  Fluid-structure interactions are a widespread phenomenon in nature. Although
their numerical modeling have come a long way, the application of numerical
design tools to these multiphysics problems is still lagging behind.
Gradient-based optimization is the most popular approach in topology
optimization currently. Hence, it's a necessity to utilize mesh deformation
techniques that have continuous, smooth derivatives. In this work, we address
mesh deformation techniques for structured, quadrilateral meshes. We discuss
and comment on two legacy mesh deformation techniques; namely the spring
analogy model and the linear elasticity model. In addition, we propose a new
technique based on the Yeoh hyperelasticity model. We focus on mesh quality as
a gateway to mesh admissibility. We propose layered selective stiffening such
that the elements adjacent to the fluid-structure interface - where the bulk of
the mesh distortion occurs - are stiffened in consecutive layers. The legacy
and the new models are able to sustain large deformations without deprecating
the mesh quality, and the results are enhanced with using layered selective
stiffening.
