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Volume Dependent Pressure Loading and its Influence on the Stability of Structures

Volume Dependent Pressure Loading and its Influence on the Stability of Structures
Autor: T. Rumpel, K. Schweizerhof
Quelle: International Journal for Numerical Methods in Engineering, 56, 2, p. 211-238, 2003

Abstract

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 quasi-static analyses and they are a very efficient tool to represent the influence of gas on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of infinite gas volumes, the current contribution is focusing on the influence of modifications of the size and shape of a finite 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 finite elements leads to standard stiffness matrix forms plus the so-called load stiffness matrices and a rank-one update for each enclosed volume part, if the loaded surface segments are identical with element surfaces. Some numerical examples show first the effectiveness 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 influence of this term on the stability of structures is shown with some specific examples.