{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71682"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71682","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Large Deflections of Structures With Small Elastic Strains (Nonlinear, Rotations)","abstract":"A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending of a beam by end loads and by its own weight, and to the bending of a long rectangular plate and of a circular plate by uniform pressure. The theory provides solutions for geometries between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff's theory for rods and the von Karman equations for plates, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior. For the plate problems considered the von Karman equations are found to provide accurate results for thin plates for which deflections are not small.","abstract_html":"A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending of a beam by end loads and by its own weight, and to the bending of a long rectangular plate and of a circular plate by uniform pressure. The theory provides solutions for geometries between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff's theory for rods and the von Karman equations for plates, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior. For the plate problems considered the von Karman equations are found to provide accurate results for thin plates for which deflections are not small.","abstract_has_math":false,"creators":["Im, Seyoung"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T19:12:32Z","date_published":"2014-12-16T19:12:32Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Applied Mechanics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8600216"],"render_values":[{"text":"(UMI)AAI8600216","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71682","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Im, Seyoung"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T19:12:32Z","10000-01-01","1985"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"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/2142/71682","(UMI)AAI8600216"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending of a beam by end loads and by its own weight, and to the bending of a long rectangular plate and of a circular plate by uniform pressure. The theory provides solutions for geometries between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff's theory for rods and the von Karman equations for plates, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior. For the plate problems considered the von Karman equations are found to provide accurate results for thin plates for which deflections are not small.","Made available in DSpace on 2014-12-16T19:12:32Z (GMT). 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The theory provides solutions for geometries between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff's theory for rods and the von Karman equations for plates, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior. For the plate problems considered the von Karman equations are found to provide accurate results for thin plates for which deflections are not small.","Made available in DSpace on 2014-12-16T19:12:32Z (GMT). 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