Shape design for controlling displacement distribution of a geometrically nonlinear structure by considering fluid-structure interaction

Abstract

This paper presents a numerical solution to shape design problem in the field of fluid--structure interaction. The square error integrals between the actual displacement distributions and target distributions to control displacement on the structural field considering geometrical nonlinearity is used as the objective functional. The adjoint variable method is used. A shape derivative is derived for the problem. Further, the $H^1$ gradient method is used to perform reshaping. A numerical analysis program is developed for the problem by using FreeFEM, and its validity is confirmed using the numerical results of 2D problems.