{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/31145"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/31145","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Analytical Modeling and Equivalent Electromechanical Loading Techniques for Adaptive Laminated Piezoelectric Structures","abstract":"Many commercial finite element programs support piezoelectric modeling and composite modeling to some extent. The popular program ABAQUS, however, has piezoelectric modeling capabilities only for continuum and one-dimensional truss elements. In situations where aspect ratio constraints and computational inefficiencies become a significant issue, such as modeling very large thin structures, alternate modeling techniques are sometimes required. Much of the focus of this thesis was to introduce equivalent methods for modeling laminated piezoelectric beams and plates. Techniques are derived based on classical beam and plate theory, classical lamination theory, and the linear theory of piezoelectricity. Finite element approximations are used with the principle of minimum potential energy to derive the static equilibrium equations for piezoelectric laminated structures. Equivalent loading techniques are derived based on the constitutive equations of piezoelectricity to simulate actuation forces within the piezoelectric layers. Finite element models using equivalent modeling techniques as well as equivalent loading techniques for piezoelectric laminated structures are developed and compared to ABAQUS models using piezoelectric elements to evaluate the error in theoretical assumptions. The analysis will prove that equivalent structural models and equivalent loading techniques provide excellent means for simplifying the analysis of thin piezoelectric laminated structures.","abstract_html":"Many commercial finite element programs support piezoelectric modeling and composite modeling to some extent. The popular program ABAQUS, however, has piezoelectric modeling capabilities only for continuum and one-dimensional truss elements. In situations where aspect ratio constraints and computational inefficiencies become a significant issue, such as modeling very large thin structures, alternate modeling techniques are sometimes required. Much of the focus of this thesis was to introduce equivalent methods for modeling laminated piezoelectric beams and plates. Techniques are derived based on classical beam and plate theory, classical lamination theory, and the linear theory of piezoelectricity. Finite element approximations are used with the principle of minimum potential energy to derive the static equilibrium equations for piezoelectric laminated structures. Equivalent loading techniques are derived based on the constitutive equations of piezoelectricity to simulate actuation forces within the piezoelectric layers. Finite element models using equivalent modeling techniques as well as equivalent loading techniques for piezoelectric laminated structures are developed and compared to ABAQUS models using piezoelectric elements to evaluate the error in theoretical assumptions. The analysis will prove that equivalent structural models and equivalent loading techniques provide excellent means for simplifying the analysis of thin piezoelectric laminated structures.","abstract_has_math":false,"creators":["Smith, Clayton L."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Inman, Daniel J."],"committee_members":["Leo, Donald J.","Austin, Eric M."],"year":2001,"date_issued":"2001-01-23","date_published":"2001-01-23","updated_at":"2026-07-22T22:20:34Z","subjects":["Finite element method","Piezoelectric","Laminated"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-02062001-101444"],"render_values":[{"text":"etd-02062001-101444","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/31145","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Inman, Daniel J."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Leo, Donald J.","Austin, Eric M."]},{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Smith, Clayton L."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:31:32Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:31:32Z","2002-02-07"]},{"key":"dc:date.issued","label":"Date","values":["2001-01-23"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical 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":["Finite element method","Piezoelectric","Laminated"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"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-02062001-101444"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/31145"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Many commercial finite element programs support piezoelectric modeling and composite modeling to some extent. The popular program ABAQUS, however, has piezoelectric modeling capabilities only for continuum and one-dimensional truss elements. In situations where aspect ratio constraints and computational inefficiencies become a significant issue, such as modeling very large thin structures, alternate modeling techniques are sometimes required. Much of the focus of this thesis was to introduce equivalent methods for modeling laminated piezoelectric beams and plates. Techniques are derived based on classical beam and plate theory, classical lamination theory, and the linear theory of piezoelectricity. Finite element approximations are used with the principle of minimum potential energy to derive the static equilibrium equations for piezoelectric laminated structures. Equivalent loading techniques are derived based on the constitutive equations of piezoelectricity to simulate actuation forces within the piezoelectric layers. Finite element models using equivalent modeling techniques as well as equivalent loading techniques for piezoelectric laminated structures are developed and compared to ABAQUS models using piezoelectric elements to evaluate the error in theoretical assumptions. The analysis will prove that equivalent structural models and equivalent loading techniques provide excellent means for simplifying the analysis of thin piezoelectric laminated structures."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Analytical Modeling and Equivalent Electromechanical Loading Techniques for Adaptive Laminated Piezoelectric Structures"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Inman, Daniel J."],"dc:contributor.committeemember":["Leo, Donald J.","Austin, Eric M."],"dc:contributor.department":["Mechanical Engineering"],"dc:creator":["Smith, Clayton L."],"dc:date.accessioned":["2014-03-14T20:31:32Z"],"dc:date.available":["2014-03-14T20:31:32Z","2002-02-07"],"dc:date.issued":["2001-01-23"],"dc:description.abstract":["Many commercial finite element programs support piezoelectric modeling and composite modeling to some extent. The popular program ABAQUS, however, has piezoelectric modeling capabilities only for continuum and one-dimensional truss elements. In situations where aspect ratio constraints and computational inefficiencies become a significant issue, such as modeling very large thin structures, alternate modeling techniques are sometimes required. Much of the focus of this thesis was to introduce equivalent methods for modeling laminated piezoelectric beams and plates. Techniques are derived based on classical beam and plate theory, classical lamination theory, and the linear theory of piezoelectricity. Finite element approximations are used with the principle of minimum potential energy to derive the static equilibrium equations for piezoelectric laminated structures. Equivalent loading techniques are derived based on the constitutive equations of piezoelectricity to simulate actuation forces within the piezoelectric layers. Finite element models using equivalent modeling techniques as well as equivalent loading techniques for piezoelectric laminated structures are developed and compared to ABAQUS models using piezoelectric elements to evaluate the error in theoretical assumptions. The analysis will prove that equivalent structural models and equivalent loading techniques provide excellent means for simplifying the analysis of thin piezoelectric laminated structures."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-02062001-101444"],"dc:identifier.uri":["http://hdl.handle.net/10919/31145"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Finite element method","Piezoelectric","Laminated"],"dc:title":["Analytical Modeling and Equivalent Electromechanical Loading Techniques for Adaptive Laminated Piezoelectric Structures"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:34Z"}