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Isogeometric fluid-structure interaction: Theory, algorithms, and computations. (English) Zbl 1169.74015
Summary: We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian-Eulerian description is utilized for the fluid subdomain, and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations; the conservation properties of the semi-discrete and fully discretized systems; a unified presentation of the generalized-\(\alpha \) time integration method for fluid-structure interaction; and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization, and three numerical examples are presented which demonstrate the good behavior of the methodology.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
74L15 Biomechanical solid mechanics
92C10 Biomechanics
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