{"id":{"repo_id":"brazil-uerj","oai_identifier":"oai:pantheon.ufrj.br:11422/3533"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-uerj/oai:pantheon.ufrj.br:11422/3533","repository":{"repo_id":"brazil-uerj","name":"Brazil UERJ","base_url":"https://pantheon.ufrj.br/oai/request"},"display":{"title":"Aplicacion del metodo de Ritz a funcionales relajados en mecanica de los solidos","abstract":"The theory of the first variations of different type of functionals is presented in this work. The Weierstrass – Erdmann corner conditions are obtained for each one of these functionals. The classical theory of the Ritz Method is developed, but when dealing with convergende of the aproximated solutions and performance of the Ritz coefficients, the theory of operators in Hilbert spaces is introduced; this makes it possible to have the problem in an elegant, clear and compact form. The concept of \"extended functionals\", a systematic way of getting them, the application of the Ritz Method to these functionals as well as mapping and the subdivition of the application domain are analyzed in this investigation. Numerical results for torsion in bars are compareci with results obtained through some other methods and also· the exact solution.","abstract_html":"The theory of the first variations of different type of functionals is presented in this work. The Weierstrass – Erdmann corner conditions are obtained for each one of these functionals. The classical theory of the Ritz Method is developed, but when dealing with convergende of the aproximated solutions and performance of the Ritz coefficients, the theory of operators in Hilbert spaces is introduced; this makes it possible to have the problem in an elegant, clear and compact form. The concept of "extended functionals", a systematic way of getting them, the application of the Ritz Method to these functionals as well as mapping and the subdivition of the application domain are analyzed in this investigation. Numerical results for torsion in bars are compareci with results obtained through some other methods and also· the exact solution.","abstract_has_math":false,"creators":["Feijóo, Raul Antonino"],"institution":"Universidade Federal do Rio de Janeiro","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Bevilacqua, Luiz"],"committee_chairs":[],"committee_members":[],"year":1973,"date_issued":"1973-06","date_published":"1973-06","updated_at":"2026-07-24T01:16:04Z","subjects":["Mecânica dos sólidos","Método dos elementos finitos"],"languages":["por"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11422/3533","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bevilacqua, Luiz"]},{"key":"dc:creator","label":"Author","values":["Feijóo, Raul Antonino"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-01-23T13:05:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-16T03:05:17Z"]},{"key":"dc:date.issued","label":"Date","values":["1973-06"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal do Rio de Janeiro"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"]},{"key":"dc:type","label":"Dc Type","values":["Dissertação"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mecânica dos sólidos","Método dos elementos finitos"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["por"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11422/3533"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The theory of the first variations of different type of functionals is presented in this work. The Weierstrass – Erdmann corner conditions are obtained for each one of these functionals. The classical theory of the Ritz Method is developed, but when dealing with convergende of the aproximated solutions and performance of the Ritz coefficients, the theory of operators in Hilbert spaces is introduced; this makes it possible to have the problem in an elegant, clear and compact form. The concept of \"extended functionals\", a systematic way of getting them, the application of the Ritz Method to these functionals as well as mapping and the subdivition of the application domain are analyzed in this investigation. Numerical results for torsion in bars are compareci with results obtained through some other methods and also· the exact solution.","Se presenta en este trabajo la teoria correspondiente a la primera variación aplicada a diferentes tipos de funcionales a la vez que las condiciones de Weierstrass-Erdmann, para la existencia de extremales con puntos angulosos esvdeducida para cada uno de ellos. El Método de Ritz es analizado en la forma clásica pero en el análisis de la convergencia de la solución aproximada como del comportamiento de los coeficientes-Ritz se recurre a la teoria de operadores en espacios de Hilbert que permite presentar el problema de una manera elegante, concisa y clara. El concepto de \"funcionales relajados\" y un camino sistemático para su obtención, la aplicación del método de Ritz a los mismos, la necesidad de subdividir la región en que están aplicados dichos funcionales a la vez que el mapeamiento de esa región son analizados a lo largo de este trabajo. También se presentan resultados numéricos para el caso de torsión en barras y su comparación con los exactos y los obtenidos por otros métodos."]},{"key":"dc:title","label":"Title","values":["Aplicacion del metodo de Ritz a funcionales relajados en mecanica de los solidos"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bevilacqua, Luiz"],"dc:creator":["Feijóo, Raul Antonino"],"dc:date.accessioned":["2018-01-23T13:05:52Z"],"dc:date.available":["2026-05-16T03:05:17Z"],"dc:date.issued":["1973-06"],"dc:description.abstract":["The theory of the first variations of different type of functionals is presented in this work. The Weierstrass – Erdmann corner conditions are obtained for each one of these functionals. The classical theory of the Ritz Method is developed, but when dealing with convergende of the aproximated solutions and performance of the Ritz coefficients, the theory of operators in Hilbert spaces is introduced; this makes it possible to have the problem in an elegant, clear and compact form. The concept of \"extended functionals\", a systematic way of getting them, the application of the Ritz Method to these functionals as well as mapping and the subdivition of the application domain are analyzed in this investigation. Numerical results for torsion in bars are compareci with results obtained through some other methods and also· the exact solution.","Se presenta en este trabajo la teoria correspondiente a la primera variación aplicada a diferentes tipos de funcionales a la vez que las condiciones de Weierstrass-Erdmann, para la existencia de extremales con puntos angulosos esvdeducida para cada uno de ellos. El Método de Ritz es analizado en la forma clásica pero en el análisis de la convergencia de la solución aproximada como del comportamiento de los coeficientes-Ritz se recurre a la teoria de operadores en espacios de Hilbert que permite presentar el problema de una manera elegante, concisa y clara. El concepto de \"funcionales relajados\" y un camino sistemático para su obtención, la aplicación del método de Ritz a los mismos, la necesidad de subdividir la región en que están aplicados dichos funcionales a la vez que el mapeamiento de esa región son analizados a lo largo de este trabajo. También se presentan resultados numéricos para el caso de torsión en barras y su comparación con los exactos y los obtenidos por otros métodos."],"dc:identifier.uri":["http://hdl.handle.net/11422/3533"],"dc:language":["por"],"dc:publisher":["Universidade Federal do Rio de Janeiro"],"dc:publisher.department":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"],"dc:rights":["Acesso Aberto"],"dc:subject":["Mecânica dos sólidos","Método dos elementos finitos"],"dc:title":["Aplicacion del metodo de Ritz a funcionales relajados en mecanica de los solidos"],"dc:type":["Dissertação"]},"updated_at":"2026-07-24T01:16:04Z"}