Shape optimization of Fluid-Structure-Interactive field using FreeFEM

Abstract

This paper presents numerical solution to a shape optimization for stationary fluid structure interactive fields. In the fluid structure interactive analysis, a weak coupled analysis is used to alternately analyze the governing equations of the flow field domain and the structural field considering geometrically nonlinear. A mean compliance minimization problem is formulated in order to achieve stiffness maximization on the structural field. Shape derivative, which means the sensitivity in the shape optimization problem, is derived theoretically by using the Lagrange multiplier method and adjoint variable method, and the formulae of the shape derivative with respect to domain variation of the distribution function. Reshaping is carried out by the H¹ gradient method proposed as an approach to solving shape optimization problems. Numerical analysis program for the problem is developed by using FreeFEM, and validity of proposed method is confirmed by numerical results of 2D problems.