{"id":"https://openalex.org/W2940971092","doi":"https://doi.org/10.1186/s40323-019-0129-8","title":"Best theory diagrams for multilayered structures via shell finite elements","display_name":"Best theory diagrams for multilayered structures via shell finite elements","publication_year":2019,"publication_date":"2019-03-25","ids":{"openalex":"https://openalex.org/W2940971092","doi":"https://doi.org/10.1186/s40323-019-0129-8","mag":"2940971092"},"language":"en","primary_location":{"id":"doi:10.1186/s40323-019-0129-8","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-019-0129-8","pdf_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-019-0129-8","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-019-0129-8","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068418311","display_name":"Marco Petrolo","orcid":"https://orcid.org/0000-0002-7843-105X"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marco Petrolo","raw_affiliation_strings":["MUL\u00b2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7843-105X","affiliations":[{"raw_affiliation_string":"MUL\u00b2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041025620","display_name":"Erasmo Carrera","orcid":"https://orcid.org/0000-0002-6911-7763"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]},{"id":"https://openalex.org/I195795380","display_name":"Tambov State Technical University","ror":"https://ror.org/04wegbp55","country_code":"RU","type":"education","lineage":["https://openalex.org/I195795380"]}],"countries":["IT","RU"],"is_corresponding":false,"raw_author_name":"Erasmo Carrera","raw_affiliation_strings":["Laboratory of Intelligent Materials and Structures, Tambov State Technical University, Sovetskaya, 106, 392000, Tambov, Russia","MUL\u00b2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Intelligent Materials and Structures, Tambov State Technical University, Sovetskaya, 106, 392000, Tambov, Russia","institution_ids":["https://openalex.org/I195795380"]},{"raw_affiliation_string":"MUL\u00b2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068418311"],"corresponding_institution_ids":["https://openalex.org/I177477856"],"apc_list":{"value":990,"currency":"GBP","value_usd":1214},"apc_paid":{"value":990,"currency":"GBP","value_usd":1214},"fwci":1.4645,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.78355999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10713","display_name":"Structural Load-Bearing Analysis","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/computer-science","display_name":"Computer science","score":0.583278477191925},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5648231506347656},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5602237582206726},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5277850031852722},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5240878462791443},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5108796954154968},{"id":"https://openalex.org/keywords/shell","display_name":"Shell (structure)","score":0.5069868564605713},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4832082986831665},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4693717956542969},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4300646185874939},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.4279882311820984},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42551523447036743},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4049292802810669},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3793483078479767},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3669895529747009},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2791878283023834},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.27305012941360474},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18047210574150085},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14324000477790833},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13908788561820984},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.12539821863174438},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09259283542633057}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.583278477191925},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5648231506347656},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5602237582206726},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5277850031852722},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5240878462791443},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5108796954154968},{"id":"https://openalex.org/C2781052500","wikidata":"https://www.wikidata.org/wiki/Q2230313","display_name":"Shell (structure)","level":2,"score":0.5069868564605713},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4832082986831665},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4693717956542969},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4300646185874939},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.4279882311820984},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42551523447036743},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4049292802810669},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3793483078479767},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3669895529747009},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2791878283023834},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.27305012941360474},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18047210574150085},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14324000477790833},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13908788561820984},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.12539821863174438},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09259283542633057},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1186/s40323-019-0129-8","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-019-0129-8","pdf_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-019-0129-8","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04514187v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04514187","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://link.springer.com/article/10.1186/s40323-019-0129-8/fulltext.html","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:d4e0e4274ca24591a940eee9e637db59","is_oa":true,"landing_page_url":"https://doaj.org/article/d4e0e4274ca24591a940eee9e637db59","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences, Vol 