{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/76007"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/76007","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Comparison of energy minimization with direct stiffness for linear structural analysis","abstract":"This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method.","abstract_html":"This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method.","abstract_has_math":false,"creators":["Griffith, David Thomas"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Civil Engineering","degree_department":"Civil Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1979,"date_issued":"1979","date_published":"1979","updated_at":"2026-07-22T22:19:31Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/76007","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Civil Engineering"]},{"key":"dc:creator","label":"Author","values":["Griffith, David Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-03-09T21:35:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-03-09T21:35:11Z"]},{"key":"dc:date.issued","label":"Date","values":["1979"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute and State University"]},{"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":["Civil 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":"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.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/76007"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Comparison of energy minimization with direct stiffness for linear structural analysis"]}]}],"canonical_facts":{"dc:contributor.department":["Civil Engineering"],"dc:creator":["Griffith, David Thomas"],"dc:date.accessioned":["2017-03-09T21:35:11Z"],"dc:date.available":["2017-03-09T21:35:11Z"],"dc:date.issued":["1979"],"dc:description.abstract":["This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/76007"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Comparison of energy minimization with direct stiffness for linear structural analysis"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:31Z"}