Sensitivity Analysis of fluid-structure interaction problems

摘要

Interactions between solids and fluids(FSI)have been a topic of interest for engineers for many years.The behavior of vessels subject to wave loads,of planes in flight condition as well as submarine or transmission lines are but a few examples. rnIn an attempt to address these problems,the present paper presents a formulation which allows to treat in- teractions between an incompressible flow and a struc- ture undergoing large displacements.We assume exis- tence and unicity of the solution.The interested reader is referred [3],for a mathematical discussion of exis- tence and unicity. rnThe approach to coupling can be addressed in two ways:weakly-coupled methods for which algorithms for structure and fluid are segregated,as is commonly done for simplicity and often because engineers have access to existing structural and fluid codes;and tightly-coupled or monolithic methods,for which the formulation guarantees satisfaction of equilibrium of the interface between the fluid and the solid.The latter has been chosen as it allows for quadratic convergence of Newton’s method. rnThe paper begins with the description of the steady state governing equations for laminar incompressible fluids,hyperelastic solid behaviour,pseudo-solid map- ping and fluid-structure interfaces.The weak forms of the equations are then presented.We proceed with the description of the continuous sensitivity equations for fluid-structure interactions problems.The following sections detail the adaptive finite element procedure for the fluid-structure interaction and sensitivity problems.Results are presented and the paper ends with conclusions and discussions.