On the static interaction of fluid and gas loaded multi-chamber systems in large deformation finite element analysis

Abstract

Completing previous studies [5], [6], [18], [19] and [20] on the deformation dependence of gas or fluid loadings with the assumption of finite gas and fluid volumes, the current contribution focuses on the influence of modifications of the size and shape of a finite structure filled with combinations of gas and incompressible or compressible heavy fluid. In contrast to the previous contributions [5], [18], [19] and [20], where different finite element formulations for some specific load cases were derived, this derivation provides a general formulation of a multi chamber system filled with gas and additional compressible heavy fluid. By introducing two stiffness parameters it is possible to reduce the formulation to the pure pneumatic or hydrostatic load cases described in earlier works. Further on it will be shown how to manage the modification of the load cases during the loading process. The linearization of the corresponding virtual work expression, necessary for a Newton-type solution algorithm, leads to additional terms for the volume dependence [6], [19], [20] and the expected fully symmetric stiffness matrix. The discretization of the solid structures with finite elements leads to standard stiffness matrix forms for the structures plus the so-called load stiffness matrices [26] and several dyadic rank updates -depending on the type of filling -for each filled structure part, assuming that loaded surface segments are identical with the element surfaces. A further focus is on a specific solution scheme exploiting the dyadic rank update structure. Some numerical examples show the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the linearization into account.

Nonlinear Finite Element Analysis of Inflatable Prefolded Membrane Structures under Hydrostatic Loading

“…Because all terms have already been derived in detail in [7] and [10], they will only be briefly presented in this contribution. The virtual potential…”

“…by FE or boundary elements is necessary. A further contribution of the authors group currently being in progress [7] merges all these results and thus provides a unified formulation for closed chambers containing any combination of volume dependent loading. Therefore the notations in the current contribution were adopted from [7].…”

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

“…Hence no FE discretization of the fluid or the gas is necessary. A further contribution of the authors group currently being in progress [4] merges all these results and thus provides a unified formulation for closed chambers containing any combination of volume dependent loading. Therefore the notations in the current contribution were adapted from [4].…”

“…Because all terms have already been derived in detail in [4] and [6], they will only be briefly presented in this contribution. The virtual potential…”

“…The incremental pressure changes can also be directly adapted from [9], [4]. The mass conservation of the fluid and the adiabatic state equation of an ideal gas with e.g an isentropic exponent κ = 1.4 then lead to:…”