{"id":"https://openalex.org/W7225812894","doi":"https://doi.org/10.3390/math14224140","title":"Panel-Method Loads in Density-Based Topology Optimization of Wing Interiors: Consistent Load Transfer, Design-Uniform Stability, and Verification","display_name":"Panel-Method Loads in Density-Based Topology Optimization of Wing Interiors: Consistent Load Transfer, Design-Uniform Stability, and Verification","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225812894","doi":"https://doi.org/10.3390/math14224140"},"language":"en","primary_location":{"id":"doi:10.3390/math14224140","doi":"https://doi.org/10.3390/math14224140","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224140","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14224140","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161494970","display_name":"Ricardo Lamarca","orcid":"https://orcid.org/0009-0000-0009-7293","observed_orcids":["https://orcid.org/0009-0000-0009-7293"]},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ricardo Lamarca","raw_affiliation_strings":["MAQLAB Research Group, Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain"],"raw_orcid":"https://orcid.org/0009-0000-0009-7293","affiliations":[{"raw_affiliation_string":"MAQLAB Research Group, Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5161493896","display_name":"Abraham Vadillo","orcid":"https://orcid.org/0000-0001-9888-0373","observed_orcids":["https://orcid.org/0000-0001-9888-0373"]},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Abraham Vadillo","raw_affiliation_strings":["MAQLAB Research Group, Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","Pedro Juan de Lastanosa Research Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9888-0373","affiliations":[{"raw_affiliation_string":"MAQLAB Research Group, Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Pedro Juan de Lastanosa Research Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045089866","display_name":"Cristina Castej\u00f3n","orcid":"https://orcid.org/0000-0002-5823-7372","observed_orcids":["https://orcid.org/0000-0002-5823-7372"]},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Cristina Castej\u00f3n","raw_affiliation_strings":["MAQLAB Research Group, Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","Pedro Juan de Lastanosa Research Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-5823-7372","affiliations":[{"raw_affiliation_string":"MAQLAB Research Group, Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Pedro Juan de Lastanosa Research Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5161493896"],"corresponding_institution_ids":["https://openalex.org/I50357001"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"22","first_page":"4140","last_page":"4140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0,"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/T11096","display_name":"Aeroelasticity and Vibration Control","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.7602999806404114},{"id":"https://openalex.org/C97257150","wikidata":"https://www.wikidata.org/wiki/Q161358","display_name":"Wing","level":2,"score":0.5825999975204468},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5764999985694885},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5123999714851379},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49779999256134033},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46639999747276306},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4544999897480011},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4226999878883362},{"id":"https://openalex.org/C13393347","wikidata":"https://www.wikidata.org/wiki/Q8424","display_name":"Aerodynamics","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3774999976158142},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.36800000071525574},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3353999853134155},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27070000767707825},{"id":"https://openalex.org/C155673373","wikidata":"https://www.wikidata.org/wiki/Q1648886","display_name":"Structural stability","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/math14224140","doi":"https://doi.org/10.3390/math14224140","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224140","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/math14224140","doi":"https://doi.org/10.3390/math14224140","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224140","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Wing":[0],"topology":[1],"optimization":[2],"often":[3],"uses":[4],"different":[5],"aerodynamic":[6],"and":[7,10,17,41,91,113,181],"structural":[8],"meshes,":[9],"the":[11,14,22,49,55,58,63,74,85,89,99,102,106,111,114,120,137,145,151,186,189,191,194],"effect":[12],"of":[13,18,57,88,92,105,122,144,188,193],"load":[15,19,50],"transfer":[16,177],"errors":[20],"on":[21,166],"optimum":[23],"is":[24,51,66,95,126,141,171,184],"rarely":[25],"quantified.":[26],"We":[27],"study":[28],"both":[29],"for":[30],"a":[31,67,77,123,172,176],"fixed":[32,124],"wing":[33],"shape":[34],"under":[35],"one-way":[36],"panel-method":[37],"loads.":[38],"The":[39,156],"analysis":[40],"its":[42,93,129],"full":[43],"verification":[44],"are":[45,197],"two-dimensional.":[46],"In":[47],"2D":[48],"transferred":[52],"exactly":[53],"by":[54],"adjoint":[56,187],"finite":[59],"element":[60],"trace,":[61],"so":[62],"discrete":[64],"problem":[65],"Galerkin":[68],"approximation":[69],"without":[70],"consistency":[71],"error":[72],"from":[73],"transfer.":[75],"With":[76],"clamped,":[78],"load-carrying":[79],"passive":[80,107],"skin,":[81],"we":[82],"prove":[83],"that":[84,178],"square":[86],"root":[87],"compliance,":[90],"optimum,":[94],"Lipschitz":[96],"continuous":[97],"in":[98,101,110],"load,":[100],"energy":[103],"norm":[104],"set,":[108],"uniformly":[109],"design":[112,147],"void":[115],"stiffness.":[116],"At":[117],"400":[118],"panels":[119],"compliance":[121],"rib":[125,140],"0.53%":[127],"below":[128],"value":[130],"at":[131],"12,800":[132],"panels.":[133],"Under":[134],"measured-pressure":[135],"loads,":[136],"best":[138,146],"panel-optimal":[139],"within":[142],"0.35%":[143],"found,":[148],"less":[149],"than":[150],"scatter":[152],"between":[153],"local":[154],"optima.":[155],"three-dimensional":[157],"study,":[158],"with":[159,175],"up":[160],"to":[161],"63":[162],"million":[163],"active":[164],"voxels":[165],"one":[167],"graphics":[168],"processing":[169],"unit,":[170],"feasibility":[173],"demonstration":[174],"conserves":[179],"force":[180],"moment":[182],"but":[183],"not":[185],"trace;":[190],"hypotheses":[192],"stability":[195],"result":[196],"checked":[198],"directly.":[199]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
