Iterative methods for solving a poroelastic shell model of Naghdi's type (CROSBI ID 241496)
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Podaci o odgovornosti
Ljulj, Matko ; Tambača, Josip
engleski
Iterative methods for solving a poroelastic shell model of Naghdi's type
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.
poroelasticity ; Biot’s system ; thin shell model ; undrained and fixed stress split ; iterative numerical method ; existence of solutions
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Podaci o izdanju
40 (12)
2017.
4425-4435
objavljeno
0170-4214
1099-1476
10.1002/mma.4314