{"id":"https://openalex.org/W2995682184","doi":"https://doi.org/10.1002/nme.6294","title":"Hybrid\u2010Trefftz stress elements for plate bending","display_name":"Hybrid\u2010Trefftz stress elements for plate bending","publication_year":2019,"publication_date":"2019-12-19","ids":{"openalex":"https://openalex.org/W2995682184","doi":"https://doi.org/10.1002/nme.6294","mag":"2995682184"},"language":"en","primary_location":{"id":"doi:10.1002/nme.6294","doi":"https://doi.org/10.1002/nme.6294","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nme.6294","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","dongbi-a","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"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","is_traditional":true,"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/A5054662171","display_name":"J. A. Teixeira de Freitas","orcid":"https://orcid.org/0000-0001-8496-6942","observed_orcids":["https://orcid.org/0000-0001-8496-6942"]},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Jo\u00e3o Ant\u00f3nio Teixeira de Freitas","raw_affiliation_strings":["Departamento de Engenharia Civil, Arquitectura e Georecursos, CERIS Instituto Superior T\u00e9cnico, University of Lisbon  Lisbon Portugal"],"raw_orcid":"https://orcid.org/0000-0001-8496-6942","affiliations":[{"raw_affiliation_string":"Departamento de Engenharia Civil, Arquitectura e Georecursos, CERIS Instituto Superior T\u00e9cnico, University of Lisbon  Lisbon Portugal","institution_ids":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085025327","display_name":"Carlos M. Tiago","orcid":"https://orcid.org/0000-0003-2009-4641","observed_orcids":["https://orcid.org/0000-0003-2009-4641"]},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Carlos Tiago","raw_affiliation_strings":["Departamento de Engenharia Civil, Arquitectura e Georecursos, CERIS Instituto Superior T\u00e9cnico, University of Lisbon  Lisbon Portugal"],"raw_orcid":"https://orcid.org/0000-0003-2009-4641","affiliations":[{"raw_affiliation_string":"Departamento de Engenharia Civil, Arquitectura e Georecursos, CERIS Instituto Superior T\u00e9cnico, University of Lisbon  Lisbon Portugal","institution_ids":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085025327"],"corresponding_institution_ids":["https://openalex.org/I141596103","https://openalex.org/I4387152517"],"apc_list":{"value":4400,"currency":"USD","value_usd":4400},"apc_paid":null,"fwci":0.9724,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.65572539,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"121","issue":"9","first_page":"1946","last_page":"1976"},"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":0.9916999936103821,"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":0.9916999936103821,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.003700000001117587,"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":0.002899999963119626,"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/plate-bending","display_name":"plate bending","score":0.9300000071525574},{"id":"https://openalex.org/keywords/kirchhoff-plates","display_name":"Kirchhoff plates","score":0.9769999980926514},{"id":"https://openalex.org/keywords/reissner-mindlin-plates","display_name":"Reissner-Mindlin plates","score":0.9940000176429749},{"id":"https://openalex.org/keywords/duality","display_name":"duality","score":0.6620000004768372},{"id":"https://openalex.org/keywords/triangular-and-quadrilateral-elements","display_name":"triangular and quadrilateral elements","score":0.8429999947547913},{"id":"https://openalex.org/keywords/shear-locking","display_name":"shear locking","score":0.875}],"concepts":[{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.6894318461418152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.674951434135437},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5659627914428711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5633141398429871},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.5153431296348572},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5124745965003967},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5005245208740234},{"id":"https://openalex.org/C87210426","wikidata":"https://www.wikidata.org/wiki/Q1072476","display_name":"Bending","level":2,"score":0.4937208592891693},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48740437626838684},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.4820781350135803},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4797