{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/43180"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/43180","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"An evaluation of classical and refined equivalent-single-layer laminate theories","abstract":"In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated.","abstract_html":"In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated.","abstract_has_math":false,"creators":["Bose, Partha"],"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":["Heller, Robert A.","Kriz, Ronald D."],"year":1995,"date_issued":"1995-12-18","date_published":"1995-12-18","updated_at":"2026-07-22T22:20:32Z","subjects":["Finite element method","laminated plates"],"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-06112009-063723"],"render_values":[{"text":"etd-06112009-063723","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/43180","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":["Heller, Robert A.","Kriz, Ronald D."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Bose, Partha"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:38:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:38:02Z","2009-06-11"]},{"key":"dc:date.issued","label":"Date","values":["1995-12-18"]},{"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":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Finite element method","laminated plates"]}]},{"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-06112009-063723"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/43180"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated."]},{"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":["An evaluation of classical and refined equivalent-single-layer laminate theories"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Reddy, Junuthula N."],"dc:contributor.committeemember":["Heller, Robert A.","Kriz, Ronald D."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Bose, Partha"],"dc:date.accessioned":["2014-03-14T21:38:02Z"],"dc:date.available":["2014-03-14T21:38:02Z","2009-06-11"],"dc:date.issued":["1995-12-18"],"dc:description.abstract":["In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-06112009-063723"],"dc:identifier.uri":["http://hdl.handle.net/10919/43180"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Finite element method","laminated plates"],"dc:title":["An evaluation of classical and refined equivalent-single-layer laminate theories"],"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":"2026-07-22T22:20:32Z"}