{"id":"https://openalex.org/W4405847725","doi":"https://doi.org/10.3390/sym17010032","title":"Galerkin-Type Solution of the F\u00f6ppl\u2013von K\u00e1rm\u00e1n Equations for Square Plates","display_name":"Galerkin-Type Solution of the F\u00f6ppl\u2013von K\u00e1rm\u00e1n Equations for Square Plates","publication_year":2024,"publication_date":"2024-12-27","ids":{"openalex":"https://openalex.org/W4405847725","doi":"https://doi.org/10.3390/sym17010032"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010032","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010032","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym17010032","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056874918","display_name":"\u0421. \u0410. \u041b\u044b\u0447\u0435\u0432","orcid":"https://orcid.org/0000-0001-7590-1389"},"institutions":[{"id":"https://openalex.org/I4210092536","display_name":"Institute for Problems in Mechanics","ror":"https://ror.org/00nj22y86","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210092536","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Sergey Lychev","raw_affiliation_strings":["Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia","institution_ids":["https://openalex.org/I4210092536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021786112","display_name":"Alexander Digilov","orcid":"https://orcid.org/0000-0001-6892-7740"},"institutions":[{"id":"https://openalex.org/I4210092536","display_name":"Institute for Problems in Mechanics","ror":"https://ror.org/00nj22y86","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210092536","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander Digilov","raw_affiliation_strings":["Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia","institution_ids":["https://openalex.org/I4210092536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078089865","display_name":"N. A. Djuzhev","orcid":"https://orcid.org/0000-0002-5205-0304"},"institutions":[{"id":"https://openalex.org/I204490831","display_name":"National Research University of Electronic Technology","ror":"https://ror.org/02hf6mx60","country_code":"RU","type":"education","lineage":["https://openalex.org/I204490831"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nikolay Djuzhev","raw_affiliation_strings":["MEMSEC R&D Center, National Research University of Electronic Technology (MIET), 124498 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET), 124498 Moscow, Russia","institution_ids":["https://openalex.org/I204490831"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056874918"],"corresponding_institution_ids":["https://openalex.org/I4210092536"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5258,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62320049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"32","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9993000030517578,"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/T10514","display_name":"Numerical methods in engineering","score":0.9972000122070312,"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/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9944999814033508,"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/mathematics","display_name":"Mathematics","score":0.7037787437438965},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6607438325881958},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6341619491577148},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.6000116467475891},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.48346075415611267},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4193367660045624},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.31317973136901855},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2574678063392639},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1853877604007721},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07579880952835083}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7037787437438965},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6607438325881958},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6341619491577148},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.6000116467475891},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48346075415611267},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4193367660045624},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.31317973136901855},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2574678063392639},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1853877604007721},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07579880952835083},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010032","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010032","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c154c1240db34d4d92b156e7f95eb701","is_oa":true,"landing_page_url":"https://doaj.org/article/c154c1240db34d4d92b156e7f95eb701","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 32 