Level set topology optimization for fluid-structure interactions

In this work a level set topology optimization (LSTO) method is developed in combination with a nodally integrated reproducing kernel particle method (RKPM) for solving fluid-structure interaction problems (FSI). FSI falls into a specific class of topology optimization problems known as design-depended. In this class the direction, magnitude and position of the loads depend on the structure itself. Thus, the main challenge lies in tracking the interface to correctly apply the loads and coupling conditions. The simplest class of design-dependent loading problems considering only hydrostatic pressure is addressed here, with the aim of extending the same methodology to viscous flows in the near future. The freedom RKPM offers to place particles anywhere in the domain in combination with the implicit boundary representation given by the level set method, provides an effective framework to handle the dendency of loading by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Benchmarking examples involving both constant and variable pressure loads are solved to illustrate the applicability of the methodology. For the extension to viscous flows, we set up an initial framework that utilizes the modified immersed finite element method (mIFEM) through the opensource software OpenIFEM. With mIFEM the coupled equations can be solved efficiently on a fixed fluid grid, thus avoiding to remesh for the fluid, while the solid on top of the fluid is free to move and deform. Combining LSTO, RKPM and mIFEM, the optimized results obtained for hydrostatic pressure are placed in a viscous flow field to perform a transient analysis. The LSTO defines the geometry of the structure, the solid domain is analyzed using RKPM with the naturally stabilized nodal integration technique (NSNI) and mIFEM is used to solve the coupled equations on a fixed fluid mesh