chen, Junjie Wang // Energy Conversion and Management. – Volume 226. – 2020, 113496. – ISSN 0196-8904.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">W. Liu. Review of hydrogen storage in AB3 alloys targeting stationary fuel cell applications / W. Liu, C. J. Webb, E. Mac A. Gray // International Journal of Hydrogen Energy. – Volume 41, Issue 5, 2016, Pages 3485-3507, ISSN 0360-3199.</mixed-citation><mixed-citation xml:lang="en">W. Liu. Review of hydrogen storage in AB3 alloys targeting stationary fuel cell applications / W. Liu, C. J. Webb, E. Mac A. Gray // International Journal of Hydrogen Energy. – Volume 41, Issue 5, 2016, Pages 3485-3507, ISSN 0360-3199.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Ahmed M. Elberry. Large-scale compressed hydrogen storage as part of renewable electricity storage systems / Ahmed M. Elberry, Jagruti Thakur, Annukka Santasalo-Aarnio, Martti Larmi // International Journal of Hydrogen Energy. – Volume 46, Issue 29, 2021, Pages 15671-15690.</mixed-citation><mixed-citation xml:lang="en">Ahmed M. Elberry. Large-scale compressed hydrogen storage as part of renewable electricity storage systems / Ahmed M. Elberry, Jagruti Thakur, Annukka Santasalo-Aarnio, Martti Larmi // International Journal of Hydrogen Energy. – Volume 46, Issue 29, 2021, Pages 15671-15690.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Madeleine McPherson. The role of electricity storage and hydrogen technologies in enabling global low-carbon energy transitions / Madeleine McPherson, Nils Johnson // Manfred Strubegger, Applied Energy. – Volume 216, 2018, Pages 649-661.</mixed-citation><mixed-citation xml:lang="en">Madeleine McPherson. The role of electricity storage and hydrogen technologies in enabling global low-carbon energy transitions / Madeleine McPherson, Nils Johnson // Manfred Strubegger, Applied Energy. – Volume 216, 2018, Pages 649-661.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Radoslaw Tarkowski. Underground hydrogen storage: Characteristics and prospects, Renewable and Sustainable Energy Reviews. – Volume 105, 2019, Pages86-94, ISSN 1364-0321.</mixed-citation><mixed-citation xml:lang="en">Radoslaw Tarkowski. Underground hydrogen storage: Characteristics and prospects, Renewable and Sustainable Energy Reviews. – Volume 105, 2019, Pages86-94, ISSN 1364-0321.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Aman Verma. Life cycle assessment of hydrogen production from underground coal gasification / Aman Verma, Amit Kumar // Applied Energy. – Volume 147, 2015, Pages 556-568.</mixed-citation><mixed-citation xml:lang="en">Aman Verma. Life cycle assessment of hydrogen production from underground coal gasification / Aman Verma, Amit Kumar // Applied Energy. – Volume 147, 2015, Pages 556-568.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Younggeun Lee. Comparative techno-economic and quantitative risk analysis of hydrogen delivery infrastructure options / Younggeun Lee, Ung Lee, Kyeongsu Kim A. // International Journal of Hydrogen Energy. – Volume 46, Issue 27, 2021, Pages 14857-14870.</mixed-citation><mixed-citation xml:lang="en">Younggeun Lee. Comparative techno-economic and quantitative risk analysis of hydrogen delivery infrastructure options / Younggeun Lee, Ung Lee, Kyeongsu Kim A. // International Journal of Hydrogen Energy. – Volume 46, Issue 27, 2021, Pages 14857-14870.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Ankica Kovač. Hydrogen in energy transition: A review, International. Ankica Kovač, Matej Paranos, Doria Marciuš // Journal of Hydrogen Energy. – Volume 46, Issue 16, 2021, Pages 10016-10035.</mixed-citation><mixed-citation xml:lang="en">Ankica Kovač. Hydrogen in energy transition: A review, International. Ankica Kovač, Matej Paranos, Doria Marciuš // Journal of Hydrogen Energy. – Volume 46, Issue 16, 2021, Pages 10016-10035.