Shape Sensitivity Analysis of Fluid-Structure Interaction Problems

Abstract

This paper presents a general monolithic formulation for sensitivity analysis of the steady interaction of a viscous incompressible o w with an elastic structure undergoing large displacements (geometric non-linearities). This is a direct extension of our previous work on value parameter sensitivity of such problems. 1 The coupled set of equations is solved in a direct implicit manner using a Newton-Raphson adaptive nite element method. A pseudo-solid formulation is used to manage the deformations of the uid domain. The formulation uses uid velocity, pressure, and pseudo-solid displacements as unknowns in the o w domain and displacements in the structural components. The adaptive formulation is veried on a problem with a closed form solution. It is then applied to sensitivity analysis of three elastic plates placed in a channel o w. Sensitivities are used for fast evaluation of nearby problems (i.e. for nearby values of the parameters or geometric characteristics) and for cascading uncertainty through the Computational Fluid Dynamics/Computational Structural Dynamics code to yield uncertainty estimates of the deformed plates shape.