On Mesh Deformation Techniques for Topology Optimization of Fluid-Structure Interaction Problems

TL;DR

This paper reviews and compares existing mesh deformation techniques for fluid-structure interaction topology optimization, introducing a new hyperelasticity-based method and a layered stiffening approach to improve mesh quality during large deformations.

Contribution

It proposes a novel mesh deformation technique based on the Yeoh hyperelasticity model and introduces layered selective stiffening to enhance mesh quality in FSI topology optimization.

Findings

Legacy models sustain large deformations with good mesh quality.

Layered stiffening improves mesh robustness near interfaces.

The new hyperelasticity-based method performs comparably to existing techniques.

Abstract

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.