Immersed boundary analysis with strong enforcement of essential boundary conditions

Sanne van den Boom (PhD candidate), Alejandro M. Aragón (supervisor), and Fred van Keulen (supervisor)

It is not always desirable to generate a mesh that conforms to the boundaries, for instance in cases where the boundary has a very complex shape or in cases where the boundary evolves, such as during optimization or in fluid-structure interaction. The Interface-enriched Generalized Finite Element Method (IGFEM) and Discontinuity-enriched Finite Element Method (DE-FEM) were developed for solving problems with interfaces and the combinations of interfaces and cracks, respectively. Here, we extend both methods to immersed boundary problems, where the mesh-independent boundaries might either describe a discontinuity within the object, or the boundary of the object itself. In contrast to in other immersed methods, essential boundary conditions may be prescribed strongly, and smooth traction fields are recovered.

Essential boundary conditions are strongly prescribed on an immersed geometry and a smooth reaction field is recovered
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