Naslov
Fluid-structure interaction between an incompressible, viscous 3D fluid and an elastic shell with nonlinear Koiter membrane energy

Autori
Muha, Boris ; Čanić, Sunčica

Izvornik
Interfaces and free boundaries (1463-9971) 17 (2015), 4; 465-495

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Fluid-structure interaction; Nonlinear moving-boundary problem; Nonlinear membrane; Existence of a solution

Sažetak
The long-time existence of a weak solution is proved for a nonlinear, fluid-structure interaction (FSI) problem between an incompressible, viscous fluid and a semilinear cylindrical Koiter membrane shell with inertia. No axial symmetry is assumed in the problem. The fluid flow is driven by the time-dependent dynamic pressure data prescribed at the inlet and outlet boundaries of the 3D cylindrical fluid domain. The fluid and the elastic structure are fully coupled via continuity of velocity and continuity of normal stresses. Global existence of a weak solution is proved as long as the lateral walls of the cylinder do not touch each other. The main novelty of the work is the nonlinearity in the structure model: the model accounts for the fully nonlinear Koiter membrane energy, supplemented with a small linear fourth- order derivative term modeling the bending rigidity of shells. The existence proof is constructive, and it is based on an operator splitting scheme. A version of this scheme can be implemented for the numerical simulation of the underlying FSI problem by extending the FSI solver, developed by the authors, to include the nonlinearity in the structure model discussed in this manuscript.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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