Fluid‐Structure Interaction of Slender Continua with 3‐Dimensional Flow: An Embedded Finite Element Approach

The interaction of slender bodies with fluid flow plays an important role in many industrial processes and biomedical applications. The numerical modeling of problems involving such rod‐like structures with classical continuum‐based finite elements poses a challenge because it promptly leads to locking effects as well as very large system sizes. An alternative approach leading to rather well‐posed problems is the use of 1‐dimensional beam theory. Applications of so‐called geometrically exact beam theories have proven to be a computationally efficient way to model the behavior of such slender structures. This work addresses research questions arising from the application of geometrically‐exact beam theory in the context of fluid‐structure interaction (FSI). In particular, we describe an embedded approach coupling geometrically exact beam finite elements to a background fluid mesh. Furthermore, we elaborate on the conversion between the beam's stress resultants and the 3‐dimensional formulation of the fluid field. A preliminary numerical example will demonstrate the general applicability of the proposed approach for a one‐way coupled problem.