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doctoral thesis
Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method
2022. urn:nbn:hr:157:354050
Grbac, Marin
University of Rijeka
Faculty of Civil Engineering

Cite this document

Grbac, M. (2022). Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method (Doctoral thesis). Rijeka: University of Rijeka, Faculty of Civil Engineering. Retrieved from https://urn.nsk.hr/urn:nbn:hr:157:354050

Grbac, Marin. "Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method." Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, 2022. https://urn.nsk.hr/urn:nbn:hr:157:354050

Grbac, Marin. "Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method." Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, 2022. https://urn.nsk.hr/urn:nbn:hr:157:354050

Grbac, M. (2022). 'Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method', Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, accessed 06 May 2024, https://urn.nsk.hr/urn:nbn:hr:157:354050

Grbac M. Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method [Doctoral thesis]. Rijeka: University of Rijeka, Faculty of Civil Engineering; 2022 [cited 2024 May 06] Available at: https://urn.nsk.hr/urn:nbn:hr:157:354050

M. Grbac, "Three-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method", Doctoral thesis, University of Rijeka, Faculty of Civil Engineering, Rijeka, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:157:354050

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Metadata
TitleThree-node flat shell finite elements based on the cubic linked interpolation and the assumed strain method
Title (croatian)Tročvorni konačni elementi ravnih ljuski temeljeni na kubnoj vezanoj interpolaciji i metodi usvojenih deformacija
AuthorMarin Grbac
MentorDragan Ribarić (mentor)
Committee memberGordan Jelenić (predsjednik povjerenstva)
Committee memberLeo Škec (član povjerenstva)
Committee memberBoštjan Brank (član povjerenstva)
GranterUniversity of Rijeka
Faculty of Civil Engineering
Rijeka
Defense date and country2022-10-20, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Civil Engineering
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Basic Technical Sciences
Technical Mechanics (Mechanics of Rigid and Deformable Bodies)
Universal decimal classification
(UDC)		624/625 - Civil and structural engineering. Civil engineering of land transport. Railway engineering. Highway engineering
Abstract
In this doctoral thesis, new three-node at shell finite elements for general 3D linear-elastic analysis of shells with small deformations are developed. These at shell nite elements are formed by joining two independent parts: out-of-plane Mindlin plate bending part and in-plane membrane part. The displacement-based approach with linked interpolation and the assumed strain method are employed for the development of new finite elements. Various effective finite elements have been developed in the process. Mindlin plate bending finite elements presented here are based on the two-node Timoshenko beam finite element with problem-dependent cubic linked interpolation. This beam element is free of shear locking and is capable of returning the exact results for certain load cases, and has been successfully utilised for Mindlin plate elements in the literature. Without any additional treatment, plate elements developed in such way may still suffer from shear locking in thin limit cases. This locking is avoided here by following the assumed strain method. Membrane finite elements presented here are utilising rotational (drilling) degrees of freedom which are linked to the displacement fields. Physically correct implementation of the rotational degrees of freedom is achieved by satisfying the classical theory of elasticity definition of rotation. This approach is particularly convenient when used for the in-plane membrane part in the shell nite element formulation. All finite elements have been subjected to the so-called patch tests and tested on a variety of standard numerical examples, as well as compared with the finite elements used in the Finite Element Analysis Program (FEAP), in addition to other known nite elements from the literature.
Abstract (croatian)
U ovoj doktorskoj disertaciji razvijeni su novi tročvorni konačni elementi ravnih ljuski za opću 3D linearno-elastičnu analizu ljuski s malim deformacijama. Ovi konačni elementi ravnih ljuski formiraju se spajanjem dvaju neovisnih dijela: dijela od savijanja ploča Mindlinovog tipa (izvan ravnine) i membranskog dijela (unutar ravnine). Za razvoj novih konačnih elemenata korišten je pristup koji se temelji na pomacima uz primjenu vezane interpolacije te metoda usvojenih deformacija. U tom procesu razvijeni su razni učinkoviti konačni elementi. Ovdje predstavljeni konačni elementi Mindlinovih ploča temelje se na dvočvornom Timošenkovom grednom konačnom elementu s kubnom vezanom interpolacijom koja je ovisna o problemu. Ovaj gredni element je slobodan od shear locking-a i sposoban je dati točne rezultate za određene slučajeve opterećenja, a uspješno je korišten za elemente Mindlinovih ploča u literaturi. Bez ikakvog dodatnog tretmana, tako razvijeni elementi ploča mogu i dalje patiti od shear locking-a u graničnim slučajevima tankih ploča. Ovdje se taj locking izbjegava slijedeći metodu usvojenih deformacija. Ovdje predstavljeni membranski konačni elementi koriste rotacijske stupnjeve slobode koji su povezani s poljima pomaka. Fizički ispravna implementacija rotacijskih stupnjeva slobode postiže se zadovoljavanjem definicije rotacije prema klasičnoj teoriji elastičnosti. Ovaj pristup je osobito prikladan kada se koristi za membranski dio (unutar ravnine) u formulaciji konačnog elementa ljuske. Svi konačni elementi podvrgnuti su takozvanim patch testovima i testirani su na raznim standardnim numeričkim primjerima, kao i uspoređeni s konačnim elementima koji se koriste u Finite Element Analysis Program (FEAP)-u, uz ostale poznate konačne elemente iz literature.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:157:354050
Promotion2022
ProjectNumber: IP-2016-06-4775
Title: Metoda usvojenih deformacija za konačne elemente slojevitih ploča i ljuski i njena primjena na probleme delaminacije
Title: Assumed strain method in finite elements for layered plates and shells with application on layer delamination problem
Acronym: ASDEL
Leader: Dragan Ribarić
Jurisdiction: Croatia
Funder: HRZZ
Funding stream: IP
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)
Type of resourceText
Extent106 str., 31 cm
File originBorn digital
Access conditionsOpen access
Terms of useLicence Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) icon
Created on2022-10-24 09:54:19