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.

Fig 01: Large membrane construction of the Fröttmaning train station

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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.