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Tensory a jejich aplikace v mechanice

Tensors and their applications in mechanics

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Author
Adejumobi, Mudathir
Advisor
Tomáš, Jiří
Referee
Doupovec, Miroslav
Grade
D
Alternative metrics PlumX
http://hdl.handle.net/11012/192330
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http://hdl.handle.net/11012/192330
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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.
 
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.
 
Keywords
Tensors, Manifolds, Differential manifolds, Configuration and deformation, Tensor deformation, Continuum kinematics, Gauss theorem, Stokes' theorem, Surface forces and stress, Tensors, Manifolds, Differential manifolds, Configuration and deformation, Tensor deformation, Continuum kinematics, Gauss theorem, Stokes' theorem, Surface forces and stress
Language
angličtina (English)
Study brunch
Matematické inženýrství
Composition of 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)
Date of defence
2020-07-16
Process of 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.
Result of the defence
práce byla úspěšně obhájena
Persistent identifier
http://hdl.handle.net/11012/192330
Source
ADEJUMOBI, M. Tensory a jejich aplikace v mechanice [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2020.
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  • 2020 [577]
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