{"id":"https://openalex.org/W4213255064","doi":"https://doi.org/10.1093/jcde/qwab069","title":"A heterogeneous lattice structure modeling technique supported by multiquadric radial basis function networks","display_name":"A heterogeneous lattice structure modeling technique supported by multiquadric radial basis function networks","publication_year":2021,"publication_date":"2021-11-03","ids":{"openalex":"https://openalex.org/W4213255064","doi":"https://doi.org/10.1093/jcde/qwab069"},"language":"en","primary_location":{"id":"doi:10.1093/jcde/qwab069","is_oa":true,"landing_page_url":"https://doi.org/10.1093/jcde/qwab069","pdf_url":"https://academic.oup.com/jcde/article-pdf/9/1/68/42687941/qwab069.pdf","source":{"id":"https://openalex.org/S2485147958","display_name":"Journal of Computational Design and Engineering","issn_l":"2288-4300","issn":["2288-4300","2288-5048"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Design and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://academic.oup.com/jcde/article-pdf/9/1/68/42687941/qwab069.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100390963","display_name":"Yuan Liu","orcid":"https://orcid.org/0009-0000-0292-589X"},"institutions":[{"id":"https://openalex.org/I4210158498","display_name":"Satellite Application Center for Ecology and Environment","ror":"https://ror.org/04x9p9g72","country_code":"CN","type":"government","lineage":["https://openalex.org/I204710742","https://openalex.org/I4210158498"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Liu","raw_affiliation_strings":["Beijing Institute of Satellite Environment and Engineering, Chaoyang, Beijing 100094, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Satellite Environment and Engineering, Chaoyang, Beijing 100094, China","institution_ids":["https://openalex.org/I4210158498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100319522","display_name":"Huiyuan Yang","orcid":"https://orcid.org/0000-0003-0245-6768"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Huiyuan Yang","raw_affiliation_strings":["Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0G4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0G4, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070626046","display_name":"Yaoyao Fiona Zhao","orcid":"https://orcid.org/0000-0003-4927-0514"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yaoyao Fiona Zhao","raw_affiliation_strings":["Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0G4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0G4, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101826295","display_name":"Guolei Zheng","orcid":"https://orcid.org/0009-0006-4306-4727"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guolei Zheng","raw_affiliation_strings":["School of Mechanical Engineering & Automation, Beihang University, Haidian District, Beijing 100191, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering & Automation, Beihang University, Haidian District, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070626046","https://openalex.org/A5101826295"],"corresponding_institution_ids":["https://openalex.org/I5023651","https://openalex.org/I82880672"],"apc_list":{"value":1650,"currency":"USD","value_usd":1650},"apc_paid":{"value":1650,"currency":"USD","value_usd":1650},"fwci":0.7936,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70632012,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"9","issue":"1","first_page":"68","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9995999932289124,"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":0.9995999932289124,"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/T10707","display_name":"Cellular and Composite Structures","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10783","display_name":"Additive Manufacturing and 3D Printing Technologies","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/cable-gland","display_name":"Cable gland","score":0.5538792610168457},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.504571795463562},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4310036301612854},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42592328786849976},{"id":"https://openalex.org/keywords/architectural-geometry","display_name":"Architectural geometry","score":0.41301536560058594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37501463294029236},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3585239052772522},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3525874614715576},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3404618501663208},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33936265110969543},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.327661395072937},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.32387733459472656},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16043460369110107}],"concepts":[{"id":"https://openalex.org/C110925319","wikidata":"https://www.wikidata.org/wiki/Q12855","display_name":"Cable gland","level":2,"score":0.5538792610168457},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.504571795463562},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4310036301612854},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42592328786849976},{"id":"https://openalex.org/C158436829","wikidata":"https://www.wikidata.org/wiki/Q4787054","display_name":"Architectural geometry","level":5,"score":0.41301536560058594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37501463294029236},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3585239052772522},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3525874614715576},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3404618501663208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33936265110969543},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.327661395072937},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.32387733459472656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16043460369110107},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C149091818","wikidata":"https://www.wikidata.org/wiki/Q2429814","display_name":"Software