{"id":"https://openalex.org/W3198850716","doi":"https://doi.org/10.1109/access.2021.3104909","title":"Solving the Boundary Value Problem of Curves With Prescribed Geodesic Curvature Based on a Cubic B-Spline Element Method","display_name":"Solving the Boundary Value Problem of Curves With Prescribed Geodesic Curvature Based on a Cubic B-Spline Element Method","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3198850716","doi":"https://doi.org/10.1109/access.2021.3104909","mag":"3198850716"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3104909","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3104909","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09514550.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09514550.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101665094","display_name":"Peng Zhang","orcid":"https://orcid.org/0000-0002-9179-5755"},"institutions":[{"id":"https://openalex.org/I4210154423","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210154423"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Zhang","raw_affiliation_strings":["College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-9179-5755","affiliations":[{"raw_affiliation_string":"College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]},{"raw_affiliation_string":"Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I4210154423","https://openalex.org/I56934997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008120967","display_name":"Lairong Yin","orcid":"https://orcid.org/0000-0002-8562-3148"},"institutions":[{"id":"https://openalex.org/I4210154423","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210154423"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lairong Yin","raw_affiliation_strings":["College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]},{"raw_affiliation_string":"Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I4210154423","https://openalex.org/I56934997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021720931","display_name":"Zhenhua Zhou","orcid":"https://orcid.org/0000-0002-8480-8706"},"institutions":[{"id":"https://openalex.org/I4210154423","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210154423"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenhua Zhou","raw_affiliation_strings":["College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]},{"raw_affiliation_string":"Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I4210154423","https://openalex.org/I56934997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070503574","display_name":"Long Huang","orcid":"https://orcid.org/0000-0001-7192-1024"},"institutions":[{"id":"https://openalex.org/I4210154423","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210154423"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long Huang","raw_affiliation_strings":["College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]},{"raw_affiliation_string":"Education Department of Hunan Province, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I4210154423","https://openalex.org/I56934997"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2075,"currency":"USD","value_usd":2075},"apc_paid":{"value":2075,"currency":"USD","value_usd":2075},"fwci":0.1536,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.41404884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"9","issue":null,"first_page":"119381","last_page":"119394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.9925000071525574,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9686999917030334,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6631165146827698},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6568242311477661},{"id":"https://openalex.org/keywords/b-spline","display_name":"B-spline","score":0.5489790439605713},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4286593794822693},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4224781095981598},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4219758212566376},{"id":"https://openalex.org/keywords/monotone-cubic-interpolation","display_name":"Monotone cubic interpolation","score":0.4187222123146057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39376014471054077},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3527807593345642},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34291958808898926},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.15260568261146545},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10555616021156311}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6631165146827698},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6568242311477661},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.5489790439605713},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4286593794822693},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4224781095981598},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4219758212566376},{"id":"https://openalex.org/C64485984","wikidata":"https://www.wikidata.org/wiki/Q4044484","display_name":"Monotone cubic interpolation","level":5,"score":0.4187222123146057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39376014471054077},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3527807593345642},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34291958808898926},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.15260568261146545},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10555616021156311},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3104909","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3104909","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09514550.