Efficient Finite Element Modelling and Simulation of Gas and Fluid Supported Membrane and Shell Structures

Rumpel, T.; Schweizerhof, Karl; Haßler, Marc

doi:10.1007/1-4020-3317-6_10

Cited by 17 publications

(18 citation statements)

References 6 publications

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“…later discretized by FE or BE. Sectioning both control volumesv g andv f a three dimensional projection of the geometry for the virtual gas and fluid volumes yields, see figure 2.3, 12) see also [6], [19] and [21]. According to [7] with the surface integral formulation of a first order volume moment…”

Section: Boundary Integral Representation Of the Geometrymentioning

confidence: 99%

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

Haßler

Schweizerhof

2008

Computer Methods in Applied Mechanics and Engineering

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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.

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Section: Boundary Integral Representation Of the Geometrymentioning

confidence: 99%

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

Haßler

Schweizerhof

2008

Computer Methods in Applied Mechanics and Engineering

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“…In addition a dyadic rank two update of K f elem with the vectors a and b, which couple the increments of the discrete nodal displacents ∆d with the volume change ∆v, is achieved (for further details see [3]). The residual at a time t yields the negative right hand side vector f f elem .…”

Section: Linearization and Solutionmentioning

confidence: 99%

Simulation of Hydroforming of Metal Sheets with an Efficient FE‐Formulation Based on an Analytical Meshfree Description of a Compressible Fluid

Haßler¹,

Schweizerhof²

2005

Proc Appl Math and Mech

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Hydroforming is very interesting for the automotive industry, as it offers a great variety to efficiently manufacture thin walled structures. In order to simulate such static large deformation processes under hydraulic or pneumatic pressure, an analytical meshfree description of a compressible heavy or weightless fluid is presented. Thus a fully nonlinear formulation of the fluid-structure-interaction only based on the surface of the wetted membrane structure and the constitutive equations for the fluid can be derived. Considering physically realistic boundary conditions this formulation finally leads for all combinations of fluids and gas to a symmetric tangential stiffness matrix including several dyadic rank updates, which can be cast into a very efficient solution procedure by sequential applications of the Sherman-Morrison formula. Furthermore other algorithms such as mesh refinements and structural contact can be restricted to the models for the work piece and the matrix.

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“…, [7], [8] and [9]) 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 [11], to which several rank-one updates depending on the volume containing either gas or fluid or both are added.…”

Section: Abstract Thin Shell or Membrane Structures Containing Gas Omentioning

confidence: 99%

“…For this purpose we refer to the former contributions of the authors group [7], [8] and [9] and the works of Bonet et al [1], which dealt with gas and fluid supported shell structures and considered both the shape and volume dependence of the hydrostatic pressure distribution. With these derivations it is possible to come up with an analytical formulation of the fluid/gas only described by surface integrals over the surrounding wetted structure.…”

Section: Abstract Thin Shell or Membrane Structures Containing Gas Omentioning

confidence: 99%

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

Haßler¹,

Schweizerhof²

III European Conference on Computational Mechanics

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Efficient Finite Element Modelling and Simulation of Gas and Fluid Supported Membrane and Shell Structures

Cited by 17 publications

References 6 publications

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

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

Simulation of Hydroforming of Metal Sheets with an Efficient FE‐Formulation Based on an Analytical Meshfree Description of a Compressible Fluid

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

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