{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/24071"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/24071","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Minmax topology optimization","abstract":"We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst-case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well-posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm.","abstract_html":"We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst-case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well-posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm.","abstract_has_math":false,"creators":["Brittain, Kevin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Tortorelli, Daniel A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-25T14:59:51Z","date_published":"2011-05-25T14:59:51Z","updated_at":"2026-07-22T22:25:23Z","subjects":["Topology Optimization","Homogenization","Robust Design"],"languages":["en"],"rights":["Copyright 2011 by Kevin Brittain"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/24071","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Tortorelli, Daniel A."]},{"key":"dc:creator","label":"Author","values":["Brittain, Kevin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-25T14:59:51Z","2011-05"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Topology Optimization","Homogenization","Robust Design"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2011 by Kevin Brittain"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/24071"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst-case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well-posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-04-27T21:07:20Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Brittain_Kevin.pdf: 637625 bytes, checksum: 68ae8353ae33e304e7e6e7f1e8332b23 (MD5)","Made available in DSpace on 2011-05-25T14:59:51Z (GMT). No. of bitstreams: 2 Brittain_Kevin.pdf: 637625 bytes, checksum: 68ae8353ae33e304e7e6e7f1e8332b23 (MD5) license.txt: 4064 bytes, checksum: 6bbbabf6fc5b776c38d28fe49384fc88 (MD5)"]},{"key":"dc:title","label":"Title","values":["Minmax topology optimization"]}]}],"canonical_facts":{"dc:contributor":["Tortorelli, Daniel A."],"dc:creator":["Brittain, Kevin"],"dc:date":["2011-05-25T14:59:51Z","2011-05"],"dc:description":["We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst-case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well-posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-04-27T21:07:20Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Brittain_Kevin.pdf: 637625 bytes, checksum: 68ae8353ae33e304e7e6e7f1e8332b23 (MD5)","Made available in DSpace on 2011-05-25T14:59:51Z (GMT). No. of bitstreams: 2 Brittain_Kevin.pdf: 637625 bytes, checksum: 68ae8353ae33e304e7e6e7f1e8332b23 (MD5) license.txt: 4064 bytes, checksum: 6bbbabf6fc5b776c38d28fe49384fc88 (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/24071"],"dc:language":["en"],"dc:rights":["Copyright 2011 by Kevin Brittain"],"dc:subject":["Topology Optimization","Homogenization","Robust Design"],"dc:title":["Minmax topology optimization"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:23Z"}