{"id":"https://openalex.org/W1995233963","doi":"https://doi.org/10.1145/1236246.1236272","title":"Level set based method for simultaneous optimization of material property and topology of functionally graded structures","display_name":"Level set based method for simultaneous optimization of material property and topology of functionally graded structures","publication_year":2007,"publication_date":"2007-06-04","ids":{"openalex":"https://openalex.org/W1995233963","doi":"https://doi.org/10.1145/1236246.1236272","mag":"1995233963"},"language":"en","primary_location":{"id":"doi:10.1145/1236246.1236272","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1236246.1236272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 ACM symposium on Solid and physical modeling","raw_type":"proceedings-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/A5101579221","display_name":"Qi Xia","orcid":"https://orcid.org/0000-0002-6489-6622"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Xia","raw_affiliation_strings":["The Chinese University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003737045","display_name":"Michael Y. Wang","orcid":"https://orcid.org/0000-0002-8981-6385"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Michael Y. Wang","raw_affiliation_strings":["The Chinese University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101579221"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18825152,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"171","last_page":"182"},"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":0.9991999864578247,"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/T10514","display_name":"Numerical methods in engineering","score":0.9957000017166138,"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":0.908836841583252},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5724737644195557},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5377159118652344},{"id":"https://openalex.org/keywords/level-set-method","display_name":"Level set method","score":0.5359027981758118},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5161107778549194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4925125539302826},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.48042774200439453},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.4762416183948517},{"id":"https://openalex.org/keywords/level-set","display_name":"Level set (data structures)","score":0.4279364049434662},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.42397546768188477},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41221195459365845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3644426167011261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35862019658088684},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2441047728061676},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22987255454063416},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10414391756057739},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.07983699440956116},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.07774853706359863}],"concepts":[{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.908836841583252},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5724737644195557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5377159118652344},{"id":"https://openalex.org/C125269122","wikidata":"https://www.wikidata.org/wiki/Q1751397","display_name":"Level set method","level":4,"score":0.5359027981758118},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5161107778549194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4925125539302826},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.48042774200439453},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4762416183948517},{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.4279364049434662},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42397546768188477},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41221195459365845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3644426167011261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35862019658088684},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2441047728061676},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22987255454063416},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10414391756057739},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.07983699440956116},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.07774853706359863},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1236246.1236272","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1236246.1236272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 ACM symposium on Solid and physical modeling","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.560.434","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.560.434","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.mae.cuhk.edu.hk/~cmdl/publications/conference/LS_SPM07.pdf","raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-74430","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-74430","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W168874853","https://openalex.org/W580896045","https://openalex.org/W583033002","https://openalex.org/W622265174","https://openalex.org/W1495295109","https://openalex.org/W1516100775","https://openalex.org/W1560055494","https://openalex.org/W1573886828","https://openalex.org/W1575923498","https://openalex.org/W1584280986","https://openalex.org/W1973067660","https://openalex.org/W1973282871","https://openalex.org/W1973481688","https://openalex.org/W1977758817","https://openalex.org/W1982739078","https://openalex.org/W1984061339","https://openalex.org/W1991113069","https://openalex.org/W1993120441","https://openalex.org/W1995928937","https://openalex.org/W1997200257","https://openalex.org/W1999480622","https://openalex.org/W2004464467","https://openalex.org/W2004679400","https://openalex.org/W2007759888","https://openalex.org/W2016413885","https://openalex.org/W2019879822","https://openalex.org/W2024978924","https://openalex.org/W2037649436","https://openalex.org/W2038642345","https://openalex.org/W2039749563","https://openalex.org/W2045618004","https://openalex.org/W2052185199","https://openalex.org/W2054143712","https://openalex.org/W2061333207","https://openalex.org/W2068256610","https://openalex.org/W2068668671","https://openalex.org/W2068669955","https://openalex.org/W2069697210","https://openalex.org/W2079578802","https://openalex.org/W2080379317","https://openalex.org/W2084002682","https://openalex.org/W2086620292","https://openalex.org/W2086674516","https://openalex.org/W2092801729","https://openalex.org/W2093834886","https://openalex.org/W2095529928","https://openalex.org/W2101560656","https://openalex.org/W2103648137","https://openalex.org/W2107271019","https://openalex.org/W2108142674","https://openalex.org/W2118555989","https://openalex.org/W2122535308","https://openalex.org/W2132034927","https://openalex.org/W2137726847","https://openalex.org/W2142136198","https://openalex.org/W2144598163","https://openalex.org/W2148395215","https://openalex.org/W2151964378","https://openalex.org/W2155897712","https://openalex.org/W2160231337","https://openalex.org/W2165734775","https://openalex.org/W2181453853","https://openalex.org/W2491281109","https://openalex.org/W3010292040","https://openalex.org/W3023562175","https://openalex.org/W3029645440","https://openalex.org/W3042462629","https://openalex.org/W4235666583","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2367921179","https://openalex.org/W2707457586","https://openalex.org/W2354244208","https://openalex.org/W3080476861","https://openalex.org/W657288383","https://openalex.org/W2084173031","https://openalex.org/W2539716919","https://openalex.org/W2565276936","https://openalex.org/W2032697618","https://openalex.org/W2790144624"],"abstract_inverted_index":{"A":[0],"level":[1,76],"set":[2,77],"based":[3],"method":[4,49],"is":[5,21,96,106],"proposed":[6,48],"for":[7,126],"simultaneous":[8,81],"optimization":[9,104,132],"of":[10,15,39,129],"material":[11,26,29],"property":[12,27],"and":[13,32,52,69,117],"topology":[14,34],"functionally":[16],"graded":[17],"structures.":[18],"The":[19,103],"objective":[20,92],"to":[22,35,98,112],"determine":[23],"the":[24,37,40,47,61,70,83,100,110,127],"optimal":[25],"(via":[28],"volume":[30,50],"fraction)":[31],"structural":[33,53],"maximize":[36],"performance":[38],"structure":[41],"in":[42,133],"a":[43,66,90,113],"given":[44],"application.":[45],"In":[46],"fraction":[51],"boundary":[54],"are":[55,87,124],"considered":[56],"as":[57,65,109],"design":[58,85],"variables,":[59],"with":[60],"former":[62],"being":[63,72],"discretized":[64],"scaler":[67],"field":[68],"latter":[71],"implicitly":[73],"represented":[74],"by":[75],"method.":[78],"To":[79],"perform":[80],"optimization,":[82],"two":[84,134],"variables":[86],"integrated":[88],"into":[89],"common":[91],"functional.":[93],"Sensitivity":[94],"analysis":[95],"conducted":[97],"obtain":[99],"descent":[101],"directions.":[102],"process":[105],"then":[107],"expressed":[108],"solution":[111],"coupled":[114],"Hamilton-Jacobi":[115],"equation":[116],"diffusion":[118],"partial":[119],"differential":[120],"equation.":[121],"Numerical":[122],"results":[123],"provided":[125],"problem":[128],"mean":[130],"compliance":[131],"dimensions.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
