Volume-dependent pressure loading and its influence on the stability of structures

Deformation-dependent pressure loading on solid structures is created by the interaction of gas with the deformable surface of a structure. Such fairly simple load models are valid for static and quasistatic analyses and they are a very e cient tool to represent the in uence of gas on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of in nite gas volumes, the current contribution is focusing on the in uence of modi cations of the size and shape of a nite volume containing the gas in particular on the stability of structures. The linearization of the corresponding virtual work expression necessary for a Newton-type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. The discretization with nite elements leads to standard sti ness matrix forms plus the so-called load sti ness matrices and a rankone update for each enclosed volume part, if the loaded surface segments are identical with element surfaces. Some numerical examples show rst the e ectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the following linearization into account, and second the particular in uence of this term on the stability of structures is shown with some speci c examples.