  The interaction between thin structures and incompressible Newtonian fluids
is ubiquitous both in nature and in industrial applications. In this paper we
present an isogeometric formulation of such problems which exploits a boundary
integral formulation of Stokes equations to model the surrounding flow, and a
non linear Kirchhoff-Love shell theory to model the elastic behaviour of the
structure. We propose three different coupling strategies: a monolithic, fully
implicit coupling, a staggered, elasticity driven coupling, and a novel
semi-implicit coupling, where the effect of the surrounding flow is
incorporated in the non-linear terms of the solid solver through its damping
characteristics. The novel semi-implicit approach is then used to demonstrate
the power and robustness of our method, which fits ideally in the isogeometric
paradigm, by exploiting only the boundary representation (B-Rep) of the thin
structure middle surface.
