Computational engineering for wind-exposed thin-walled structures

Computational engineering for
wind-exposed thin-walled structures
Ansgar Halfmann, Ernst Rank
Lehrstuhl für Bauinformatik, TU München
Markus Glück, Michael Breuer, Franz Durst
Lehrstuhl für Strömungsmechanik,
Universität Erlangen-Nürnberg
Jürgen Bellmann, Casimir Katz
SOFiSTiK AG, München
März 2001
Bauinformatik
BAUINGENIEUR− UND VERMESSUNGSWESEN
TECHNISCHE UNIVERSITÄT MÜNCHEN

Prof.Dr.rer.nat. Ernst Rank
Lehrstuhl für Bauinformatik
TECHNISCHE
UNIVERSITÄT
MÜNCHEN
Fakultät für Bauingenieur- und Vermessungswesen
Technische Universität München
Arcisstr. 21
D-80290 München
email: rank@bv.tum.de Telefon: int++49 (89) 289 23048
www: http://www.inf.bauwesen.tu-muenchen.de/ Telefax: int++49 (89) 289 25051

Computational engineering for
wind-exposed thin-walled structures
Ansgar Halfmann, Ernst Rank
Lehrstuhl für Bauinformatik, TU München
Markus Glück, Michael Breuer, Franz Durst
Lehrstuhl für Strömungsmechanik,
Universität Erlangen-Nürnberg
Jürgen Bellmann, Casimir Katz
SOFiSTiK AG, München
März 2001

Computational engineering for wind-exposed
thin-walled structures
Ansgar Halfmann 1 , Ernst Rank 1 , Markus Gluck 2 ,Michael Breuer 2 ,Franz
Durst 2 ,Jurgen Bellmann 3 , and Casimir Katz 3
1 Lehrstuhl fur Bauinformatik, Technische Universitat Munchen, 80290 Munchen,
Germany
2 Lehrstuhl fur Stromungsmechanik, Universitat Erlangen-Nurnberg,
91058 Erlangen, Germany
3 SOFiSTiK AG, 81541 Munchen, Germany
Abstract. In this paper a computer-aided simulation approach for uid-structure
interaction of wind-exposed structures is presented. In the center of our software
architecture is the geometric model of the structure, from which a nite element
mesh for the structure and a nite volume mesh for the uid are derived. The
attention is concentrated to thin-walled structures like membranes and thin shells
composed of light and exible materials. The interaction of uid and structure is
eected by wind-induced vibrations and causes large elastic deformations of the
structure. A powerful simulation tool is provided by couplingtwo codesdeveloped
for ow simulation and structural dynamics by a fully implicit coupling algorithm.
Results of three-dimensional simulations of uid-structure interaction for several
test cases as well as for a real-life example will be presented.
1 Introduction
During the last few years much progress has been achieved to integrate
analysis and design in civil engineering [9]. The computer-aided design process
starts by setting up a geometric model being used for the denition
of all structural properties as well as for the loads on the construction.
From this geometric model a computational model is derived as the basis
for the following dimensioning of the construction. This computer-aided
engineering process has to support
eciently the primary goals of any
civil engineering design, i.e. the development
of constructions satisfying
the requirements of safety during
their whole lifetime, resisting all
expected inuences they might be
exposed to. Considering for example
light textile constructions like
the convertible shade roof for a
large court of the Prophet's Mosque
in Madinah consisting of several Fig. 1. Convertible shade roof [10]

2 Ansgar Halfmann et al.
large umbrellas (Fig. 1 [10]), the most demanding engineering task is to
dimension the construction so that it will resist wind loads. Following the
Davenport-Wind-Load-Chain an assumed local wind prole for a given terrain
can be established according to the European Design Code EC 1 [5].
This wind distribution causes a pressure eld on the structure. If simplied,
conventional load assumptions for this pressure distribution are made, the
structures may be strongly over-designed. Yet, also an under-design with the
danger of a collapse may result from this simplied procedure, as the mutual
inuence of neighbouring constructions could change the wind pressure eld
dramatically. Therefore, todays standard of practice are time-consuming and
costly experiments in wind tunnels. A model of the construction is considered
and wind pressure elds on its surface are measured to be used for later
numerical structural analysis. One of the major drawbacks of this mixed computational
and experimental approach is the diculty toquickly change the
geometry of the model construction for the wind tunnel experiment. Therefore,
it would be highly desirable to have a'numerical wind tunnel' available,
being directly integrated in the civil engineering design and analysis process,
and enabling to investigate a structure also under the inuence of neighbouring
constructions. Several steps in this direction have been performed by the
authors in a joint research project during the past two years and will be
presented in this contribution.
2 Software architecture
The software architecture shown in Fig. 2 is inuenced by the idea of a loose
coupling strategy based on highly specialized and well evaluated simulation
codes, each developed for the special eld of the interacting system. In a
rst step, the structural model is dened, using a classical CAD environment
onaPCoraworkstation. Toconsider
dierent stress distributions
in a membrane, it is possible to
compute the geometric shape of
pure membrane structures in a
formnding process [2]. Thereby
the deformed shape of the structure
under dead load is computed
by a nite element analysis starting
from an inital geometry. Using
special membrane elements
and assuming an initial stiness
caused by isotropic prestressing
PC / workstation
supercomputer
STL-file
ICEM-CFD
fluid-simulation
FASTEST-3D
Geometrical Model
+boundary conditions
AutoCAD / SOFiPLUS
formfinding process
MpCCI
SOFiMESH
DO_MESH
structure-simulation
ASE
creates
PC / workstation TECPLOT / Explorer Wingraf / Animator
CDBASE
Fig. 2. Software structure
and neglecting any bending stiness, the deformed shape will lead to the
soap lm form with its constant isotropic stress distribution. All geometric
information is stored in a database describing a b-rep (boundary repre-

