On the Influence of Fluid-structure-interaction on the Stability of Thin-walled Shell Structures

The purpose of this contribution is to investigate the stabilizing influence of hydrostatic fluid and/or gas pressure supports (especially the effect of the volume dependency on gas or fluid pressures) on the stability, namely the eigenvalues and eigenmodes of the stiffness matrix of shell or membrane-like structures undergoing large displacements. For this purpose, an analytical mesh free or lumped parameter description for the fluid/gas (see also Refs. 3, 12, 13 and 14) is taken, which yields a special structure of the nonlinear equations representing the change of the gas or fluid volume or alternatively the change of the wetted part of the shell surface. Finally this procedure leads to a stiffness matrix with several rank updates — depending on the volume containing either gas or fluid or both. These rank updates are a key part in the stability analysis: they describe the different coupling of the fluid or gas volume change with the structural displacements in addition to the deformation dependence of the standard pressure. The specific rank updates allow the derivation of a very efficient algorithm to compute the modifications of the eigenvalues and eigenmodes of the original stiffness matrix without gas or fluid loading or support.