{"id":"https://openalex.org/W2599520070","doi":"https://doi.org/10.1007/s00366-017-0503-4","title":"A meshless method for multi-material topology optimization based on the alternating active-phase algorithm","display_name":"A meshless method for multi-material topology optimization based on the alternating active-phase algorithm","publication_year":2017,"publication_date":"2017-03-15","ids":{"openalex":"https://openalex.org/W2599520070","doi":"https://doi.org/10.1007/s00366-017-0503-4","mag":"2599520070"},"language":"en","primary_location":{"id":"doi:10.1007/s00366-017-0503-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00366-017-0503-4","pdf_url":null,"source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050718842","display_name":"Mingtao Cui","orcid":"https://orcid.org/0000-0001-5909-3203"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]},{"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","CN"],"is_corresponding":true,"raw_author_name":"Mingtao Cui","raw_affiliation_strings":["Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 2K6, Canada","School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 2K6, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088172064","display_name":"Hongfang Chen","orcid":"https://orcid.org/0000-0001-9186-8814"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongfang Chen","raw_affiliation_strings":["School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110963432","display_name":"Jingling Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingling Zhou","raw_affiliation_strings":["School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070291373","display_name":"Fanglin Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanglin Wang","raw_affiliation_strings":["School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechano-electronic Engineering, Xidian University, Xi\u2019an, 710071, People\u2019s Republic of China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050718842"],"corresponding_institution_ids":["https://openalex.org/I149594827","https://openalex.org/I5023651"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.2446,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.85919114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"33","issue":"4","first_page":"871","last_page":"884"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9997000098228455,"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":0.9997000098228455,"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9984999895095825,"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/T11558","display_name":"Composite Material Mechanics","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.6765648126602173},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6318066120147705},{"id":"https://openalex.org/keywords/moving-least-squares","display_name":"Moving least squares","score":0.6030368208885193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.599499523639679},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5485884547233582},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5478236675262451},{"id":"https://openalex.org/keywords/regularized-meshless-method","display_name":"Regularized meshless method","score":0.5173808336257935},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5066836476325989},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4908497929573059},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.48351195454597473},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45741432905197144},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4425402879714966},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4381101429462433},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4368399977684021},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29037368297576904},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.15855249762535095},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.12189629673957825},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.10455110669136047}],"concepts":[{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.6765648126602173},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6318066120147705},{"id":"https://openalex.org/C2780580100","wikidata":"https://www.wikidata.org/wiki/Q6927143","display_name":"Moving least squares","level":2,"score":0.6030368208885193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.599499523639679},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5485884547233582},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5478236675262451},{"id":"https://openalex.org/C177562122","wikidata":"https://www.wikidata.org/wiki/Q7309629","display_name":"Regularized meshless method","level":5,"score":0.5173808336257935},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5066836476325989},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4908497929573059},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.48351195454597473},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45741432905197144},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4425402879714966},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4381101429462433},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4368399977684021},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29037368297576904},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.15855249762535095},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.12189629673957825},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.10455110669136047},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00366-017-0503-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00366-017-0503-4","pdf_url":null,"source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G210254373","display_name":null,"funder_award_id":"201506965015","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1575923498","https://openalex.org/W1967649517","https://openalex.org/W1979168015","https://openalex.org/W1995695068","https://openalex.org/W1997742472","https://openalex.org/W2004464467","https://openalex.org/W2004485777","https://openalex.org/W2011482492","https://openalex.org/W2016582483","https://openalex.org/W2018554548","https://openalex.org/W2020003164","https://openalex.org/W2032832285","https://openalex.org/W2047202559","https://openalex.org/W2054732436","https://openalex.org/W2066652988","https://openalex.org/W2069933136","https://openalex.org/W2075912492","https://openalex.org/W2080977367","https://openalex.org/W2088508142","https://openalex.org/W2090783970","https://openalex.org/W2113883281","https://openalex.org/W2122397978","https://openalex.org/W2132034927","https://openalex.org/W2139513792","https://openalex.org/W2141377530","https://openalex.org/W2142136198","https://openalex.org/W2145364658","https://openalex.org/W2146674345","https://openalex.org/W2147169375","https://openalex.org/W2153190576","https://openalex.org/W2162697234","https://openalex.org/W2165920433","https://openalex.org/W2166405181","https://openalex.org/W2167633747","https://openalex.org/W2168414272"],"related_works":["https://openalex.org/W2140171609","https://openalex.org/W2058788502","https://openalex.org/W2382079121","https://openalex.org/W2057265674","https://openalex.org/W1975248355","https://openalex.org/W1997562791","https://openalex.org/W1971899538","https://openalex.org/W2597348797","https://openalex.org/W2801875094","https://openalex.org/W2012062214"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}