{"id":"https://openalex.org/W2035846800","doi":"https://doi.org/10.1137/140951473","title":"Linear Models for Composite Thin-Walled Beams by $\\Gamma$-Convergence. Part I: Open Cross Sections","display_name":"Linear Models for Composite Thin-Walled Beams by $\\Gamma$-Convergence. Part I: Open Cross Sections","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2035846800","doi":"https://doi.org/10.1137/140951473","mag":"2035846800"},"language":"en","primary_location":{"id":"doi:10.1137/140951473","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140951473","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11390/1001346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017169103","display_name":"Cesare Davini","orcid":"https://orcid.org/0000-0002-1438-248X"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"C. Davini","raw_affiliation_strings":["University of Udine"],"affiliations":[{"raw_affiliation_string":"University of Udine","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039500113","display_name":"Lorenzo Freddi","orcid":"https://orcid.org/0000-0002-6954-4773"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"L. Freddi","raw_affiliation_strings":["University of Udine"],"affiliations":[{"raw_affiliation_string":"University of Udine","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020633971","display_name":"Roberto Paroni","orcid":"https://orcid.org/0000-0003-3040-0112"},"institutions":[{"id":"https://openalex.org/I159650629","display_name":"University of Sassari","ror":"https://ror.org/01bnjbv91","country_code":"IT","type":"education","lineage":["https://openalex.org/I159650629"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"R. Paroni","raw_affiliation_strings":["University of Sassari"],"affiliations":[{"raw_affiliation_string":"University of Sassari","institution_ids":["https://openalex.org/I159650629"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017169103"],"corresponding_institution_ids":["https://openalex.org/I129043915"],"apc_list":null,"apc_paid":null,"fwci":0.7122,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71412265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"5","first_page":"3296","last_page":"3331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":1.0,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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/zero","display_name":"Zero (linguistics)","score":0.6876600980758667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6549886465072632},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.635358989238739},{"id":"https://openalex.org/keywords/beam","display_name":"Beam (structure)","score":0.5930413603782654},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.569786012172699},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5516576766967773},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5501948595046997},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.530038595199585},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.456143856048584},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.433878630399704},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.42497682571411133},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4193270206451416},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.35246753692626953},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32446569204330444},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17176809906959534},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1031087338924408}],"concepts":[{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6876600980758667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6549886465072632},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.635358989238739},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.5930413603782654},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.569786012172699},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5516576766967773},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5501948595046997},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.530038595199585},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.456143856048584},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.433878630399704},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.42497682571411133},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4193270206451416},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35246753692626953},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32446569204330444},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17176809906959534},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1031087338924408},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140951473","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140951473","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:air.uniud.it:11390/1001346","is_oa":true,"landing_page_url":"http://hdl.handle.net/11390/1001346","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arpi.unipi.it:11568/885746","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/885746","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"1 Contributo su Rivista::1.1 Articolo in rivista"}],"best_oa_location":{"id":"pmh:oai:air.uniud.it:11390/1001346","is_oa":true,"landing_page_url":"http://hdl.handle.net/11390/1001346","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W63412434","https://openalex.org/W105606343","https://openalex.org/W112023339","https://openalex.org/W226239495","https://openalex.org/W590178533","https://openalex.org/W656727543","https://openalex.org/W1491891466","https://openalex.org/W1565627164","https://openalex.org/W1773851459","https://openalex.org/W1988221005","https://openalex.org/W2004065836","https://openalex.org/W2022382371","https://openalex.org/W2027463241","https://openalex.org/W2063968613","https://openalex.org/W2105340951","https://openalex.org/W2111845009","https://openalex.org/W2488947967","https://openalex.org/W2963791485","https://openalex.org/W3127333241","https://openalex.org/W4229943838"],"related_works":["https://openalex.org/W141820298","https://openalex.org/W4378770497","https://openalex.org/W2049584446","https://openalex.org/W1971715485","https://openalex.org/W27212783","https://openalex.org/W2079781215","https://openalex.org/W2064404759","https://openalex.org/W2076389328","https://openalex.org/W2002854980","https://openalex.org/W2029082315"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,8,15,19,30,51,87,113,132],"beam":[3,32,85,143],"whose":[4,23],"cross":[5],"section":[6],"is":[7,56,78],"tubular":[9],"neighborhood,":[10],"with":[11,14,26],"thickness":[12],"scaling":[13],"parameter":[16,53],"$\\delta_{\\varepsilon}$,":[17],"of":[18,48,67,141,148],"simple":[20],"curve":[21,77],"$\\gamma$":[22],"length":[24],"scales":[25],"$\\varepsilon$.":[27],"To":[28],"model":[29],"thin-walled":[31,126],"we":[33,44,70,95],"assume":[34],"that":[35,83],"$\\delta_{\\varepsilon}$":[36],"goes":[37],"to":[38,105],"zero":[39],"faster":[40],"than":[41],"$\\varepsilon$,":[42],"and":[43,61,116,135],"measure":[45],"the":[46,57,68,73,76,81,84,121,142,146],"rate":[47],"convergence":[49],"by":[50,101],"slenderness":[52],"$\\mathfrak{s}$":[54],"which":[55],"ratio":[58],"between":[59],"$\\varepsilon^2$":[60],"$\\delta_{\\varepsilon}$.":[62],"In":[63],"this":[64],"Part":[65],"I":[66],"work":[69],"focus":[71],"on":[72],"case":[74],"where":[75],"open.":[79],"Under":[80],"assumption":[82],"has":[86],"linearly":[88],"elastic":[89],"behavior,":[90],"for":[91,112,124],"$\\mathfrak{s}\\in":[92],"\\{0,":[93],"1\\}$":[94],"derive":[96],"two":[97],"one-dimensional":[98],"$\\Gamma$-limit":[99],"problems":[100],"letting":[102],"$\\varepsilon$":[103],"go":[104],"zero.":[106],"The":[107,128],"limit":[108],"models":[109,144],"are":[110],"obtained":[111],"fully":[114],"anisotropic":[115],"inhomogeneous":[117],"material,":[118],"thus":[119],"making":[120],"theory":[122,147],"applicable":[123],"composite":[125],"beams.":[127],"approach":[129],"recovers":[130],"in":[131,145],"systematic":[133],"way,":[134],"gives":[136],"account":[137],"of,":[138],"many":[139],"features":[140],"Vlasov.":[149]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}