462224960327},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.45734453201293945},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4428475499153137},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.4278479218482971},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37252750992774963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3629978895187378},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.21324530243873596},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09708422422409058},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09455826878547668},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.08559882640838623},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nme.6294","doi":"https://doi.org/10.1002/nme.6294","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nme.6294","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","dongbi-a","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1496365809","https://openalex.org/W1533058090","https://openalex.org/W1573186872","https://openalex.org/W1759836442","https://openalex.org/W1812695178","https://openalex.org/W1857223419","https://openalex.org/W1967758632","https://openalex.org/W1972705284","https://openalex.org/W1973661619","https://openalex.org/W1974638732","https://openalex.org/W2000768589","https://openalex.org/W2001651247","https://openalex.org/W2002433610","https://openalex.org/W2003877150","https://openalex.org/W2009146274","https://openalex.org/W2010141026","https://openalex.org/W2012366807","https://openalex.org/W2016969945","https://openalex.org/W2031980956","https://openalex.org/W2035575980","https://openalex.org/W2036293451","https://openalex.org/W2039218364","https://openalex.org/W2052710105","https://openalex.org/W2060833621","https://openalex.org/W2073156013","https://openalex.org/W2079530938","https://openalex.org/W2086497019","https://openalex.org/W2087052022","https://openalex.org/W2089359498","https://openalex.org/W2128596934","https://openalex.org/W2129577202","https://openalex.org/W2163844652","https://openalex.org/W2171552795","https://openalex.org/W2327734394","https://openalex.org/W2573993005","https://openalex.org/W2994195585"],"related_works":["https://openalex.org/W4408835851","https://openalex.org/W4402739526","https://openalex.org/W2163844652","https://openalex.org/W2095816555","https://openalex.org/W820096804","https://openalex.org/W1857223419","https://openalex.org/W2012366807","https://openalex.org/W2044582537","https://openalex.org/W4403879928","https://openalex.org/W2124581898"],"abstract_inverted_index":{"Summary":[0],"The":[1,21,40,92],"hybrid\u2010Trefftz":[2],"stress":[3],"element":[4,22,89],"is":[5,23,27,43,83,127,147],"used":[6,71,84],"to":[7,57,64,72,85,119,149,153],"emulate":[8,65],"conventional":[9,66],"finite":[10],"elements":[11,109,138],"for":[12,98],"analysis":[13],"of":[14,33,48,52,79,102,116,134,157],"Kirchhoff":[15],"and":[16,36,96,100,107,112,121,139,161],"Mindlin\u2010Reissner":[17],"plate":[18],"bending":[19],"problems.":[20],"hybrid":[24],"because":[25],"it":[26],"based":[28],"on":[29,45,76],"the":[30,34,46,49,53,59,74,77,80,88,155,159],"independent":[31],"approximation":[32,163],"stress\u2010resultant":[35,60],"boundary":[37,78,162],"displacement":[38],"fields.":[39],"Trefftz":[41],"variant":[42],"consequent":[44],"use":[47],"formal":[50],"solutions":[51,103],"governing":[54],"Lagrange":[55],"equation":[56],"approximate":[58,73],"field.":[61],"In":[62],"order":[63],"elements,":[67],"nodal":[68],"functions":[69],"are":[70,104,110],"displacements":[75],"element.":[81],"Duality":[82],"set":[86],"up":[87],"solving":[90],"system.":[91],"associated":[93],"variational":[94],"statements":[95],"conditions":[97],"existence":[99],"uniqueness":[101],"recovered.":[105],"Triangular":[106],"quadrilateral":[108],"tested":[111],"characterized":[113],"in":[114],"terms":[115],"convergence,":[117],"sensitivity":[118],"shear\u2010locking,":[120],"shape":[122],"distortion.":[123],"Their":[124],"relative":[125,145],"performance":[126],"assessed":[128],"using":[129],"assumed":[130],"strain":[131],"Mixed":[132],"Interpolation":[133],"Tensorial":[135],"Components":[136],"(MITC)":[137],"recently":[140],"proposed":[141],"Trefftz\u2010based":[142],"elements.":[143],"This":[144],"assessment":[146],"extended":[148],"a":[150],"hypersingular":[151],"problem":[152],"illustrate":[154],"effect":[156],"enriching":[158],"domain":[160],"bases.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2019-12-26T00:00:00"}