system","level":3,"score":0.0},{"id":"https://openalex.org/C186846655","wikidata":"https://www.wikidata.org/wiki/Q3398377","display_name":"Software construction","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/jcde/qwab069","is_oa":true,"landing_page_url":"https://doi.org/10.1093/jcde/qwab069","pdf_url":"https://academic.oup.com/jcde/article-pdf/9/1/68/42687941/qwab069.pdf","source":{"id":"https://openalex.org/S2485147958","display_name":"Journal of Computational Design and Engineering","issn_l":"2288-4300","issn":["2288-4300","2288-5048"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Design and Engineering","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1093/jcde/qwab069","is_oa":true,"landing_page_url":"https://doi.org/10.1093/jcde/qwab069","pdf_url":"https://academic.oup.com/jcde/article-pdf/9/1/68/42687941/qwab069.pdf","source":{"id":"https://openalex.org/S2485147958","display_name":"Journal of Computational Design and Engineering","issn_l":"2288-4300","issn":["2288-4300","2288-5048"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Design and Engineering","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6499999761581421}],"awards":[{"id":"https://openalex.org/G216304052","display_name":null,"funder_award_id":"RGPIN-2018-05971","funder_id":"https://openalex.org/F4320335793","funder_display_name":"Academic Excellence Foundation of BUAA for PHD Students"},{"id":"https://openalex.org/G4275895383","display_name":null,"funder_award_id":"201806020095","funder_id":"https://openalex.org/F4320335793","funder_display_name":"Academic Excellence Foundation of BUAA for PHD Students"},{"id":"https://openalex.org/G7345722713","display_name":null,"funder_award_id":"JCKY2018203A001","funder_id":"https://openalex.org/F4320335793","funder_display_name":"Academic Excellence Foundation of BUAA for PHD Students"}],"funders":[{"id":"https://openalex.org/F4320335793","display_name":"Academic Excellence Foundation of BUAA for PHD Students","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1820253700","https://openalex.org/W1903329854","https://openalex.org/W1965299016","https://openalex.org/W1967607445","https://openalex.org/W1977237800","https://openalex.org/W1977758817","https://openalex.org/W2003994872","https://openalex.org/W2014168314","https://openalex.org/W2026386605","https://openalex.org/W2035698832","https://openalex.org/W2038113037","https://openalex.org/W2039210839","https://openalex.org/W2051109672","https://openalex.org/W2056696017","https://openalex.org/W2061024511","https://openalex.org/W2068668671","https://openalex.org/W2073623435","https://openalex.org/W2084398066","https://openalex.org/W2088298833","https://openalex.org/W2153483491","https://openalex.org/W2337047629","https://openalex.org/W2528461507","https://openalex.org/W2560639189","https://openalex.org/W2562977032","https://openalex.org/W2781986319","https://openalex.org/W2782571233","https://openalex.org/W2783747068","https://openalex.org/W2790305286","https://openalex.org/W2790615739","https://openalex.org/W2792943514","https://openalex.org/W2819724056","https://openalex.org/W2859081733","https://openalex.org/W2898661567","https://openalex.org/W2903620338","https://openalex.org/W2908892937","https://openalex.org/W2943663204","https://openalex.org/W2944945533","https://openalex.org/W2945600671","https://openalex.org/W2946150985","https://openalex.org/W2946351433","https://openalex.org/W3009715745","https://openalex.org/W3014566476","https://openalex.org/W3015334581","https://openalex.org/W3015949216","https://openalex.org/W3023483281","https://openalex.org/W3037751387","https://openalex.org/W3125305940","https://openalex.org/W3129074108","https://openalex.org/W3136900496","https://openalex.org/W3163461862","https://openalex.org/W3165018672","https://openalex.org/W3168197740","https://openalex.org/W3171172264","https://openalex.org/W3201884713","https://openalex.org/W6770546891"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2385717644","https://openalex.org/W2383262592","https://openalex.org/W2394071366","https://openalex.org/W2265330654","https://openalex.org/W2349276566","https://openalex.org/W2373674951","https://openalex.org/W2367912026","https://openalex.org/W2357333691","https://openalex.org/W2389139698"],"abstract_inverted_index":{"ABSTRACT":[0],"With":[1],"the":[2,6,12,18,30,33,40,56,60,128,138],"rapid":[3],"advancement":[4],"of":[5,43,62,99,127],"multimaterial":[7,34,132],"additive":[8],"manufacturing":[9],"(AM)":[10],"technology,":[11,64],"heterogeneous":[13],"lattice":[14],"structures":[15],"(HLSs)":[16],"comprising":[17],"multiphase":[19],"materials":[20],"with":[21,73,131],"gradual":[22],"variations":[23],"have":[24,37],"become":[25],"feasible":[26],"and":[27,48,76,83,92,121],"accessible":[28],"to":[29,46,114],"industry.":[31],"However,":[32],"AM":[35,63],"capabilities":[36],"far":[38],"outpaced":[39],"modeling":[41,71,82,85],"capability":[42],"design":[44,50,57],"systems":[45],"model":[47],"thus":[49],"novel":[51],"HLSs.":[52],"To":[53],"further":[54],"expand":[55],"space":[58],"for":[59,70],"utilization":[61],"this":[65],"paper":[66],"proposes":[67],"a":[68,90,105,148],"method":[69],"HLS":[72,100,116],"complex":[74],"geometries":[75],"smooth":[77,124],"material":[78,84,118,125,140],"transitions.":[79],"The":[80,96,123],"geometric":[81,97],"problems":[86],"are":[87,134],"formulated":[88],"in":[89],"rigorous":[91],"computationally":[93],"effective":[94],"manner.":[95],"complexity":[98],"is":[101,112],"significantly":[102],"reduced":[103],"by":[104,136],"semi-analytical":[106],"unit":[107],"cell":[108],"decomposition":[109],"strategy":[110],"that":[111],"applied":[113],"split":[115],"into":[117],"units:":[119],"struts":[120,133],"connectors.":[122],"transitions":[126],"connector":[129],"associated":[130],"realized":[135],"interpolating":[137],"discrete":[139],"property":[141],"values":[142],"defined":[143],"at":[144],"control":[145],"points":[146],"using":[147],"multiquadric":[149],"radial":[150],"basis":[151],"function":[152],"network.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3}],"updated_date":"2026-06-18T08:10:14.011955","created_date":"2025-10-10T00:00:00"}
