{"id":"https://openalex.org/W2082265270","doi":"https://doi.org/10.1177/1045389x04043944","title":"Topology Optimization of Smart Structures Using a Homogenization Approach","display_name":"Topology Optimization of Smart Structures Using a Homogenization Approach","publication_year":2004,"publication_date":"2004-08-01","ids":{"openalex":"https://openalex.org/W2082265270","doi":"https://doi.org/10.1177/1045389x04043944","mag":"2082265270"},"language":"en","primary_location":{"id":"doi:10.1177/1045389x04043944","doi":"https://doi.org/10.1177/1045389x04043944","is_oa":false,"landing_page_url":"https://doi.org/10.1177/1045389x04043944","pdf_url":null,"source":{"id":"https://openalex.org/S45331193","display_name":"Journal of Intelligent Material Systems and Structures","issn_l":"1045-389X","issn":["1045-389X","1530-8138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Material Systems and Structures","raw_type":"journal-article"},"volume":null,"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/A5011504360","display_name":"Markus J. Buehler","orcid":"https://orcid.org/0000-0002-4173-9659","observed_orcids":["https://orcid.org/0000-0002-4173-9659"]},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Markus J. Buehler","raw_affiliation_strings":["Department of Mechanical Engineering \u2014 Engineering Mechanics,                         Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering \u2014 Engineering Mechanics,                         Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA","institution_ids":["https://openalex.org/I11957088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109105236","display_name":"Bernhard P. Bettig","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bernhard Bettig","raw_affiliation_strings":["Department of Mechanical Engineering \u2014 Engineering Mechanics,                         Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931,                         USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering \u2014 Engineering Mechanics,                         Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931,                         USA,","institution_ids":["https://openalex.org/I11957088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068242131","display_name":"Gordon G. Parker","orcid":"https://orcid.org/0000-0001-8503-6624","observed_orcids":["https://orcid.org/0000-0001-8503-6624"]},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gordon G. Parker","raw_affiliation_strings":["Department of Mechanical Engineering \u2014 Engineering Mechanics,                         Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering \u2014 Engineering Mechanics,                         Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA","institution_ids":["https://openalex.org/I11957088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I11957088"],"apc_list":{"value":4150,"currency":"USD","value_usd":4150},"apc_paid":null,"fwci":14.4909,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.98512389,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"15","issue":"8","first_page":"655","last_page":"667"},"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/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"}},{"id":"https://openalex.org/T10707","display_name":"Cellular and Composite Structures","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topology-optimization","display_name":"topology optimization","score":1.0},{"id":"https://openalex.org/keywords/smart-structures","display_name":"smart structures","score":0.8759999871253967},{"id":"https://openalex.org/keywords/piezoelectric-materials","display_name":"piezoelectric materials","score":0.9110000133514404},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.9860000014305115},{"id":"https://openalex.org/keywords/microstructure","display_name":"microstructure","score":0.6869999766349792},{"id":"https://openalex.org/keywords/effective-properties","display_name":"effective properties","score":0.8629999756813049},{"id":"https://openalex.org/keywords/material-distribution","display_name":"material distribution","score":0.5070000290870667},{"id":"https://openalex.org/keywords/parameter-optimization","display_name":"parameter optimization","score":0.6169999837875366},{"id":"https://openalex.org/keywords/piezoelectric-actuation","display_name":"piezoelectric actuation","score":0.7329999804496765}],"concepts":[{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.8997888565063477},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8191480040550232},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5678622126579285},{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.5326476097106934},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.48140549659729004},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4578624367713928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.450175017118454},{"id":"https://openalex.org/C31555180","wikidata":"https://www.wikidata.org/wiki/Q3523867","display_name":"Material