6, Iss 1, Pp 1-23 (2019)","raw_type":"article"},{"id":"pmh:oai:zenodo.org:28481","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/28481","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1186/s40323-019-0129-8","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-019-0129-8","pdf_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-019-0129-8","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.800000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3595358111","display_name":null,"funder_award_id":"No. 18-19-00092","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"},{"id":"https://openalex.org/G3652048868","display_name":null,"funder_award_id":"18-19-","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"},{"id":"https://openalex.org/G7837078937","display_name":null,"funder_award_id":"18-19-00092","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2940971092.pdf","grobid_xml":"https://content.openalex.org/works/W2940971092.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W210967392","https://openalex.org/W382512326","https://openalex.org/W1547781576","https://openalex.org/W1976496016","https://openalex.org/W1981605565","https://openalex.org/W1981779247","https://openalex.org/W1990486320","https://openalex.org/W2011019069","https://openalex.org/W2016667548","https://openalex.org/W2076220025","https://openalex.org/W2088712815","https://openalex.org/W2104446230","https://openalex.org/W2261621682","https://openalex.org/W2266285536","https://openalex.org/W2298588850","https://openalex.org/W2319780829","https://openalex.org/W2356847050","https://openalex.org/W2480272034","https://openalex.org/W2510803618","https://openalex.org/W2533723587","https://openalex.org/W2542860108","https://openalex.org/W2554078641","https://openalex.org/W2556552365","https://openalex.org/W2575296977","https://openalex.org/W2607265988","https://openalex.org/W2735167189","https://openalex.org/W2738608673","https://openalex.org/W2748957330","https://openalex.org/W2750972735","https://openalex.org/W2751700501","https://openalex.org/W2758544202","https://openalex.org/W2768152121","https://openalex.org/W2769410986","https://openalex.org/W2777391033","https://openalex.org/W2782866647","https://openalex.org/W2790704335","https://openalex.org/W2797887977","https://openalex.org/W2801803359","https://openalex.org/W2807790068","https://openalex.org/W2924813572","https://openalex.org/W2963218884","https://openalex.org/W2976477962"],"related_works":["https://openalex.org/W2375684291","https://openalex.org/W2354676191","https://openalex.org/W3188646203","https://openalex.org/W2909957174","https://openalex.org/W136674370","https://openalex.org/W4246278799","https://openalex.org/W2105527480","https://openalex.org/W2052387497","https://openalex.org/W2050203848","https://openalex.org/W2050191802"],"abstract_inverted_index":{"Composite":[0],"structures":[1,85],"are":[2,49,178],"convenient":[3],"structural":[4,34],"solutions":[5],"for":[6],"many":[7],"engineering":[8],"fields,":[9],"but":[10],"their":[11,189,199],"design":[12,155],"is":[13,41],"challenging":[14],"and":[15,46,79,86,104,124,164,180,198],"may":[16,201],"lead":[17],"to":[18,21,74,83],"oversizing":[19],"due":[20],"the":[22,28,37,42,54,65,76,81,96,110,116,120,125,134,137,142,159,171,182,185,203,206],"significant":[23],"amount":[24],"of":[25,50,56,67,99,102,119,136,144,154,175,205],"uncertainties":[26],"concerning":[27],"current":[29],"modeling":[30],"capabilities.":[31],"From":[32],"a":[33],"analysis":[35],"standpoint,":[36],"finite":[38],"element":[39],"method":[40],"most":[43,172],"used":[44],"approach":[45],"shell":[47,93],"elements":[48,69,94,108],"primary":[51,186],"importance":[52],"in":[53,188],"case":[55],"thin":[57],"structures.":[58],"Current":[59],"research":[60],"efforts":[61],"aim":[62],"at":[63],"improving":[64],"accuracy":[66,204],"such":[68,157],"with":[70,95],"limited":[71],"computational":[72],"overheads":[73],"improve":[75],"predictive":[77],"capabilities":[78],"widen":[80],"applicability":[82],"complex":[84],"nonlinear":[87],"cases.":[88],"The":[89,148,167],"present":[90],"paper":[91,130],"presents":[92],"minimum":[97],"number":[98],"nodal":[100],"degrees":[101],"freedom":[103],"maximum":[105],"accuracy.":[106],"Such":[107],"compose":[109],"best":[111],"theory":[112],"diagram":[113],"stemming":[114],"from":[115],"combined":[117],"use":[118],"Carrera":[121],"Unified":[122],"Formulation":[123],"Axiomatic/Asymptotic":[126],"Method.":[127],"Moreover,":[128,191],"this":[129],"provides":[131],"guidelines":[132],"on":[133],"choice":[135],"proper":[138],"higher-order":[139,176],"terms":[140,177,193],"via":[141],"introduction":[143],"relevance":[145],"factor":[146],"diagrams.":[147],"numerical":[149],"cases":[150],"consider":[151],"various":[152],"sets":[153],"parameters":[156],"as":[158],"thickness,":[160],"curvature,":[161],"stacking":[162],"sequence,":[163],"boundary":[165],"conditions.":[166],"results":[168],"show":[169],"that":[170,181],"relevant":[173],"set":[174],"third-order":[179],"thickness":[183],"plays":[184],"role":[187],"choice.":[190],"certain":[192],"have":[194],"very":[195],"high":[196],"influence,":[197],"neglect":[200],"affect":[202],"model":[207],"significantly.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}