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## Iterative methods for solving a poroelastic shell model of Naghdi's type

Ljulj, Matko; Tambača, Josip
Iterative methods for solving a poroelastic shell model of Naghdi's type // Mathematical methods in the applied sciences, 40 (2017), 12; 4425-4435 doi:10.1002/mma.4314 (međunarodna recenzija, članak, znanstveni)

Naslov
Iterative methods for solving a poroelastic shell model of Naghdi's type

Autori
Ljulj, Matko ; Tambača, Josip

Izvornik
Mathematical methods in the applied sciences (0170-4214) 40 (2017), 12; 4425-4435

Ključne riječi
Poroelasticity ; Biot’s system ; thin shell model ; undrained and fixed stress split ; iterative numerical method ; existence of solutions

Sažetak
In this paper, we first formulate a linear quasi-static poroelastic shell model of Naghdi’s type. The model is given in three unknowns: displacement u of the middle surface, infinitesimal rotation omega of the cross section of the shell, and the pressure pi. The model has the structure of the quasi- static Biot’s system and can be seen as a system of the shell equation with pressure term as forcing and the parabolic type equation for the pressure with divergence of the filtration velocity as forcing term. On the basis of the ideas of the operator splitting methods, we formulate two sequences of approximate solutions, corresponding to ‘undrained split’ and ‘fixed stress split’ methods. We show that these sequences converge to the solution of the poroelastic shell model. Therefore, the iterations constitute two numerical methods for the model. Moreover, both methods are optimized in a certain sense producing schemes with smallest contraction coefficient and thus faster convergence rates. Also, these convergences imply existence of solutions for the model.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0693014-2765 - Matematička analiza kompozitnih i tankih struktura (Zvonimir Tutek, )
HRZZ-IP-2013-11-9345 - Matematičko modeliranje, analiza i računanje s primjenama na kompleksne mehaničke sustave (Zlatko Drmač, )

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

• MathSciNet