Shape Optimisation of Fluid-Structure Interactive Field Considering Geometrically Nonlinear Structure

Abstract

This paper presents a numerical solution to a shape optimisation of stationary fluid-structure-interactive (FSI) fields. The minimisation problem for total dissipation energy in the viscous flow field and the mean compliance minimisation problem in order to achieve stiffness maximisation in the structural field are considered for the shape optimisation. In the FSI analysis, a weak coupled analysis is used to alternately analyse the governing equations of the flow field and the structural field considering geometrically nonlinear. Shape derivative function of the shape optimisation problem is derived theoretically using the 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 gradient method proposed as an approach to solving shape optimisation. Numerical analysis program for the shape optimisation problem is developed by using FreeFEM, and the validity of the proposed method is confirmed by the results of 2D problems.