{"id":"https://openalex.org/W4312379897","doi":"https://doi.org/10.21638/spbu01.2022.301","title":"Boundary layers on the upper/lower surfaces of reinforced plates","display_name":"Boundary layers on the upper/lower surfaces of reinforced plates","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312379897","doi":"https://doi.org/10.21638/spbu01.2022.301"},"language":"en","primary_location":{"id":"doi:10.21638/spbu01.2022.301","doi":"https://doi.org/10.21638/spbu01.2022.301","is_oa":true,"landing_page_url":"https://doi.org/10.21638/spbu01.2022.301","pdf_url":"https://math-mech-astr-journal.spbu.ru/article/download/14555/9855","source":{"id":"https://openalex.org/S4210218253","display_name":"Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy","issn_l":"1025-3106","issn":["1025-3106","2587-5884"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://math-mech-astr-journal.spbu.ru/article/download/14555/9855","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112331677","display_name":"Boris D. Annin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210151517","display_name":"Lavrentyev Institute of Hydrodynamics","ror":"https://ror.org/04t5w6b17","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210127387","https://openalex.org/I4210151517","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Boris D. Annin","raw_affiliation_strings":["\u0418\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0433\u0438\u0434\u0440\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0438 \u0438\u043c. \u041b\u0430\u0432\u0440\u0435\u043d\u0442\u044c\u0435\u0432\u0430 \u0421\u041e \u0420\u0410\u041d, \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u044f, 630090, \u041d\u043e\u0432\u043e\u0441\u0438\u0431\u0438\u0440\u0441\u043a, \u043f\u0440. \u041b\u0430\u0432\u0440\u0435\u043d\u0442\u044c\u0435\u0432\u0430, 15"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0418\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0433\u0438\u0434\u0440\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0438 \u0438\u043c. \u041b\u0430\u0432\u0440\u0435\u043d\u0442\u044c\u0435\u0432\u0430 \u0421\u041e \u0420\u0410\u041d, \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u044f, 630090, \u041d\u043e\u0432\u043e\u0441\u0438\u0431\u0438\u0440\u0441\u043a, \u043f\u0440. \u041b\u0430\u0432\u0440\u0435\u043d\u0442\u044c\u0435\u0432\u0430, 15","institution_ids":["https://openalex.org/I4210151517"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112883741","display_name":"Aleksandr G. Kolpakov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aleksandr G. Kolpakov","raw_affiliation_strings":["SysAn - \u0421\u0438\u0441\u0442\u0435\u043c\u043d\u044b\u0439\u0430\u043d\u0430\u043b\u0438\u0437 \u0432 \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u043d\u043e\u043c \u0434\u0435\u043b\u0435, \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u044f, 630075, \u041d\u043e\u0432\u043e\u0441\u0438\u0431\u0438\u0440\u0441\u043a, \u0443\u043b. \u0410. \u041d\u0435\u0432\u0441\u043a\u043e\u0433\u043e, 12"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SysAn - \u0421\u0438\u0441\u0442\u0435\u043c\u043d\u044b\u0439\u0430\u043d\u0430\u043b\u0438\u0437 \u0432 \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u043d\u043e\u043c \u0434\u0435\u043b\u0435, \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u044f, 630075, \u041d\u043e\u0432\u043e\u0441\u0438\u0431\u0438\u0440\u0441\u043a, \u0443\u043b. \u0410. \u041d\u0435\u0432\u0441\u043a\u043e\u0433\u043e, 12","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"SysAn - System Analysis in Engineering","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210135727","display_name":"Siberian Transport University","ror":"https://ror.org/02v157r64","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210135727"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"SysAn - System Analysis in Engineering","raw_affiliation_strings":["\u0421\u0438\u0431\u0438\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u043f\u0443\u0442\u0435\u0439 \u0441\u043e\u043e\u0431\u0449\u0435\u043d\u0438\u0439, \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u044f, 630090, \u041d\u043e\u0432\u043e\u0441\u0438\u0431\u0438\u0440\u0441\u043a, \u0443\u043b. \u0414\u0443\u0441\u0438 \u041a\u043e\u0432\u0430\u043b\u044c\u0447\u0443\u043a, 191"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0421\u0438\u0431\u0438\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u043f\u0443\u0442\u0435\u0439 \u0441\u043e\u043e\u0431\u0449\u0435\u043d\u0438\u0439, \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u044f, 630090, \u041d\u043e\u0432\u043e\u0441\u0438\u0431\u0438\u0440\u0441\u043a, \u0443\u043b. \u0414\u0443\u0441\u0438 \u041a\u043e\u0432\u0430\u043b\u044c\u0447\u0443\u043a, 191","institution_ids":["https://openalex.org/I4210135727"]}]},{"author_position":"last","author":{"id":null,"display_name":"Sergey I. Rakin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sergey I. Rakin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14543414,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"3","first_page":"391","last_page":"404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9164999723434448,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9164999723434448,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.05339999869465828,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.003000000026077032,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boundary-layer","display_name":"boundary layer","score":0.8999999761581421},{"id":"https://openalex.org/keywords/fiber-reinforced-plates","display_name":"fiber-reinforced plates","score":0.8820000290870667},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.8619999885559082},{"id":"https://openalex.org/keywords/free-surface","display_name":"free