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27
FSI
for membrane structures
Aaron
Kneer, Tinnits Technologies GmbH
Buildings with membrane structures are often used to cover large areas, and are often subjected to large loads, both thermal and structural. Wind loading is by nature unsteady, fluctuating in direction and amplitude in response to both discrete gusts and longer-term diurnal variation. Even in an apparently steady wind, the membrane loading will be influenced by the unsteady wake of nearby buildings.
In
order to fully simulate the membrane behaviour in the design process,
it is
usually necessary to couple a CFD code with a structural
analysis code.
In this article we describe how this can be achieved
by coupling CD-adapco’s CFD software with the membrane code SCOOP
(which is based on the Finite Element Method).
Fluid-structure
coupling method The coupling is achieved on a node-to-node basis,
using an automated process that constructs the structural mesh directly
from the boundary of the CFD mesh, obviating the need to map or
interpolate data between the solvers.
The membrane is represented
as a baffle in the CFD code and as
a shell element in the FEM
solver. At each time-step the FEM solver calculates
the membrane
displacements from the pressure loading calculated by the CFD model.
Displacements are calculated for each node of the membrane and,
within the CFD solver, used to distort the membrane and surrounding
mesh to the new position. In order to maintain the quality of the hexahedral
cells
adjacent to the membrane a number of smoothing cycles are performed.
The
CFD solver then calculates new pressure loadings, which are used
by the FEM solver to calculate new displacements in the next timestep.
The modularity of the SCOOP framework, its flexible data structures
and intelligent interface methods allowed a very tight coupling
between the membrane solver and CD-adapco’s CFD software.
The membrane parameters for the structural model were taken from the results of material tests performed by Labor Blum (Figure 2) so that the model could take account not only of the actual membrane stresses, but also of warp and weft orientation, surface curvatures, load ratios and load history.
Figure 3 shows a simple test case that represents the flow through a channel containing a membrane with a hole in the middle. A fixed air velocity of 1 m/s is prescribed at the inlet boundary, and the simulation shows how flow is accelerated through the orifice and how the calculated pressure loading distorts the membrane.
FSI
model of Fröttmaning station
In
order to validate this approach using a realistic scenario, a coupled
analysis was performed for the 5,054m2 roof membrane of Fröttmaning
station in Germany (Figure 1), for which extensive model-scale wind
tunnel data has been gathered. A computational model was constructed
that included not only the station and its roof, but also the surrounding
buildings and topography.
The station roof is constructed from fifteen identical membrane segments that are stabilized using a steel construction with a wall protecting the rear of the station. To represent this a computational mesh of 550,000 hexahedra was constructed, with some 10,000 baffle cells representing the membrane. In addition to the station itself, the mesh also includes solid obstructions that represent surrounding buildings, trains and bridges (Figure 4). For the preliminary simulation an oblique wind direction was prescribed and pressure loadings and displacements are shown in Figures 5 and 6 and predict a maximum membrane displacement of around 10mm.
Conclusion
The
methods and results presented within this article show that large
membrane structures can be modelled in using fully coupled fluid-structure
interaction modelling. Using this FSI-technology realistic displacements
of membrane constructions can be computed under different wind loadings,
providing valuable design data to the membrane community.
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