{"id":"https://openalex.org/W1509166644","doi":"https://doi.org/10.1007/978-3-0348-0133-1_12","title":"On Shape Optimization with Stochastic Loadings","display_name":"On Shape Optimization with Stochastic Loadings","publication_year":2011,"publication_date":"2011-10-28","ids":{"openalex":"https://openalex.org/W1509166644","doi":"https://doi.org/10.1007/978-3-0348-0133-1_12","mag":"1509166644"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-0348-0133-1_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-0348-0133-1_12","pdf_url":null,"source":{"id":"https://openalex.org/S4210197284","display_name":"International series of numerical mathematics","issn_l":"0373-3149","issn":["0373-3149","2296-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Series of Numerical Mathematics","raw_type":"book-chapter"},"type":"book-chapter","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/A5004152243","display_name":"Pradeep Atwal","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Pradeep Atwal","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","Universit\u00e4t Bonn >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Universit\u00e4t Bonn >  >  >  >","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086193278","display_name":"Sergio Conti","orcid":"https://orcid.org/0000-0001-7987-9174"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sergio Conti","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","Universit\u00e4t Bonn >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Universit\u00e4t Bonn >  >  >  >","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048607744","display_name":"Benedict Geihe","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Benedict Geihe","raw_affiliation_strings":["Institut f\u00fcr Numerische Simulation, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","Universit\u00e4t Bonn >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Numerische Simulation, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Universit\u00e4t Bonn >  >  >  >","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009421805","display_name":"Martin Pach","orcid":null},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Pach","raw_affiliation_strings":["Martin Pach and R\u00fcdiger Schultz Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Duisburg-Essen, Forsthausweg 2, D-47057, Duisburg, Germany","Universitat Duisburg-Essen,"],"affiliations":[{"raw_affiliation_string":"Martin Pach and R\u00fcdiger Schultz Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Duisburg-Essen, Forsthausweg 2, D-47057, Duisburg, Germany","institution_ids":["https://openalex.org/I62318514"]},{"raw_affiliation_string":"Universitat Duisburg-Essen,","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063603168","display_name":"Martin Rumpf","orcid":"https://orcid.org/0000-0001-6049-9390"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Rumpf","raw_affiliation_strings":["Institut f\u00fcr Numerische Simulation, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","Universit\u00e4t Bonn >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Numerische Simulation, Universit\u00e4t Bonn, Endenicher Allee 60, D-53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Universit\u00e4t Bonn >  >  >  >","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021741090","display_name":"R\u00fcdiger Schultz","orcid":null},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"R\u00fcdiger Schultz","raw_affiliation_strings":["Martin Pach and R\u00fcdiger Schultz Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Duisburg-Essen, Forsthausweg 2, D-47057, Duisburg, Germany","Universitat Duisburg-Essen,"],"affiliations":[{"raw_affiliation_string":"Martin Pach and R\u00fcdiger Schultz Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Duisburg-Essen, Forsthausweg 2, D-47057, Duisburg, Germany","institution_ids":["https://openalex.org/I62318514"]},{"raw_affiliation_string":"Universitat Duisburg-Essen,","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5004152243"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":1.7065,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84208004,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"215","last_page":"243"},"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.6065687537193298},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5769519209861755},{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.5369541049003601},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.5362640619277954},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.529136061668396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5186649560928345},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.47975385189056396},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.47487756609916687},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45164722204208374},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45100322365760803},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.44103744626045227},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4346487522125244},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.43440741300582886},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38432934880256653},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3417704105377197},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3376848101615906},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22628751397132874},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14852610230445862},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.07815158367156982}],"concepts":[{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.6065687537193298},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5769519209861755},{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.5369541049003601},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.5362640619277954},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.529136061668396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5186649560928345},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.47975385189056396},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.47487756609916687},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45164722204208374},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45100322365760803},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.44103744626045227},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4346487522125244},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.43440741300582886},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38432934880256653},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3417704105377197},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3376848101615906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22628751397132874},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14852610230445862},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.07815158367156982},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-0348-0133-1_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-0348-0133-1_12","pdf_url":null,"source":{"id":"https://openalex.org/S4210197284","display_name":"International series of numerical mathematics","issn_l":"0373-3149","issn":["0373-3149","2296-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Series of Numerical Mathematics","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.228.4646","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.228.4646","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://numod.ins.uni-bonn.de/research/papers/public/AtCoGe10.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W21432690","https://openalex.org/W65479554","https://openalex.org/W158123262","https://openalex.org/W178344362","https://openalex.org/W229300124","https://openalex.org/W1494466405","https://openalex.org/W1540846857","https://openalex.org/W1554045033","https://openalex.org/W1567262822","https://openalex.org/W1584280986","https://openalex.org/W1963682553","https://openalex.org/W1964022794","https://openalex.org/W1966268934","https://openalex.org/W1967849536","https://openalex.org/W1976330321","https://openalex.org/W1979905552","https://openalex.org/W1982739078","https://openalex.org/W1994133356","https://openalex.org/W1995067704","https://openalex.org/W1995878217","https://openalex.org/W2000388899","https://openalex.org/W2003130132","https://openalex.org/W2003738530","https://openalex.org/W2004110058","https://openalex.org/W2016413885","https://openalex.org/W2026500470","https://openalex.org/W2029881990","https://openalex.org/W2037004190","https://openalex.org/W2038572388","https://openalex.org/W2042016018","https://openalex.org/W2042507437","https://openalex.org/W2048546972","https://openalex.org/W2058456766","https://openalex.org/W2060709740","https://openalex.org/W2065668980","https://openalex.org/W2068668671","https://openalex.org/W2080417806","https://openalex.org/W2085262565","https://openalex.org/W2085740870","https://openalex.org/W2086948940","https://openalex.org/W2094251381","https://openalex.org/W2097641368","https://openalex.org/W2101712703","https://openalex.org/W2104232537","https://openalex.org/W2112305902","https://openalex.org/W2123871098","https://openalex.org/W2129412583","https://openalex.org/W2135301926","https://openalex.org/W2135397228","https://openalex.org/W2137439317","https://openalex.org/W2139513792","https://openalex.org/W2167407723","https://openalex.org/W2885749508","https://openalex.org/W3142828186","https://openalex.org/W3143969212","https://openalex.org/W3145997355","https://openalex.org/W3214283411","https://openalex.org/W4230378860","https://openalex.org/W4241610645","https://openalex.org/W4247165901","https://openalex.org/W4251616545","https://openalex.org/W4293183906","https://openalex.org/W4300599381","https://openalex.org/W4302609762","https://openalex.org/W6603867535"],"related_works":["https://openalex.org/W1871620607","https://openalex.org/W2171553724","https://openalex.org/W596237000","https://openalex.org/W4283738289","https://openalex.org/W4293570283","https://openalex.org/W2059051965","https://openalex.org/W2343967215","https://openalex.org/W2913526350","https://openalex.org/W1509166644","https://openalex.org/W4213227513"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
