On the Stability Analysis of Thin Walled Shell Structures Containing Gas or Fluid

Thin shell or membrane structures containing gas or fluid are widely standard, such as oil and water tanks, gas containers or even atmospheric balloons, pressurized girders or inflatable dams. For such thin walled structures the gas or fluid can be considered either as support or loading. It may have a major influence on the stability behavior under other external loading as for example in the Tensairity-concept [

2

], where internal air pressure in combination with some external strengthening is used to overcome buckling of thin walled girders. The goal of this contribution is to present some investigation of the influence of such a gas or fluid support on the stability, here the eigenvalues and eigenmodes of the stiffness matrix of shell or membrane-like structures undergoing large displacements. For this purpose an analytical meshfree or lumped parameter description for the fluid/gas (see also [

1

], [

3

], [

4

])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 first to the so-called load-stiffness matrix [

5

], to which several rank-one updates depending on the volumes containing either gas or fluid or both are added. These rank updates are a key part in the stability analysis: They describe the different coupling of the fluid or gas volume modification with the structural displacements in addition to the deformation dependence of the standard pressure. The specific rank-one updates allow the derivation of a very efficient algorithm to compute the change of the eigenvalues and eigenmodes of the original stiffness matrix without gas or fluid loading or support.