properties","level":2,"score":0.4372618794441223},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.42549076676368713},{"id":"https://openalex.org/C2777152284","wikidata":"https://www.wikidata.org/wiki/Q17590603","display_name":"Material Design","level":2,"score":0.4190906286239624},{"id":"https://openalex.org/C88484716","wikidata":"https://www.wikidata.org/wiki/Q1474679","display_name":"Smart material","level":2,"score":0.41496068239212036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3462299704551697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32149454951286316},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.30358320474624634},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.24718192219734192},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.2139166295528412},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18634694814682007},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1177/1045389x04043944","doi":"https://doi.org/10.1177/1045389x04043944","is_oa":false,"landing_page_url":"https://doi.org/10.1177/1045389x04043944","pdf_url":null,"source":{"id":"https://openalex.org/S45331193","display_name":"Journal of Intelligent Material Systems and Structures","issn_l":"1045-389X","issn":["1045-389X","1530-8138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Material Systems and Structures","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p-3549","doi":null,"is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/2559","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.7207000255584717,"id":"https://metadata.un.org/sdg/9"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1545574955","https://openalex.org/W1547249381","https://openalex.org/W1562512484","https://openalex.org/W1972073233","https://openalex.org/W1978778091","https://openalex.org/W2025259063","https://openalex.org/W2027068156","https://openalex.org/W2031605731","https://openalex.org/W2044571399","https://openalex.org/W2051437557","https://openalex.org/W2052028690","https://openalex.org/W2059077275","https://openalex.org/W2069697210","https://openalex.org/W2073929471","https://openalex.org/W2086620292","https://openalex.org/W2088873153","https://openalex.org/W2092801729","https://openalex.org/W2100804804","https://openalex.org/W2137726847","https://openalex.org/W2141089045","https://openalex.org/W2144502729","https://openalex.org/W2149034424","https://openalex.org/W2149192791","https://openalex.org/W2151683826","https://openalex.org/W2163262826","https://openalex.org/W2170657165","https://openalex.org/W2886594745","https://openalex.org/W4235666583","https://openalex.org/W4300943935"],"related_works":["https://openalex.org/W2025259063","https://openalex.org/W2052028690","https://openalex.org/W2035418108","https://openalex.org/W2283411454","https://openalex.org/W1966344424","https://openalex.org/W2151683826","https://openalex.org/W4404930872","https://openalex.org/W4390849643","https://openalex.org/W4399696918","https://openalex.org/W7223192972"],"abstract_inverted_index":{"Engineers":[0],"are":[1,171],"often":[2],"required":[3],"to":[4,8,132,152,173,180],"design":[5,39,109],"mechanical":[6],"structures":[7,182],"meet":[9],"specific":[10],"loading":[11],"conditions.":[12],"Topology":[13],"optimization":[14,56,83,145],"automates":[15],"the":[16,55,60,68,75,78,81,99,108,112,117,134,160,175,178,185,191],"process":[17],"of":[18,35,62,70,80,88,98,119,136,163,177],"finding":[19,137],"an":[20,41,138,164],"optimal":[21,42,139],"structural":[22],"design,":[23],"allowing":[24],"for":[25,159],"size,":[26],"shape,":[27],"and":[28,38,106,154],"topology":[29,82],"variations.":[30],"For":[31],"a":[32,48,85,103,143,188],"given":[33],"set":[34],"boundary":[36],"conditions":[37],"specifications,":[40],"structure":[43],"is":[44,95,114,150,194],"computed,":[45],"based":[46],"on":[47],"formulated":[49],"cost":[50],"function.":[51],"In":[52,77],"this":[53],"paper,":[54],"considers":[57],"not":[58],"only":[59],"distribution":[61,69,141],"conventional":[63,93],"material,":[64],"but":[65],"also":[66],"simultaneously":[67],"active":[71],"piezoelectric":[72,192],"material":[73,94,121,140,157,193],"within":[74],"domain.":[76,110],"formulation":[79],"problem,":[84],"microstructure":[86,100,113],"consisting":[87],"smart":[89],"as":[90,92,142],"well":[91],"used.":[96],"Instances":[97],"occur":[101],"in":[102],"rectangular":[104],"grid":[105],"cover":[107],"Since":[111],"defined":[115],"parametrically,":[116],"density":[118],"each":[120,127],"can":[122],"be":[123],"controlled":[124],"individually":[125],"at":[126,187],"point.":[128],"This":[129],"enables":[130],"us":[131],"formulate":[133],"problem":[135],"parameter":[144],"problem.":[146],"A":[147],"homogenization":[148],"approach":[149],"used":[151],"find":[153,181],"use":[155],"effective":[156],"properties":[158],"limiting":[161],"case":[162],"infinitely":[165],"small":[166],"microstructure.":[167],"Several":[168],"numerical":[169],"examples":[170],"provided":[172],"demonstrate":[174],"application":[176],"method":[179],"that":[183],"maximize":[184],"deflection":[186],"point":[189],"when":[190],"activated.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}
