This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-dimensional background fluid mesh, referred to as fluid–beam interaction (FBI) in analogy to the well-established notion of FSI. Here, the fluid is described by the incompressible isothermal Navier–Stokes equations for Newtonian fluids. In particular, we present algorithmic aspects regarding the solution of the resulting one-way coupling schemes and, through selected numerical examples, analyze their spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.
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.
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