{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/89080"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/89080","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Free form finding of grid shell structures","abstract":"The general shape of a shell structure can have a great impact on its structural performance. This thesis presents a numerical implementation that finds the funicular form of grid shell structures. Two methods are implemented for the form finding: the potential energy method (PEM) and the force density method (FDM). The PEM, inspired by the 3D hanging chain model, find the funicular form by minimization of the total potential energy. On the other hand, the FDM find the funicular form by solving a linear system, in which a geometric stiffness matrix is constructed with the force density and nodal connectivity information. The form finding process is nonlinear, because the nodal loads are calculated with the rationale of tributary area and evolve with the structural form. Apart from the form finding, a member sizing procedure is implemented for a preliminary estimation of the member cross sectional area. In the member sizing, the stress-ratio method is used to achieve a fully-stressed design. Finally, three numerical examples are examined to demonstrate the effectiveness of the current implementation.","abstract_html":"The general shape of a shell structure can have a great impact on its structural performance. This thesis presents a numerical implementation that finds the funicular form of grid shell structures. Two methods are implemented for the form finding: the potential energy method (PEM) and the force density method (FDM). The PEM, inspired by the 3D hanging chain model, find the funicular form by minimization of the total potential energy. On the other hand, the FDM find the funicular form by solving a linear system, in which a geometric stiffness matrix is constructed with the force density and nodal connectivity information. The form finding process is nonlinear, because the nodal loads are calculated with the rationale of tributary area and evolve with the structural form. Apart from the form finding, a member sizing procedure is implemented for a preliminary estimation of the member cross sectional area. In the member sizing, the stress-ratio method is used to achieve a fully-stressed design. Finally, three numerical examples are examined to demonstrate the effectiveness of the current implementation.","abstract_has_math":false,"creators":["Jiang, Yang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Paulino, Glaucio H"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-03-02T19:45:04Z","date_published":"2016-03-02T19:45:04Z","updated_at":"2026-07-22T22:26:32Z","subjects":["Form Finding","Grid Shell"],"languages":["en"],"rights":["Copyright 2015 Yang Jiang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/89080","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Paulino, Glaucio H"]},{"key":"dc:creator","label":"Author","values":["Jiang, Yang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-03-02T19:45:04Z","2015-12-11","2015-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil 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":["Form Finding","Grid Shell"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Yang Jiang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/89080"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The general shape of a shell structure can have a great impact on its structural performance. This thesis presents a numerical implementation that finds the funicular form of grid shell structures. Two methods are implemented for the form finding: the potential energy method (PEM) and the force density method (FDM). The PEM, inspired by the 3D hanging chain model, find the funicular form by minimization of the total potential energy. On the other hand, the FDM find the funicular form by solving a linear system, in which a geometric stiffness matrix is constructed with the force density and nodal connectivity information. The form finding process is nonlinear, because the nodal loads are calculated with the rationale of tributary area and evolve with the structural form. Apart from the form finding, a member sizing procedure is implemented for a preliminary estimation of the member cross sectional area. In the member sizing, the stress-ratio method is used to achieve a fully-stressed design. Finally, three numerical examples are examined to demonstrate the effectiveness of the current implementation.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-03-02 without embargo terms","The student, Yang Jiang, accepted the attached license on 2015-12-10 at 19:51.","The student, Yang Jiang, submitted this Thesis for approval on 2015-12-11 at 16:05.","This Thesis was approved for publication on 2015-12-11 at 16:29.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8982 on 2016-03-02 at 12:52:59","Made available in DSpace on 2016-03-02T19:45:04Z (GMT). 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Two methods are implemented for the form finding: the potential energy method (PEM) and the force density method (FDM). The PEM, inspired by the 3D hanging chain model, find the funicular form by minimization of the total potential energy. On the other hand, the FDM find the funicular form by solving a linear system, in which a geometric stiffness matrix is constructed with the force density and nodal connectivity information. The form finding process is nonlinear, because the nodal loads are calculated with the rationale of tributary area and evolve with the structural form. Apart from the form finding, a member sizing procedure is implemented for a preliminary estimation of the member cross sectional area. In the member sizing, the stress-ratio method is used to achieve a fully-stressed design. Finally, three numerical examples are examined to demonstrate the effectiveness of the current implementation.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-03-02 without embargo terms","The student, Yang Jiang, accepted the attached license on 2015-12-10 at 19:51.","The student, Yang Jiang, submitted this Thesis for approval on 2015-12-11 at 16:05.","This Thesis was approved for publication on 2015-12-11 at 16:29.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8982 on 2016-03-02 at 12:52:59","Made available in DSpace on 2016-03-02T19:45:04Z (GMT). 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