{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/79680"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/79680","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Implementation of Third Order Plate Theory for use in Existing Finite Element Software","abstract":"Sandwich plates and layered composites are common in many structural applications because of their combination of high stiffness and low weight. These plates combine top and bottom layers of high Young's modulus with intermediate layers of material carrying predominantly shear loads. Finite elements developed for the analysis of sandwich plates need to accurately model transverse shear stresses through the plate thickness. This study was inspired by an Office of Naval Research project to investigate the suitability of steel sandwich plates as ship hulls. A finite element implementation based on a third-order shear deformation element was used in a standard finite element program to model transverse shear stresses in a simply supported plate. Four elements based on third-order theory are developed and tested. Using static condensation to reduce the number of degrees of freedom required by a third-order plate element does not preserve the element's accuracy in either displacements or stresses, and stresses do not converge with refinement of the mesh. For the thin isotropic plate case, some condensed elements give reasonable displacement and stress results, but only for certain choices of mesh and the element is less versatile than one based on first order plate theory. None of the condensed elements give good results for composite plates of any thickness.","abstract_html":"Sandwich plates and layered composites are common in many structural applications because of their combination of high stiffness and low weight. These plates combine top and bottom layers of high Young's modulus with intermediate layers of material carrying predominantly shear loads. Finite elements developed for the analysis of sandwich plates need to accurately model transverse shear stresses through the plate thickness. This study was inspired by an Office of Naval Research project to investigate the suitability of steel sandwich plates as ship hulls. A finite element implementation based on a third-order shear deformation element was used in a standard finite element program to model transverse shear stresses in a simply supported plate. Four elements based on third-order theory are developed and tested. Using static condensation to reduce the number of degrees of freedom required by a third-order plate element does not preserve the element's accuracy in either displacements or stresses, and stresses do not converge with refinement of the mesh. For the thin isotropic plate case, some condensed elements give reasonable displacement and stress results, but only for certain choices of mesh and the element is less versatile than one based on first order plate theory. None of the condensed elements give good results for composite plates of any thickness.","abstract_has_math":false,"creators":["Portier, Sarah"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace and Ocean Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Kapania, Rakesh K."],"committee_members":["Hughes, Owen F.","Patil, Mayuresh J."],"year":2006,"date_issued":"2006-05-12","date_published":"2006-05-12","updated_at":"2026-07-22T22:18:55Z","subjects":["Static Condensation","Finite element method","Third Order Plate Theory","Plate Element"],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05192006-093252"],"render_values":[{"text":"etd-05192006-093252","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/79680","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Kapania, Rakesh K."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Hughes, Owen F.","Patil, Mayuresh J."]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Portier, Sarah"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-10-18T04:18:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-10-18T04:18:11Z","2008-07-11"]},{"key":"dc:date.issued","label":"Date","values":["2006-05-12"]},{"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":["Aerospace and Ocean Engineering"]},{"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":["Static Condensation","Finite element method","Third Order Plate Theory","Plate Element"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"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-05192006-093252"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/79680"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Sandwich plates and layered composites are common in many structural applications because of their combination of high stiffness and low weight. These plates combine top and bottom layers of high Young's modulus with intermediate layers of material carrying predominantly shear loads. Finite elements developed for the analysis of sandwich plates need to accurately model transverse shear stresses through the plate thickness. This study was inspired by an Office of Naval Research project to investigate the suitability of steel sandwich plates as ship hulls. A finite element implementation based on a third-order shear deformation element was used in a standard finite element program to model transverse shear stresses in a simply supported plate. Four elements based on third-order theory are developed and tested. Using static condensation to reduce the number of degrees of freedom required by a third-order plate element does not preserve the element's accuracy in either displacements or stresses, and stresses do not converge with refinement of the mesh. For the thin isotropic plate case, some condensed elements give reasonable displacement and stress results, but only for certain choices of mesh and the element is less versatile than one based on first order plate theory. None of the condensed elements give good results for composite plates of any thickness."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Implementation of Third Order Plate Theory for use in Existing Finite Element Software"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Kapania, Rakesh K."],"dc:contributor.committeemember":["Hughes, Owen F.","Patil, Mayuresh J."],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Portier, Sarah"],"dc:date.accessioned":["2017-10-18T04:18:11Z"],"dc:date.available":["2017-10-18T04:18:11Z","2008-07-11"],"dc:date.issued":["2006-05-12"],"dc:description.abstract":["Sandwich plates and layered composites are common in many structural applications because of their combination of high stiffness and low weight. These plates combine top and bottom layers of high Young's modulus with intermediate layers of material carrying predominantly shear loads. Finite elements developed for the analysis of sandwich plates need to accurately model transverse shear stresses through the plate thickness. This study was inspired by an Office of Naval Research project to investigate the suitability of steel sandwich plates as ship hulls. A finite element implementation based on a third-order shear deformation element was used in a standard finite element program to model transverse shear stresses in a simply supported plate. Four elements based on third-order theory are developed and tested. Using static condensation to reduce the number of degrees of freedom required by a third-order plate element does not preserve the element's accuracy in either displacements or stresses, and stresses do not converge with refinement of the mesh. For the thin isotropic plate case, some condensed elements give reasonable displacement and stress results, but only for certain choices of mesh and the element is less versatile than one based on first order plate theory. None of the condensed elements give good results for composite plates of any thickness."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-05192006-093252"],"dc:identifier.uri":["http://hdl.handle.net/10919/79680"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Static Condensation","Finite element method","Third Order Plate Theory","Plate Element"],"dc:title":["Implementation of Third Order Plate Theory for use in Existing Finite Element Software"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Aerospace and Ocean Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:55Z"}