Title
Isogeometric approach in dynamic analysis of spatial curved beams: doctoral dissertation
Creator
Jočković, Miloš, 1988-, 58145033
Copyright date
2021
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Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 25.08.2021.
Other responsibilities
mentor
Nefovska-Danilović, Marija, 1972-, 6923111
mentor
Baitsch, Matthias, 1955-, 76072713
član komisije
Mandić, Rastislav, 1982-, 5614439
član komisije
Borković, Aleksandar, 1986-, 35709031
član komisije
Marjanović, Miroslav, 31060839
Academic Expertise
Tehničko-tehnološke nauke
University
Univerzitet u Beogradu
Faculty
Građevinski fakultet
Alternative title
Izogeometrijski pristup u dinamičkoj analizi prostornih krivolinijskih grednih nosača
Publisher
[M.M. Jočković]
Format
XX, 112 str.
description
Civil Engineering - Engineering Mechanics and Theory of Structures / Gradjevinarstvo
Tehnicka mehanika i teorija konstrukcija
Abstract (sr)
Accurate numerical modeling of curved beams is of significant importance in different engineering
fields. Several challenges can be present during the curved beam formulation, primarily due to
the issues regarding the beam geometry, discretization and beam theory assumptions.
In this dissertation, the isogeometric approach is applied in the dynamic analysis of spatial
curved beams. A novel beam element was formulated using the Bernoulli - Euler hypothesis
and the fundamental relations of the differential geometry, as well as the Cauchy continuum
beam model. The geometry of the beam, as well as the displacement, velocity and acceleration
fields, were defined using the Non-Uniform Rational B-Spline (NURBS) basis functions, which
present the basis concept of the isogeometric approach. Complex geometry of the curved beams
can be modeled accurately using NURBS - based isogeometric approach. Formulation of the
spatial beam is conducted for the linear case, while the geometrically nonlinear formulation is
conducted only for the plane curved beam using an explicit integration procedure. Free and
forced vibration analyses of the curved beams are studied. In the latter, the influence of the
moving mass on the curved beams is analyzed. The presented approach had shown that, in
comparison to the classical finite element method (FEM), a less number of degrees of freedom
are required in order to obtain accurate results. Consequently, fewer computational resources
are needed to reach the appropriate level of accuracy for the curved beams. This makes the
presented approach competitive with the conventional FEM, especially in the analysis of the
flexible spatial engineering structures with complex geometry.
Abstract (sr)
Tacno numericko modelitanje krivolinijskih gredna nosac je od izuzetnog znacaja u mnogim
inženjerskim oblastima. Geometrija krivolinijskog grednog nosaca, diskretizacija grede kao i
potrebne pretpostavke grede, predstavljaju poteškoce prilikom formulacije krivolinijskog grednog
elementa.
U ovom radu je primenjen izogeometrijski pristup u dinamickoj analizi prostornih krivolinijskih
grednih nosaca. Novi gredni element je definisan primenom Bernuli - Ojelerove pretpostavke, kao
i osnovnih relacija diferencijalne geometrije i mehanike kontinuuma Košijeve grede. Geometrija
grede, kao i polje pomeranja, brzine i ubrzanja su definisani primenom NURBS baznih funkcija,
što predstavlja fundamentalnu osobinu isogeometrijskog pristupa. Složena geometrija krivolinijskog
grednog nosaca može se tacno modelirati primenom izogeometrijskog pristupa zasnovanog
na NURBS baznim funkcijama. Formulacija prostornog krivolinijskog grednog nosaca je izvedena
u uslovina linearne teorije, dok je geometrijski nelinearna teorija primenjena samo na ravanskom
krivolinijskom grednom nosacu, primenom eksplicitne metode integracije. Izvšena je analiza
slobodnih i prinudnih vibracija. Analiza prinudnih vibracija je fokusirana na uticaj pokretnog
opterecenja na krivolinijski gredni nosac. Primenom date formulacije dobijeni su rezultati
zadovoljavajuce tacnosti sa manje stepeni slobode u poredjenju sa klasicnom metodom konacnih
elemenata. U sladu sa tim, u cilju dobijanja rezultata zadovoljavajuce tacnosti krivolinijskog
grednog nosaca nepohodna je primena manje resursa. Ovo cini prikazani pristup konkurentnijim
klasicnoj metodi konacnih elemenata u analizi fleksibilnih inženjerskih konstrukcija sa složenom
geometrijom.
Authors Key words
Isogeometric analysis, Bernoulli - Euler beam, Free and transient analysis, Geometrically
nonlinear formulation
Authors Key words
Izogeometrijska analiza, Bernuli - Ojlerova greda, Slobodne i prinudne vibracije,
Geometrijski nelinearna formulacija
Classification
624.01:691.3 (043.3)
Type
Tekst
Abstract (sr)
Accurate numerical modeling of curved beams is of significant importance in different engineering
fields. Several challenges can be present during the curved beam formulation, primarily due to
the issues regarding the beam geometry, discretization and beam theory assumptions.
In this dissertation, the isogeometric approach is applied in the dynamic analysis of spatial
curved beams. A novel beam element was formulated using the Bernoulli - Euler hypothesis
and the fundamental relations of the differential geometry, as well as the Cauchy continuum
beam model. The geometry of the beam, as well as the displacement, velocity and acceleration
fields, were defined using the Non-Uniform Rational B-Spline (NURBS) basis functions, which
present the basis concept of the isogeometric approach. Complex geometry of the curved beams
can be modeled accurately using NURBS - based isogeometric approach. Formulation of the
spatial beam is conducted for the linear case, while the geometrically nonlinear formulation is
conducted only for the plane curved beam using an explicit integration procedure. Free and
forced vibration analyses of the curved beams are studied. In the latter, the influence of the
moving mass on the curved beams is analyzed. The presented approach had shown that, in
comparison to the classical finite element method (FEM), a less number of degrees of freedom
are required in order to obtain accurate results. Consequently, fewer computational resources
are needed to reach the appropriate level of accuracy for the curved beams. This makes the
presented approach competitive with the conventional FEM, especially in the analysis of the
flexible spatial engineering structures with complex geometry.
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