An adaptive isogeometric boundary integral method using analysis-suitable T-splines for fluid-shell interactions at low Reynolds numbers

An adaptive isogeometric boundary integral method is developed for fluid–structure interaction analysis of the deformation of a hyperelastic sheet in a viscous fluid. An isogeometric Kirchhoff–Love shell formulation for solid mechanics is coupled with a boundary integral formulation for fluid mechanics at the Stokes flow regime. Knot insertion and removal based on analysis-suitable T-splines are applied to mesh refinement and coarsening. Compression- and curvature-dependent refinement and coarsening rules are used to capture complex fold formations. Flow-induced deformation due to extensional and simple shear flows, and growth-induced deformation due to swelling and shrinking are simulated. Protrusion and retraction of the leading edge of a membrane are also simulated. These numerical examples demonstrate that the developed method is capable of simulating a variety of fold formation problems in viscous environments while saving computational costs.