Shape design optimization of fluid-structure interactions using SPH and geometrically exact interfaces

Fluid-Structure Interaction problems are solved by applying a smoothed particle hydrodynamics method to a weakly compressible Navier-Stokes equation as well as an equilibrium equation for geometrically nonlinear structures in updated Lagrangian formulation. The geometrically exact interface, consisting of B-spline basis functions and the corresponding control points, includes the high order geometric information such as tangent, normal, and curvature. The exactness of interface is kept by updating the control points according to the kinematics obtained from response analysis. Under the scheme of explicit time integration and updated Lagrangian formulation, the required shape design velocity should be updated at every single step. The update scheme of design velocity is developed using the sensitivity of physical velocity. The developed sensitivity analysis method is further utilized in gradient-based shape optimization problems and turns out to be very efficient since the interaction pairs of particles determined in the response analysis can be directly utilized.