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8b321cd8eb1e40709770f0b7469e0cf8","is_oa":true,"landing_page_url":"https://doaj.org/article/8b321cd8eb1e40709770f0b7469e0cf8","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":"IEEE Access, Vol 9, Pp 119381-119394 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3104909","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3104909","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09514550.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4099999964237213,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1443825992","display_name":null,"funder_award_id":"51705034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1902675759","display_name":null,"funder_award_id":"17C0045","funder_id":"https://openalex.org/F4320311213","funder_display_name":"Education Department of Hunan Province"},{"id":"https://openalex.org/G2287530946","display_name":null,"funder_award_id":"51705036","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3854144009","display_name":null,"funder_award_id":"2018JJ3542","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320311213","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3198850716.pdf","grobid_xml":"https://content.openalex.org/works/W3198850716.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1165082989","https://openalex.org/W1600752240","https://openalex.org/W1980509896","https://openalex.org/W1985096289","https://openalex.org/W1987574052","https://openalex.org/W1993444280","https://openalex.org/W2016361136","https://openalex.org/W2018292290","https://openalex.org/W2022518223","https://openalex.org/W2024001333","https://openalex.org/W2027131571","https://openalex.org/W2030382224","https://openalex.org/W2030411069","https://openalex.org/W2030821727","https://openalex.org/W2037915328","https://openalex.org/W2048077665","https://openalex.org/W2081230146","https://openalex.org/W2087013513","https://openalex.org/W2089330793","https://openalex.org/W2089639992","https://openalex.org/W2093205068","https://openalex.org/W2129612824","https://openalex.org/W2162870748","https://openalex.org/W2294268804","https://openalex.org/W2620887990","https://openalex.org/W2777979794","https://openalex.org/W2900241290","https://openalex.org/W3045195567","https://openalex.org/W4205649593","https://openalex.org/W4230895895","https://openalex.org/W4244802394"],"related_works":["https://openalex.org/W2070774473","https://openalex.org/W2964021668","https://openalex.org/W2102842245","https://openalex.org/W2338042004","https://openalex.org/W2131662362","https://openalex.org/W2052425187","https://openalex.org/W1968191315","https://openalex.org/W2766141905","https://openalex.org/W3153287478","https://openalex.org/W3084529718"],"abstract_inverted_index":{"Composite":[0],"manufacturing":[1],"processes":[2],"such":[3,160],"as":[4],"automated":[5,183],"tape":[6,184],"placement":[7,185],"(ATP)":[8],"and":[9,30,70,106,124,158],"filament":[10],"winding":[11],"process":[12],"(FW)":[13],"put":[14],"forward":[15],"specific":[16],"requirements":[17],"for":[18,43,139,182],"the":[19,23,27,45,60,66,79,118,121,125,128,137,150,153,168],"geodesic":[20,53,144],"curvature":[21,145],"along":[22],"layup":[24],"paths":[25],"of":[26,49,59,111,120,170,176],"composite":[28],"tows":[29],"tapes.":[31],"In":[32],"this":[33,177],"paper,":[34],"a":[35,71,109],"non-uniform":[36],"cubic":[37],"b-spline":[38],"element":[39],"method":[40,88,133,178],"is":[41,63,75,89,164,179],"proposed":[42,87,122,132],"solving":[44],"boundary":[46],"value":[47],"problem":[48],"curves":[50,140,155],"with":[51,101,136],"prescribed":[52],"curvature.":[54],"The":[55,86,131],"differential":[56],"equation":[57],"system":[58],"target":[61,171],"curve":[62],"discretized":[64],"through":[65],"point":[67],"collocation":[68],"method,":[69],"quasi-Newton":[72],"iteration":[73],"scheme":[74],"adopted":[76],"to":[77,91,116,166],"approach":[78,123],"real":[80],"solution":[81],"from":[82],"an":[83],"initial":[84],"approximation.":[85],"proved":[90],"have":[92],"third":[93],"order":[94],"accuracy,":[95],"which":[96],"shows":[97],"more":[98],"superiorities":[99],"comparing":[100],"existing":[102],"numerical":[103],"methods.":[104],"Simulations":[105],"experiments":[107],"on":[108],"series":[110],"parametric":[112],"surfaces":[113],"are":[114,156],"performed":[115],"investigate":[117],"performance":[119],"results":[126],"verify":[127],"high":[129],"efficiency.":[130],"could":[134],"cope":[135],"BVP":[138],"no":[141],"matter":[142],"their":[143],"vanishes":[146],"or":[147],"not.":[148],"At":[149],"same":[151],"time,":[152],"computed":[154],"natural":[157],"smooth":[159],"that":[161],"interpolation":[162],"technique":[163],"unnecessary":[165],"ensure":[167],"continuity":[169],"curves.":[172],"One":[173],"potential":[174],"application":[175],"trajectory":[180],"optimization":[181],"process.":[186]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
