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doctoral thesis
Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations
doctoral thesis
2015. urn:nbn:hr:188:775665
Gaćeša, Maja
University of Rijeka
Faculty of Civil Engineering

Cite this document

Gaćeša, M. (2015). Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis (Doctoral thesis). Rijeka: University of Rijeka, Faculty of Civil Engineering. Retrieved from https://urn.nsk.hr/urn:nbn:hr:188:775665

Gaćeša, Maja. "Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis." Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, 2015. https://urn.nsk.hr/urn:nbn:hr:188:775665

Gaćeša, Maja. "Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis." Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, 2015. https://urn.nsk.hr/urn:nbn:hr:188:775665

Gaćeša, M. (2015). 'Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis', Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, accessed 03 December 2024, https://urn.nsk.hr/urn:nbn:hr:188:775665

Gaćeša M. Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis [Doctoral thesis]. Rijeka: University of Rijeka, Faculty of Civil Engineering; 2015 [cited 2024 December 03] Available at: https://urn.nsk.hr/urn:nbn:hr:188:775665

M. Gaćeša, "Fixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis", Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, Rijeka, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:188:775665

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Metadata
TitleFixed-Pole Concept in 3D Beam Finite Elements - Relationship to Standard Approaches and Analysis of Different Interpolations : doctoral thesis
AuthorMaja Gaćeša
MentorGordan Jelenić (mentor)
Committee memberNenad Bićanić (predsjednik povjerenstva)
Committee memberGoran Turkalj (član povjerenstva)
Committee memberDragan Ribarić (član povjerenstva)
Committee memberMiran Saje (član povjerenstva)
VIAF: 49154440184035342518
Committee memberDejan Zupan (član povjerenstva)
VIAF: 305606640
GranterUniversity of Rijeka
Faculty of Civil Engineering
Rijeka
Defense date and country2015-01-01, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Civil Engineering
Universal decimal classification
(UDC)		624/625 - Civil and structural engineering. Civil engineering of land transport. Railway engineering. Highway engineering
Abstract
A family of geometrically exact spatial beam finite elements based on the fixed-pole approach is developed and presented in this thesis. All the proposed elements are derived from the principle of virtual work by interpolating the virtual spins (or virtual congurational spins). The fixed-pole element is derived from the configuration-tensor approach. By utilising the standard Galerkin approach this element turns out to have non-standard six-dimensional system unknowns. In order to reap the benets of the fixed-pole approach, but still be able to have standard system unknowns, a modification of the fixed-pole approach is proposed: the nonstandard and standard virtual quantities are related at the nodal level. This results in a family of modified-fixed pole elements, consisting of three interpolation options. The fixed-pole and the modified fixed-pole formulations are tested with respect to their accuracy, strain-invariance, path-independence and robustness on a number of planar and spatial numerical examples. The results show that non-invariance and path-dependence is present in all formulations - in some formulations even in the planar case. In the case of the modified-fixed pole formulation, these problems are overcome by (i) interpolating only the relative rotations between two nodes and (ii) implementing the generalised shape-functions. The repeated numerical tests show that results are strain-invariant, pathindependent and that the solution procedure is more robust. Although the results obtained by employing Interpolation option 3 are somewhat improved in comparison to those before this intervention, they still exhibit some non-invariant and path-dependent behaviour. In the case of the fixed-pole formulation, strain-invariance and path-independence is achieved by (i) interpolating only the relative congurations between two nodes and and (ii) by deriving and implementing six-dimensional shape functions. The results of the repeated numerical tests conrm that this intervention leads to strain-invariant, path-independent and more robust elements.
Abstract (croatian)
U disertaciji je predložena familija geometrijski točnih prostornih grednih elemenata koji su temeljeni na tzv. konceptu nepomičnog pola (fixed-pole approach). Sve predložene formulacije izvedene su iz principa virtualnoga rada uz interpolaciju virtualnih spinova (ili virtualnih konfiguracijskih spinova). Fixed-pole element izveden je iz pristupa temeljenog na konfiguracijskome tenzoru. Primjenjujući standardnu Galerkinovu metodu diskretizacije, takav pristup rezultira nestandardnim stupnjevima slobode. Kako bi se zadržale prednosti fixed-pole pristupa uz istovremeno zadržavanje standardnih stupnjeva slobode, predlaže se modifikacija fixed-pole formulacije temeljena na povezivanju standardnih i nestandardnih virtualnih veličina na razini čvorova. Takva modifikacija rezultira familijom modificiranih fixed-pole elemenata koja se sastoji od tri interpolacijske opcije. Kod svih predloženih formulacija ispitana je njihova točnost, objektivnost deformacija s obzirom na pomak krutoga tijela, ovisnost o putanji ka rješenju te robustnost. Zaključak numeričkih primjera je da sve predložene formulacije iskazuju nepovoljna svojstva neobjektivnosti i ovisnosti o putanji ka rješenju te da im je smanjena robustnost u odnosu na standardne formulacije. U slučaju modificirane fixed-pole formulacije, problemi neobjektivnosti, ovisnosti o putanji ka rješenju te robustnosti rješeni su (i) interpolacijom relativnih rotacija između dva čvora te (ii) ugrađivanjem generaliziranih funkcija oblika. Ponovljeni numerički testovi pokazuju da su rezultati objektivni, ne ovise o putanji ka rješenju te da je povećana robustnost same procedure. Iako su i rezultati dobiveni korištenjem treće interpolacijske opcije poboljšani u odnosu na one prije ove intervencije, oni i dalje pokazuju znakove neobjektivnosti i ovisnosti o putanji ka rješenju, no u manjoj mjeri. U slučaju fixed-pole formulacije, problem je otklonjen (i) interpolacijom relativnih konfiguracija između dva čvora te (ii) izvođenjem te ugrađivanjem novih, šesterodimenzionalnih funkcija oblika. Ponovljenim numeričkim testovima potvrđeno je da ovakva intervencija dovodi do objektivnih, neovisnih o putanji ka rješenju te robustnijih elemenata.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:188:775665
Study programmeTitle: Civil Engineering; specializations in: Hydrotechnics and geotechnics, Mechanics
Course: Hydrotechnics and geotechnics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje tehničkih znanosti (doktor/doktorica znanosti, područje tehničkih znanosti)
Catalog URLhttps://libraries.uniri.hr/cgi-bin/unilib.cgi?form=D1130716088
Type of resourceText
Extent113 str; 30 cm
File originBorn digital
Access conditionsOpen access
Terms of useLicence Attribution 4.0 International (CC BY 4.0) icon
Created on2017-01-19 17:50:01