{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/104125"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/104125","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A strain tensor method for three-dimensional optimal Michell structures","abstract":"In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by A.G.M. Michell (1904) and has been mostly used for two-dimensional structures so far. This thesis develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- dimensional cases.","abstract_html":"In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by A.G.M. Michell (1904) and has been mostly used for two-dimensional structures so far. This thesis develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- dimensional cases.","abstract_has_math":false,"creators":["Jacot, Benjamin (Benjamin Paul Emmanuel)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Civil and Environmental Engineering.","school":null,"contributors":[],"advisors":["Caitlin T. Mueller."],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-22T22:21:49Z","subjects":["Civil and Environmental Engineering."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/104125","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Caitlin T. Mueller."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Civil and Environmental Engineering."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Department of Civil and Environmental Engineering."]},{"key":"dc:creator","label":"Author","values":["Jacot, Benjamin (Benjamin Paul Emmanuel)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-09-13T18:07:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-09-13T18:07:36Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Civil and Environmental Engineering."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/104125"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2016.","This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.","Cataloged from student-submitted PDF version of thesis.","Includes bibliographical references (pages 94-95)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by A.G.M. Michell (1904) and has been mostly used for two-dimensional structures so far. This thesis develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- dimensional cases."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M. Eng."]},{"key":"dc:title","label":"Title","values":["A strain tensor method for three-dimensional optimal Michell structures"]}]}],"canonical_facts":{"dc:contributor.advisor":["Caitlin T. Mueller."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Civil and Environmental Engineering."],"dc:contributor.other":["Massachusetts Institute of Technology. Department of Civil and Environmental Engineering."],"dc:creator":["Jacot, Benjamin (Benjamin Paul Emmanuel)"],"dc:date.accessioned":["2016-09-13T18:07:36Z"],"dc:date.available":["2016-09-13T18:07:36Z"],"dc:date.issued":["2016"],"dc:description":["Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2016.","This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.","Cataloged from student-submitted PDF version of thesis.","Includes bibliographical references (pages 94-95)."],"dc:description.abstract":["In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by A.G.M. Michell (1904) and has been mostly used for two-dimensional structures so far. This thesis develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- dimensional cases."],"dc:description.degree":["M. Eng."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/104125"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Civil and Environmental Engineering."],"dc:title":["A strain tensor method for three-dimensional optimal Michell structures"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:49Z"}