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010032","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010032","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1640306384","display_name":null,"funder_award_id":"15.SIN.21.0004","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G4131289842","display_name":null,"funder_award_id":"075-15-2021-135","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G6444257319","display_name":null,"funder_award_id":"075-15-","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G6882095834","display_name":null,"funder_award_id":"75-15-2021-1350","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G843232141","display_name":null,"funder_award_id":"075-15-2021-1350","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W13650753","https://openalex.org/W21295503","https://openalex.org/W40750035","https://openalex.org/W148387595","https://openalex.org/W266420308","https://openalex.org/W420636012","https://openalex.org/W627490500","https://openalex.org/W1483238466","https://openalex.org/W1601791200","https://openalex.org/W1972502206","https://openalex.org/W1972671389","https://openalex.org/W1973307650","https://openalex.org/W1988171071","https://openalex.org/W1990030758","https://openalex.org/W1991275150","https://openalex.org/W1993682504","https://openalex.org/W1996610012","https://openalex.org/W2007139247","https://openalex.org/W2008942973","https://openalex.org/W2018871406","https://openalex.org/W2021438718","https://openalex.org/W2029438887","https://openalex.org/W2030632857","https://openalex.org/W2031826754","https://openalex.org/W2043507657","https://openalex.org/W2044240876","https://openalex.org/W2044429716","https://openalex.org/W2047349627","https://openalex.org/W2048209913","https://openalex.org/W2053863478","https://openalex.org/W2060251591","https://openalex.org/W2060296330","https://openalex.org/W2076676190","https://openalex.org/W2078200611","https://openalex.org/W2078821481","https://openalex.org/W2091651356","https://openalex.org/W2095197130","https://openalex.org/W2097912134","https://openalex.org/W2156061401","https://openalex.org/W2157481491","https://openalex.org/W2251396662","https://openalex.org/W2254371980","https://openalex.org/W2300138450","https://openalex.org/W2312470754","https://openalex.org/W2317909877","https://openalex.org/W2373484552","https://openalex.org/W2599489739","https://openalex.org/W2716443610","https://openalex.org/W2727042074","https://openalex.org/W2765453314","https://openalex.org/W2782707322","https://openalex.org/W3004728858","https://openalex.org/W3030573821","https://openalex.org/W3034881787","https://openalex.org/W3040098636","https://openalex.org/W3103303518","https://openalex.org/W3121878551","https://openalex.org/W3134567289","https://openalex.org/W4243386153","https://openalex.org/W4297851792","https://openalex.org/W4319979174","https://openalex.org/W4390765778","https://openalex.org/W4391170191","https://openalex.org/W4391928200","https://openalex.org/W4394842743","https://openalex.org/W4400988437","https://openalex.org/W6600574865","https://openalex.org/W6619022850","https://openalex.org/W6676751472","https://openalex.org/W6691842743","https://openalex.org/W6791449784","https://openalex.org/W6871794348"],"related_works":["https://openalex.org/W2014800978","https://openalex.org/W2061421451","https://openalex.org/W1969730698","https://openalex.org/W1552276833","https://openalex.org/W2132583619","https://openalex.org/W1995228206","https://openalex.org/W4243371733","https://openalex.org/W2147129399","https://openalex.org/W2013379693","https://openalex.org/W3106362747"],"abstract_inverted_index":{"The":[0,29,64,107],"solution":[1,51],"of":[2,14,19,31,44,59,66,74,115],"the":[3,12,32,37,41,49,60,67,71,75,94,98,112,121],"non-linear":[4,57],"F\u00f6ppl\u2013von":[5],"K\u00e1rm\u00e1n":[6],"equations":[7],"for":[8],"square":[9],"plates":[10],"in":[11,70],"form":[13],"expansion":[15,33],"over":[16],"a":[17,23,56,87,132],"system":[18,43],"eigenfunctions,":[20],"generated":[21],"by":[22,111,125],"linear":[24],"self-adjoint":[25],"operator,":[26],"is":[27,69,102,109],"obtained.":[28],"coefficients":[30],"are":[34],"determined":[35],"via":[36],"reduction":[38],"method":[39],"from":[40],"infinite-dimensional":[42],"cubic":[45],"equations.":[46],"This":[47],"allows":[48],"proposed":[50,99],"to":[52,83],"be":[53],"considered":[54],"as":[55],"generalization":[58],"classical":[61],"Galerkin":[62],"approach.":[63],"novelty":[65],"study":[68],"strict":[72],"formulation":[73],"auxiliary":[76],"boundary":[77],"problem,":[78],"which":[79],"makes":[80],"it":[81,101],"possible":[82],"take":[84],"into":[85],"account":[86],"rigid":[88],"fixation":[89],"against":[90],"any":[91],"displacements":[92],"along":[93],"boundary.":[95],"To":[96],"verify":[97],"solution,":[100],"compared":[103],"with":[104],"experimental":[105],"data.":[106],"latter":[108],"obtained":[110],"holographic":[113],"interferometry":[114],"small":[116],"deflection":[117,123],"increments":[118],"superimposed":[119],"on":[120],"large":[122],"caused":[124],"initial":[126],"pressure.":[127],"Experiment":[128],"and":[129],"theory":[130],"show":[131],"good":[133],"agreement.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
