{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69944"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69944","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Symmetry, Bifurcation, and Computational Methods in Nonlinear Structural Mechanics (Buckling, Stability, Group)","abstract":"The computation of global (equilibrium) solution branches of one-parameter systems arising in nonlinear structural mechanics is considered in this work. Particular emphasis is given to systems possessing spatial symmetry and to the exploitation of that symmetry in computational schemes.","abstract_html":"The computation of global (equilibrium) solution branches of one-parameter systems arising in nonlinear structural mechanics is considered in this work. Particular emphasis is given to systems possessing spatial symmetry and to the exploitation of that symmetry in computational schemes.","abstract_has_math":false,"creators":["Healey, Timothy James"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T20:36:14Z","date_published":"2014-12-15T20:36:14Z","updated_at":"2026-07-22T22:26:01Z","subjects":["Applied Mechanics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8511616"],"render_values":[{"text":"(UMI)AAI8511616","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69944","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Healey, Timothy James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T20:36:14Z","10000-01-01","1985"]},{"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":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"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":["Applied Mechanics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69944","(UMI)AAI8511616"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The computation of global (equilibrium) solution branches of one-parameter systems arising in nonlinear structural mechanics is considered in this work. Particular emphasis is given to systems possessing spatial symmetry and to the exploitation of that symmetry in computational schemes.","Strategies for accurately locating and classifying singular points, and methods for continuation through limit points and bifurcation points are presented. The techniques allow for branch switching at simple and multiple bifurcation points.","The equilibrium equations of general nonlinearly elastic structures and solids possessing symmetry are shown to be covariant with respect to a specific set of linear transformations. These transformations form a group and are derived from the symmetry of the physical system. It is shown that the identification of covariance leads to a reduction in the original problem. Moreover, the group transformations can be used to generate new solution branches from known ones.","The analysis of a lattice dome under uniform loading is presented. The structure possesses symmetry, which is exploited in the group-theoretic reduction procedure. Considerable computational advantage results on combining the continuation methods with the group-theoretic techniques. Several global solution branches were computed and are illustrated. The structure possesses an almost bewildering array of equilibrium states, and the solution set is rich in singular points. The computations include continuation through a variety of singular points, and branch switching at simple and multiple bifurcation points.","Made available in DSpace on 2014-12-15T20:36:14Z (GMT). No. of bitstreams: 1 8511616.pdf: 7235860 bytes, checksum: 6422bc4e097e76aa46fd2c5f669f112b (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 70110 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","321 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."]},{"key":"dc:title","label":"Title","values":["Symmetry, Bifurcation, and Computational Methods in Nonlinear Structural Mechanics (Buckling, Stability, Group)"]}]}],"canonical_facts":{"dc:creator":["Healey, Timothy James"],"dc:date":["2014-12-15T20:36:14Z","10000-01-01","1985"],"dc:description":["The computation of global (equilibrium) solution branches of one-parameter systems arising in nonlinear structural mechanics is considered in this work. Particular emphasis is given to systems possessing spatial symmetry and to the exploitation of that symmetry in computational schemes.","Strategies for accurately locating and classifying singular points, and methods for continuation through limit points and bifurcation points are presented. The techniques allow for branch switching at simple and multiple bifurcation points.","The equilibrium equations of general nonlinearly elastic structures and solids possessing symmetry are shown to be covariant with respect to a specific set of linear transformations. These transformations form a group and are derived from the symmetry of the physical system. It is shown that the identification of covariance leads to a reduction in the original problem. Moreover, the group transformations can be used to generate new solution branches from known ones.","The analysis of a lattice dome under uniform loading is presented. The structure possesses symmetry, which is exploited in the group-theoretic reduction procedure. Considerable computational advantage results on combining the continuation methods with the group-theoretic techniques. Several global solution branches were computed and are illustrated. The structure possesses an almost bewildering array of equilibrium states, and the solution set is rich in singular points. The computations include continuation through a variety of singular points, and branch switching at simple and multiple bifurcation points.","Made available in DSpace on 2014-12-15T20:36:14Z (GMT). No. of bitstreams: 1 8511616.pdf: 7235860 bytes, checksum: 6422bc4e097e76aa46fd2c5f669f112b (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 70110 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","321 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."],"dc:identifier":["http://hdl.handle.net/2142/69944","(UMI)AAI8511616"],"dc:subject":["Applied Mechanics"],"dc:title":["Symmetry, Bifurcation, and Computational Methods in Nonlinear Structural Mechanics (Buckling, Stability, Group)"],"dc:type":["text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:01Z"}