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Morozov E. M. Comparison of notch geometries in local-strength analysis / Morozov E. M. Sapunov V. T. // Industrial Laboratory. – 1996. – Vol. 62, No. 2. – Pр. 113-116.</mixed-citation><mixed-citation xml:lang="en">Morozov E. M. Comparison of notch geometries in local-strength analysis / Morozov E. M. Sapunov V. T. // Industrial Laboratory. – 1996. – Vol. 62, No. 2. – Pр. 113-116.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Morozov E. M. A concept of ultimate crack resistance Materials Science. – 1998. – Vol. 34, No. 5. – Pр. 709-713.</mixed-citation><mixed-citation xml:lang="en">Morozov E. M. A concept of ultimate crack resistance Materials Science. – 1998. – Vol. 34, No. 5. – Pр. 709-713.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Matvienko Yu. G., Morozov E. M. Calculation of the energy J-integral for bodies with notches and cracks / Matvienko Yu. G. // International Journal of Fracture. – 2004. – Volume. 125, No. 3-4. – Pages 249-261.</mixed-citation><mixed-citation xml:lang="en">Matvienko Yu. G., Morozov E. M. Calculation of the energy J-integral for bodies with notches and cracks / Matvienko Yu. G. // International Journal of Fracture. – 2004. – Volume. 125, No. 3-4. – Pages 249-261.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Anderson T. L., Fracture Mechanics. Fundamentals and Application, Boca Raton: CRC, 2017 / Fracture Mechanics. Theory, Applications and Research, Robertson J. C., Ed., New York: Nova Science, 2017.</mixed-citation><mixed-citation xml:lang="en">Anderson T. L., Fracture Mechanics. Fundamentals and Application, Boca Raton: CRC, 2017 / Fracture Mechanics. Theory, Applications and Research, Robertson J. C., Ed., New York: Nova Science, 2017.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Andreas-Nizar Granitzer. Implementation and appraisal of stress recovery techniques for embedded finite elements with frictional contact / Andreas-Nizar Granitzer, Franz Tschuchnigg, Haris Felic, Paul Bonnier, Sandro Brasile, Computers and Geotechnics. – Volume 172, 2024, 106457.</mixed-citation><mixed-citation xml:lang="en">Andreas-Nizar Granitzer. Implementation and appraisal of stress recovery techniques for embedded finite elements with frictional contact / Andreas-Nizar Granitzer, Franz Tschuchnigg, Haris Felic, Paul Bonnier, Sandro Brasile, Computers and Geotechnics. – Volume 172, 2024, 106457.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Morozov E. M. Use of the finite-element method in fracture mechanics Soviet / Morozov E. M., G. P. Nikishkov // Materials Science. – 1983. – Volume. 18, No. 4. – Pages 299-314.</mixed-citation><mixed-citation xml:lang="en">Morozov E. M. Use of the finite-element method in fracture mechanics Soviet / Morozov E. M., G. P. Nikishkov // Materials Science. – 1983. – Volume. 18, No. 4. – Pages 299-314.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Sachenkov O. A. Implementation of contact interaction in a finite – element formulation / Sachenkov O. A., Mitryaikin V. I., Zaitseva T. A., Konoplev Y. G. // Applied Mathematical Sciences. – 2014. – Volume. 8, No. 157-160. – Pages 7889-7897.</mixed-citation><mixed-citation xml:lang="en">Sachenkov O. A. Implementation of contact interaction in a finite – element formulation / Sachenkov O. A., Mitryaikin V. I., Zaitseva T. A., Konoplev Y. G. // Applied Mathematical Sciences. – 2014. – Volume. 8, No. 157-160. – Pages 7889-7897.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Basar Y. Constitutive model and finite element formulation for large strain elasto-plastic analysis of shells / Basar Y., Itskov M. // Computational Mechanics. – 1999. – Volume. 23, No. 5-6. – Pages 466-481.</mixed-citation><mixed-citation xml:lang="en">Basar Y. Constitutive model and finite element formulation for large strain elasto-plastic analysis of shells / Basar Y., Itskov M. // Computational Mechanics. – 1999. – Volume. 23, No. 5-6. – Pages 466-481.