Reduction for Fluid-Structure Interaction Problems with Structural Non-Linearities

摘要

This paper presents a modal reduction method for a fluid structure interaction problem including localized non-linearities. Researches have been usually focused on linear coupling problem, but non-linear effects appear in many industrial applications. A study of a structure presenting non-linear behaviour due to the large displacements imposed, coupled with a fluid presenting linear behaviour is carried out. The description of the variation formulation based on structural displacement and fluid pressure variation is first presented. Matrix equation using the finite element method (FEM) is written in the time domain. Using uncoupled modal bases for modal reduction leads to an inadequate model compared to the original one. Coupling is considered by including residues issued from the fluid response due to the structure. Non-linear information is added to the Ritz basis by inserting the static response of the structure due to unit forces applied on the localized nonlinear degrees of freedom. A singular value decomposition of the basis is finally used to insure proper conditioning of the problem. In the time domain, the problem is solved by using the implicit Newmark algorithm coupled with a Newton-Raphson correction to take into account the nonlinear effects. A numerical application based on an exhaust is presented. The comparisons between the full and reduced models show the necessity to include residue terms in the Ritz bases to ensure fast convergence.