surface","score":0.8100000023841858},{"id":"https://openalex.org/keywords/thermoelasticity","display_name":"thermoelasticity","score":0.8460000157356262},{"id":"https://openalex.org/keywords/elastic-plates","display_name":"elastic plates","score":0.6079999804496765},{"id":"https://openalex.org/keywords/unidirectional-composites","display_name":"unidirectional composites","score":0.8289999961853027},{"id":"https://openalex.org/keywords/transverse-reinforcement","display_name":"transverse reinforcement","score":0.6660000085830688}],"concepts":[{"id":"https://openalex.org/C92458943","wikidata":"https://www.wikidata.org/wiki/Q7783171","display_name":"Thermoelastic damping","level":3,"score":0.7946583032608032},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7042676210403442},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.6127356290817261},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5909112691879272},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.5405541658401489},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49953770637512207},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4831632971763611},{"id":"https://openalex.org/C2778744346","wikidata":"https://www.wikidata.org/wiki/Q1152224","display_name":"Distinctive feature","level":2,"score":0.42572927474975586},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17369216680526733},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.1657106876373291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14291566610336304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1073121428489685},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.07615500688552856},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07200184464454651},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.059055984020233154},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.21638/spbu01.2022.301","doi":"https://doi.org/10.21638/spbu01.2022.301","is_oa":true,"landing_page_url":"https://doi.org/10.21638/spbu01.2022.301","pdf_url":"https://math-mech-astr-journal.spbu.ru/article/download/14555/9855","source":{"id":"https://openalex.org/S4210218253","display_name":"Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy","issn_l":"1025-3106","issn":["1025-3106","2587-5884"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy","raw_type":"journal-article"},{"id":"pmh:oai:dspace.spbu.ru:11701/38282","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11701/38282","pdf_url":null,"source":{"id":"https://openalex.org/S4306402062","display_name":"Research Repository Saint Petersburg State University (Saint Petersburg State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I172901346","host_organization_name":"St Petersburg University","host_organization_lineage":["https://openalex.org/I172901346"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.21638/spbu01.2022.301","doi":"https://doi.org/10.21638/spbu01.2022.301","is_oa":true,"landing_page_url":"https://doi.org/10.21638/spbu01.2022.301","pdf_url":"https://math-mech-astr-journal.spbu.ru/article/download/14555/9855","source":{"id":"https://openalex.org/S4210218253","display_name":"Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy","issn_l":"1025-3106","issn":["1025-3106","2587-5884"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7799999713897705}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312379897.pdf","grobid_xml":"https://content.openalex.org/works/W4312379897.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W29367858","https://openalex.org/W581286606","https://openalex.org/W617112512","https://openalex.org/W646950880","https://openalex.org/W1069874463","https://openalex.org/W1530859481","https://openalex.org/W1676467742","https://openalex.org/W1777272878","https://openalex.org/W1969814791","https://openalex.org/W1975817813","https://openalex.org/W1977721093","https://openalex.org/W1981069097","https://openalex.org/W1985451478","https://openalex.org/W2003526318","https://openalex.org/W2015363477","https://openalex.org/W2029655403","https://openalex.org/W2039526187","https://openalex.org/W2069595593","https://openalex.org/W2149456776","https://openalex.org/W2312957290","https://openalex.org/W2332157443","https://openalex.org/W2511672308","https://openalex.org/W2807918638","https://openalex.org/W2898202383","https://openalex.org/W2971219503","https://openalex.org/W2998568272","https://openalex.org/W3018830496","https://openalex.org/W3033477314","https://openalex.org/W3033749929","https://openalex.org/W3140320990"],"related_works":["https://openalex.org/W2054919018","https://openalex.org/W2001550513","https://openalex.org/W2090764544","https://openalex.org/W2128585177","https://openalex.org/W3208881875","https://openalex.org/W2016092895","https://openalex.org/W2325690970","https://openalex.org/W2944231641","https://openalex.org/W2059631326","https://openalex.org/W4388101082"],"abstract_inverted_index":{"The":[0,46],"periodicity":[1,22],"cell":[2],"problems":[3],"of":[4,20,24,30,48],"the":[5,21,25,28],"homogenization":[6],"theory,":[7],"both":[8],"elastic":[9],"and":[10,54],"thermoelastic,":[11],"are":[12,58],"discussed":[13],"for":[14,52],"a":[15],"fiber-reinforced":[16],"plate.":[17],"A":[18],"feature":[19],"cells":[23],"plates":[26,57],"is":[27],"presence":[29],"free":[31,44],"surfaces":[32],"in":[33],"them.":[34],"As":[35],"follows":[36],"from":[37],"our":[38],"calculations,":[39],"boundary":[40,50],"layers":[41,51],"appear":[42],"on":[43],"surfaces.":[45],"characteristics":[47],"these":[49],"unidirectional":[53],"transverse":[55],"reinforced":[56],"investigated.":[59]},"counts_by_year":[],"updated_date":"2026-09-08T07:41:39.490200","created_date":"2025-10-10T00:00:00"}
