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## A new linear Naghdi type shell model for shells with little regularity

Tambača, Josip; Tutek, Zvonimir
A new linear Naghdi type shell model for shells with little regularity // Applied mathematical modelling, 40 (2016), 23/24; 10549-10562 doi:10.1016/j.apm.2016.07.007 (međunarodna recenzija, članak, znanstveni)

Naslov
A new linear Naghdi type shell model for shells with little regularity

Autori
Tambača, Josip ; Tutek, Zvonimir

Izvornik
Applied mathematical modelling (0307-904X) 40 (2016), 23/24; 10549-10562

Ključne riječi
Elastic shell model ; Naghdi shell model ; Little regularity ; Corners ; Junctions

Sažetak
In this paper, a new linear shell model of Naghdi type is formulated for shells with little regularity, namely the shells whose middle surface is parameterized by a W1, ∞ function. Thus corners in the undeformed geometry are inherent in the formulation. Unknowns in the model are the displacement View the MathML source of the middle surface of the shell and the infinitesimal rotation View the MathML source of the shell cross-section. In difference to the classical shell models, the existence and uniqueness of the solution is obtained for View the MathML source with a very simple proof without usage of almost any differential geometry of surfaces. We relate the new model with known shell models in two ways. In the first we show that asymptotically, with respect to small thickness of the shell, the model behaves as the membrane model or the flexural shell model in the corresponding regime. In the second, for smooth enough middle surface, we relate the terms in the weak formulation of the model with terms in the classical Naghdi shell model. Further, we prove continuous dependence of the solution of the model on the change of the undeformed middle surface. At the end, we also present a numerical approximation of the model for the middle surface with a corner at the joint of two pieces that dominantly behave differently (one as a membrane and the other one as a flexural shell).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0693014-2765 - Matematička analiza kompozitnih i tankih struktura (Zvonimir Tutek, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts