Shape design for controlling structural displacement distribution in unsteady fluid-structure-interaction

This paper presents a numerical solution for the shape design problem in unsteady fluid-structure-interaction (FSI) fields with viscous flow. The FSI analysis uses a strongly coupled approach based on the Arbitrary Lagrange-Eulerian (ALE) method. The shape design problem is formulated as a shape optimization aimed at controlling displacement distribution within a sub-domain of the structural domain. This problem is treated as an inverse problem, where the objective is to minimize the squared error integral between actual and target structural displacement distributions in the sub-domain. The shape gradient for this design problem is theoretically derived using the adjoint variable method and the shape derivative formula. Shape updates are performed using the conventional H1 gradient method, along with a newly proposed iterative H1 gradient method, both of which are approaches to solving the shape optimization problem. A numerical analysis program for this shape design problem was developed using FreeFEM. The validity of the proposed method was confirmed through 2D numerical analysis results.