{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/43286"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/43286","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"On the behavior of shear deformable plate elements","abstract":"An investigation of the behavior of shear deformable plate finite elements is conducted to determine why and under what conditions these elements lock, or become overly stiff. For this purpose, a new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side-tothickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and they are easily interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. Moreover, the technique is applicable to any displacement-based shear deformable beam, plate or shell element regardless of the shear deformation theory or the order of the Gauss-Legendre integration rule which is used to numerically evaluate the stiffness coefficients. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various Mindlin and Reddy-type beam and plate elements. These analytical findings are then compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behavior of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration.","abstract_html":"An investigation of the behavior of shear deformable plate finite elements is conducted to determine why and under what conditions these elements lock, or become overly stiff. For this purpose, a new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side-tothickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and they are easily interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. Moreover, the technique is applicable to any displacement-based shear deformable beam, plate or shell element regardless of the shear deformation theory or the order of the Gauss-Legendre integration rule which is used to numerically evaluate the stiffness coefficients. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various Mindlin and Reddy-type beam and plate elements. These analytical findings are then compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behavior of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration.","abstract_has_math":false,"creators":["Averill, Ronald C."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Reddy, Junuthula N."],"committee_members":["Griffin, Odis Hayden Jr.","Smith, Charles W."],"year":1989,"date_issued":"1989-07-05","date_published":"1989-07-05","updated_at":"2026-07-22T22:19:03Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06122010-020608"],"render_values":[{"text":"etd-06122010-020608","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/43286","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Reddy, Junuthula N."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Griffin, Odis Hayden Jr.","Smith, Charles W."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Averill, Ronald C."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:38:27Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:38:27Z","2010-06-12"]},{"key":"dc:date.issued","label":"Date","values":["1989-07-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06122010-020608"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/43286"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["An investigation of the behavior of shear deformable plate finite elements is conducted to determine why and under what conditions these elements lock, or become overly stiff. For this purpose, a new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side-tothickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and they are easily interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. Moreover, the technique is applicable to any displacement-based shear deformable beam, plate or shell element regardless of the shear deformation theory or the order of the Gauss-Legendre integration rule which is used to numerically evaluate the stiffness coefficients. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various Mindlin and Reddy-type beam and plate elements. These analytical findings are then compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behavior of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On the behavior of shear deformable plate elements"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Reddy, Junuthula N."],"dc:contributor.committeemember":["Griffin, Odis Hayden Jr.","Smith, Charles W."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Averill, Ronald C."],"dc:date.accessioned":["2014-03-14T21:38:27Z"],"dc:date.available":["2014-03-14T21:38:27Z","2010-06-12"],"dc:date.issued":["1989-07-05"],"dc:description.abstract":["An investigation of the behavior of shear deformable plate finite elements is conducted to determine why and under what conditions these elements lock, or become overly stiff. 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These analytical findings are then compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behavior of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-06122010-020608"],"dc:identifier.uri":["http://hdl.handle.net/10919/43286"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["On the behavior of shear deformable plate elements"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Engineering Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:03Z"}