Vibration Analysis of Thin-Walled - Gas or Fluid Filled - Struc- tures Including the Effect of the Inflation/Filling Process

Fluid-structure interaction problems involving thin-walled membrane and shell-type structures undergoing large deformations can be considered in a step-wise fashion. Using conventional finite elements [1],[6],[8] for the discretization of the fluid or gas domain leads to heavily distorted meshes for the fluid if e.g. inflation or filling processes including large deformations are to be investigated. Although with ALE based algorithms this problem can be solved by a permanent remeshing of the fluid domain parts in the vicinity of the structural mesh, this is at the expense of high computational effort. Benefitting from an algorithm, which replaces the fluid or gas filling by an energetically equivalent volume dependent surface loading (see e.g. [2]-[5] and [7]) such primarily static inflation processes can be simulated without discretizing the fluid or gas domain. Thus the deformation dependent inner state variables of the fluid or gas can be computed avoiding the previously mentioned difficulties with mesh distortions in an efficient way. In a following step the fluid parameters such as fluid level and information about the wetted structural parts can then be used to define properly the initial conditions for a dynamic finite element analysis of gas or fluid filled structures while using standard acoustic finite elements to compute e.g. vibration modes. 1 Virtual Work Approach of Gas or Fluid Loaded Structures For a state of equilibrium in a system consisting of a fluid domain F and a solid domain B the variation δE of the total energy has to fulfill δE = δE + δE = 0 . (1) Assuming an adiabatic system, without any heat change δQ, the energy conservation in the fluid and solid domain only consists of the variations δT B∪F and δU of the kinetic and the internal energy and of the virtual work δW of the external forces. δE = δT B∪F + δU − δW = 0 (2) Introducing the virtual displacement field δu, the accelerations ü and the density ρ, the variation of the total kinetic energy can be written as δT B∪F = ∫ B∪F ρü · δu dv . (3)