{"id":"https://openalex.org/W2172003187","doi":"https://doi.org/10.1002/nme.1620240309","title":"A new efficient mixed formulation for thin shell finite element models","display_name":"A new efficient mixed formulation for thin shell finite element models","publication_year":1987,"publication_date":"1987-03-01","ids":{"openalex":"https://openalex.org/W2172003187","doi":"https://doi.org/10.1002/nme.1620240309","mag":"2172003187"},"language":"en","primary_location":{"id":"doi:10.1002/nme.1620240309","doi":"https://doi.org/10.1002/nme.1620240309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nme.1620240309","pdf_url":null,"source":{"id":"https://openalex.org/S165651092","display_name":"International Journal for Numerical Methods in Engineering","issn_l":"0029-5981","issn":["0029-5981","1097-0207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-2","norway-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal for Numerical Methods in Engineering","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068531832","display_name":"J. J. Rhiu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. J. Rhiu","raw_affiliation_strings":["Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, U.S.A","Research Associate"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, U.S.A","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Research Associate","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062004802","display_name":"S. W. Lee","orcid":"https://orcid.org/0009-0007-6268-9981","observed_orcids":["https://orcid.org/0009-0007-6268-9981"]},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. W. Lee","raw_affiliation_strings":["Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, U.S.A","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062004802"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":{"value":4250,"currency":"USD","value_usd":4250},"apc_paid":null,"fwci":12.5186,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.99216689,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"3","first_page":"581","last_page":"604"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.012199999764561653,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/thin-shell-elements","display_name":"thin shell elements","score":0.7329999804496765},{"id":"https://openalex.org/keywords/mixed-formulation","display_name":"mixed formulation","score":0.9200000166893005},{"id":"https://openalex.org/keywords/hellinger-reissner-principle","display_name":"Hellinger-Reissner principle","score":0.875},{"id":"https://openalex.org/keywords/locking","display_name":"locking","score":0.453000009059906},{"id":"https://openalex.org/keywords/stability-of-motion","display_name":"motion stability","score":0.8640000224113464}],"concepts":[{"id":"https://openalex.org/C2781052500","wikidata":"https://www.wikidata.org/wiki/Q2230313","display_name":"Shell (structure)","level":2,"score":0.7591931223869324},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6805629134178162},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.6192405819892883},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.6026641726493835},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5530954003334045},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5371926426887512},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5349392294883728},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.4590649902820587},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4588930606842041},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42574816942214966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41438522934913635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35803231596946716},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.3103099465370178},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2945689857006073},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20530134439468384},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.19652003049850464},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.15560927987098694},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.09314250946044922},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nme.1620240309","doi":"https://doi.org/10.1002/nme.1620240309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nme.1620240309","pdf_url":null,"source":{"id":"https://openalex.org/S165651092","display_name":"International Journal for Numerical Methods in Engineering","issn_l":"0029-5981","issn":["0029-5981","1097-0207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-2","norway-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal for Numerical Methods in Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1971666834","https://openalex.org/W1980199375","https://openalex.org/W1991682659","https://openalex.org/W1998786196","https://openalex.org/W2004049383","https://openalex.org/W2005715043","https://openalex.org/W2009993675","https://openalex.org/W2024164041","https://openalex.org/W2024321552","https://openalex.org/W2030911466","https://openalex.org/W2046454555","https://openalex.org/W2046468638","https://openalex.org/W2120868368","https://openalex.org/W2132782245","https://openalex.org/W2167690270","https://openalex.org/W2169254529"],"related_works":["https://openalex.org/W2389973625","https://openalex.org/W2081971496","https://openalex.org/W2379196245","https://openalex.org/W2119256031","https://openalex.org/W2381658119","https://openalex.org/W4294096282","https://openalex.org/W2983729671","https://openalex.org/W631435443","https://openalex.org/W4380030486","https://openalex.org/W1600069777"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"nine":[2,77],"node":[3,78],"shell":[4,18],"element":[5,19,79],"is":[6,21,41,80,92],"developed":[7],"by":[8,55],"a":[9,34,62,67,112],"new":[10,17,39],"and":[11,30,66,89,91],"more":[12,43],"efficient":[13,44],"mixed":[14,53],"formulation.":[15],"The":[16,38],"formulation":[20,40,54],"based":[22],"on":[23],"the":[24,31,51,57,75,98,103,109],"Hellinger\u2013Reissner":[25],"principle":[26],"with":[27,102],"independent":[28],"strain":[29,59,107],"concept":[32],"of":[33,47,82,111],"degenerate":[35],"solid":[36],"shell.":[37],"made":[42],"in":[45],"terms":[46],"computing":[48],"time":[49],"than":[50],"conventional":[52],"dividing":[56],"assumed":[58,106],"fields":[60],"into":[61],"lower":[63],"order":[64,69,105],"part":[65],"higher":[68,104],"part.":[70],"Numerical":[71],"results":[72],"demonstrate":[73],"that":[74],"present":[76],"free":[81],"locking":[83],"even":[84],"for":[85],"very":[86],"thin":[87],"plates":[88],"shells":[90],"also":[93],"kinematically":[94],"stable.":[95],"In":[96],"fact":[97],"stiffness":[99],"matrix":[100],"associated":[101],"plays":[108],"role":[110],"stabilization":[113],"matrix.":[114]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}