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Cai C. Modeling of Material Damping Properties in ANSYS / Cai C., Zheng H., Khan M. S., Hung K. C. Defense Systems Division, Institute of High Performance Computing 89C Science Park Drive, Singapore Science Park I, Singapore 118261.</mixed-citation><mixed-citation xml:lang="en">Cai C. Modeling of Material Damping Properties in ANSYS / Cai C., Zheng H., Khan M. S., Hung K. C. Defense Systems Division, Institute of High Performance Computing 89C Science Park Drive, Singapore Science Park I, Singapore 118261.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Cheng H. Development and application of a fully-coupled two-dimensional finite element approach to deformation and pressure diffusion around a bore-hole / Cheng H., Dusseault M. B. J. Can. Petr. Tech. – 1993. – Volume 32(10). – Pages 28-38.</mixed-citation><mixed-citation xml:lang="en">Cheng H. Development and application of a fully-coupled two-dimensional finite element approach to deformation and pressure diffusion around a bore-hole / Cheng H., Dusseault M. B. J. Can. Petr. Tech. – 1993. – Volume 32(10). – Pages 28-38.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Parish H. A. Critical survey of the J-node degenerated shell element with special emphasis on thin shell application and reduced integration // Computer Methods in Applied Mechanics and Engineering, 1979. – Volume 20. – № 3. – Pages 323-350.</mixed-citation><mixed-citation xml:lang="en">Parish H. A. Critical survey of the J-node degenerated shell element with special emphasis on thin shell application and reduced integration // Computer Methods in Applied Mechanics and Engineering, 1979. – Volume 20. – № 3. – Pages 323-350.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Panda S. Finite element analysis of laminated composite plates / Panda S., Natarajan R. // International Journal for Numerical Methods in Engineering. – 1979. – Volume 14. – № 1. – Pages 69-79.</mixed-citation><mixed-citation xml:lang="en">Panda S. Finite element analysis of laminated composite plates / Panda S., Natarajan R. // International Journal for Numerical Methods in Engineering. – 1979. – Volume 14. – № 1. – Pages 69-79.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Surana Karan S. Transition finite elements for three-dimensional stress analysis // Int. J. Numer. Meth. Eng. – 1980. – Volume 15. – № 7. – Pages 991-1020.</mixed-citation><mixed-citation xml:lang="en">Surana Karan S. Transition finite elements for three-dimensional stress analysis // Int. J. Numer. Meth. Eng. – 1980. – Volume 15. – № 7. – Pages 991-1020.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Surana Karan S. Three dimensional solid-shell transition finite elements for heat conduction Comput. and Struct. – 1987. – Volume 26. – № 6. – Pages 941-950.</mixed-citation><mixed-citation xml:lang="en">Surana Karan S. Three dimensional solid-shell transition finite elements for heat conduction Comput. and Struct. – 1987. – Volume 26. – № 6. – Pages 941-950.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Yang H. A survey of recent shell finite elements / Yang H. T. Y., Saigal S., Masud A., Kapania R. K. // Int. J. for numerical methods in engineering. – 2000. – Volume 47. – Pages 101-127.</mixed-citation><mixed-citation xml:lang="en">Yang H. A survey of recent shell finite elements / Yang H. T. Y., Saigal S., Masud A., Kapania R. K. // Int. J. for numerical methods in engineering. – 2000. – Volume 47. – Pages 101-127.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Sze K. Y. Three-dimensional continuum finite element models for plate/shell analysis Prog. Struct. Enging Mater. – 2002. – Volume 4. – Pages 400-407.</mixed-citation><mixed-citation xml:lang="en">Sze K. Y. Three-dimensional continuum finite element models for plate/shell analysis Prog. Struct. Enging Mater. – 2002. – Volume 4. – Pages 400-407.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">de Sousa R. J. A. