Tensors and their applications in mechanics

 dc.contributor.advisor Tomáš, Jiří en dc.contributor.author Adejumobi, Mudathir en dc.date.accessioned 2020-07-20T18:58:48Z dc.date.available 2020-07-20T18:58:48Z dc.date.created 2020 cs dc.identifier.citation ADEJUMOBI, M. Tensory a jejich aplikace v mechanice [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2020. cs dc.identifier.other 124597 cs dc.identifier.uri http://hdl.handle.net/11012/192330 dc.description.abstract The tensor theory is a branch of Multilinear Algebra that describes the relationship between sets of algebraic objects related to a vector space. Tensor theory together with tensor analysis is usually known to be tensor calculus. This thesis presents a formal category treatment on tensor notation, tensor calculus, and differential manifold. The focus lies mainly on acquiring and understanding the basic concepts of tensors and the operations over them. It looks at how tensor is adapted to differential geometry and continuum mechanics. In particular, it focuses more attention on the application parts of mechanics such as; configuration and deformation, tensor deformation, continuum kinematics, Gauss, and Stokes' theorem with their applications. Finally, it discusses the concept of surface forces and stress vector. en dc.description.abstract The tensor theory is a branch of Multilinear Algebra that describes the relationship between sets of algebraic objects related to a vector space. Tensor theory together with tensor analysis is usually known to be tensor calculus. This thesis presents a formal category treatment on tensor notation, tensor calculus, and differential manifold. The focus lies mainly on acquiring and understanding the basic concepts of tensors and the operations over them. It looks at how tensor is adapted to differential geometry and continuum mechanics. In particular, it focuses more attention on the application parts of mechanics such as; configuration and deformation, tensor deformation, continuum kinematics, Gauss, and Stokes' theorem with their applications. Finally, it discusses the concept of surface forces and stress vector. cs dc.language.iso en cs dc.publisher Vysoké učení technické v Brně. Fakulta strojního inženýrství cs dc.rights Standardní licenční smlouva - přístup k plnému textu bez omezení cs dc.subject Tensors en dc.subject Manifolds en dc.subject Differential manifolds en dc.subject Configuration and deformation en dc.subject Tensor deformation en dc.subject Continuum kinematics en dc.subject Gauss theorem en dc.subject Stokes' theorem en dc.subject Surface forces and stress en dc.subject Tensors cs dc.subject Manifolds cs dc.subject Differential manifolds cs dc.subject Configuration and deformation cs dc.subject Tensor deformation cs dc.subject Continuum kinematics cs dc.subject Gauss theorem cs dc.subject Stokes' theorem cs dc.subject Surface forces and stress cs dc.title Tensory a jejich aplikace v mechanice en dc.title.alternative Tensors and their applications in mechanics cs dc.type Text cs dcterms.dateAccepted 2020-07-16 cs dcterms.modified 2020-07-16-14:29:38 cs thesis.discipline Matematické inženýrství cs thesis.grantor Vysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematiky cs thesis.level Inženýrský cs thesis.name Ing. cs sync.item.dbid 124597 en sync.item.dbtype ZP en sync.item.insts 2020.07.20 20:58:48 en sync.item.modts 2020.07.17 08:13:37 en eprints.affiliatedInstitution.faculty Fakulta strojního inženýrství cs dc.contributor.referee Doupovec, Miroslav en dc.description.mark D cs dc.type.driver masterThesis en dc.type.evskp diplomová práce cs but.committee prof. RNDr. Josef Šlapal, CSc. (předseda) prof. RNDr. Miloslav Druckmüller, CSc. (místopředseda) doc. Ing. Luděk Nechvátal, Ph.D. (člen) doc. RNDr. Jiří Tomáš, Dr. (člen) doc. Mgr. Pavel Řehák, Ph.D. (člen) Prof. Bruno Rubino (člen) Assoc. Prof. Matteo Colangeli (člen) Assoc. Prof. Massimiliano Giuli (člen) cs but.defence Student introduced his diploma thesis Tensors and their applications in mechanics to the committee and explained the fundaments of this topic. There was no question in the reviewer's report. Student answered another questions from prof. Šlapal, doc. Tomáš and assoc. prof. Massimiliano Giuli. cs but.result práce byla úspěšně obhájena cs but.program Aplikované vědy v inženýrství cs but.jazyk angličtina (English)
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