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: de Sousa R. J. A., Cardoso R. P. R. Part I – geometrically linear applications // Int. J. for Numerical Methods in Engineering. – 2005. – Volume 62, № 7. – Pages 952-977.</mixed-citation><mixed-citation xml:lang="en">de Sousa R. J. A. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: de Sousa R. J. A., Cardoso R. P. R. Part I – geometrically linear applications // Int. J. for Numerical Methods in Engineering. – 2005. – Volume 62, № 7. – Pages 952-977.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Park К. C., Stanley G. M. A curved shell element based on assumed natural-coordinate strain // J. Appl. Mech. – 1986. – Volume 53, № 2. – Pages 278-290.</mixed-citation><mixed-citation xml:lang="en">Park К. C., Stanley G. M. A curved shell element based on assumed natural-coordinate strain // J. Appl. Mech. – 1986. – Volume 53, № 2. – Pages 278-290.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Kara N. Three-dimensional finite element for thick shells of general shape / Kara N., Kumbasar N. // Int. J. for Physical and Engineering Sciences. – 2001. – Volume 52. – Pages 1-7.</mixed-citation><mixed-citation xml:lang="en">Kara N. Three-dimensional finite element for thick shells of general shape / Kara N., Kumbasar N. // Int. J. for Physical and Engineering Sciences. – 2001. – Volume 52. – Pages 1-7.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Bonet J. and Wood R. D. 1997 Nonlinear continuum mechanics for finite element analysis (Cambridge University Press) 366.</mixed-citation><mixed-citation xml:lang="en">Bonet J. and Wood R. D. 1997 Nonlinear continuum mechanics for finite element analysis (Cambridge University Press) 366.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Abdrakhmanova A. I. The algorithm of investigation of deformations of solids with contact interaction / Abdrakhmanova A. I., Sultanov L. U. // Journal of Physics: Conference Series, Volume. 1158, Issue 2. – Kazan: Institute of Physics Publishing, 2019. – P. 022001.</mixed-citation><mixed-citation xml:lang="en">Abdrakhmanova A. I. The algorithm of investigation of deformations of solids with contact interaction / Abdrakhmanova A. I., Sultanov L. U. // Journal of Physics: Conference Series, Volume. 1158, Issue 2. – Kazan: Institute of Physics Publishing, 2019. – P. 022001.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Davydov R. L. Numerical Algorithm for Investigating Large Elasto-Plastic Deformations / Davydov R. L., Sultanov L. U. // Journal of Engineering Physics and Thermophysics. – 2015. – Volume 88, No. 5. – Pages 1280-1288.</mixed-citation><mixed-citation xml:lang="en">Davydov R. L. Numerical Algorithm for Investigating Large Elasto-Plastic Deformations / Davydov R. L., Sultanov L. U. // Journal of Engineering Physics and Thermophysics. – 2015. – Volume 88, No. 5. – Pages 1280-1288.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">Ferreira C. A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem / Ferreira C., Parlett B. // Numerische Mathematik. – 2022. – Volume 150, No. 2. – Pages 373-422.</mixed-citation><mixed-citation xml:lang="en">Ferreira C. A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem / Ferreira C., Parlett B. // Numerische Mathematik. – 2022. – Volume 150, No. 2. – Pages 373-422.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">Kandic D. B. Explicit Construction of Hyperdominant Symmetric Matrices With Assigned Spectrum / Kandic D. B., Parlett B., Reljin B. D., Vasic P. // Linear Algebra and its Applications. – 1997. – Volume 258, No. 1-3. – Pages 41-51.</mixed-citation><mixed-citation xml:lang="en">Kandic D. B. Explicit Construction of Hyperdominant Symmetric Matrices With Assigned Spectrum / Kandic D. B., Parlett B., Reljin B. D., Vasic P. // Linear Algebra and its Applications. – 1997. – Volume 258, No. 1-3. – Pages 41-51.</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>