Computational engineering for wind-exposed thin-walled structures 3
sentation) model completed by information concerning material properties
and boundary conditions [9]. For the structural part of the analysis system
this project database represents a central module. All programs used
for the structural simulation have access to the information stored in the
database. The geometric model for the uid dynamic part is also derived
from the CAD model completed by boundary conditions and discretized as a
block-structured three-dimensional grid being adequate to the nite volume
technique. Due to extremely high computational requirements, the numerical
simulation of the dynamic uid-structure interaction is performed on a
high-performance computer [8] in the next step. Thereby the data transfer between
the two simulation codes, each running on dierent nodes/processors,
is performed via a common geometric model using a suitable coupling interface
[1]. Finally, the results can be evaluated and visualized by powerful
postprocessors on a workstation or on a PC.
3 Coupling algorithm
The uid-structure interaction is described by the structural deformations
as response to wind forces, resulting in a modication of the uid ow domain.
The coupling is performed by a partitioned solution approach [3]. The
Computational Fluid Dynamics (CFD) simulations are performed by a nite
volume based code [4] solving the Reynolds-Averaged-Navier-Stokes (RANS)
equations using a two-equation k- model. It is adapted to moving grids
by an Arbitrary Lagrangian Eulerian (ALE) formulation. For the Computational
Structure Dynamics (CSD) the dynamic non-linear structural response
(large displacements/small deformations) is described by the equations of
motion based on a nite element approach and an implicit time-stepping
procedure [11]. For more details concerning the simulation codes we refer
to [6]. The time-dependent simulation process is controlled by the coupling
algorithm shown in Fig. 3. The
solution is based on an iteration
Fluid Structure
procedure between the CFD
and CSD simulation until convergence
is reached within each
Solver
inner iteration
time-step. Thereby the nodal
loads as input for the CSD
Fluid solution
outer FSI iteration
simulation are computed from
wind loads
the results of the CFD simulation
Solver
time step
(pressure and wall shear
Structural solution
stresses). The updated boundary
displacements
geometry is based on the structural
displacements as a result of
converged final solution
the CSD simulation. In cases of
large structural deformations an
Fig. 3. Coupling algorithm

4 Ansgar Halfmann et al.
under-relaxation of the update of the boundary geometry was found to improve
the convergence signicantly. A reduction of the number of iterations
within each time-step can be obtained by a predictor-corrector scheme [6].
Informations concerning the data transfer between the dierent numerical
grids can be found in [7].
4 Numerical examples
The coupling procedure presented in the previous section was applied to
several test cases. In the following the results of two elementary systems will
be discussed with respect to dierent parameters for spatial and temporal
discretization. Based on this, the coupled application was used to simulate
the uid-structure interaction of a complex membrane structure.
4.1 Vertical plate in a resting uid
The rst example describes a temporarily loaded rectangular plate clamped at
the lower boundary in a closed cavity of a resting uid. The dimensions of the
exible plate pictured in Fig. 4 are length/width/thickness = 1.0/0.4/0.06 m.
For the material properties a polyester with
a modulus of elasticity of E = 2.5 MPa, a
Poisson's ratio of =0:35 and a density of
S = 2550 kg/m 3 is assumed. The density
and dynamic viscosity of the uid are F =
1kg/m 3 and F =0:2 Pa. Using these parameters,
a laminar ow is expected. During
the rst ve time-steps a constant load
is applied in x-direction. After removing the
Fig. 4. System conguration
load the plate executes oscillations induced by the initial deection damped
by the surrounding uid ow.
In a rst simulation the inuence of the time-step size was investigated.
The uid domain was discretized by 1650 hexaeder elements, yielding 10
quadrilateral elements to describe the interface. For the structural simulation
a surface mesh of 8 elements was chosen. Both surface discretizations are
shown in Fig. 5. Due to the boundary conditions for the uid simulation
the results of the coupled three-dimensional simulation shows a quasi twodimensional
behavior. Fig. 6 points out the computed displacement of the
upper boundary of the plate for simulations with three dierent time-step
sizes. The amplitude of the plate oscillation is damped by theambient uid.
For the dierent time-step sizes only small deviations could be identied.
Therefore, t 1 =0:025 s was chosen for the following simulations.
The dependence of the displacement on dierent spatial discretizations
is depicted in Fig. 8. Starting again from a discretization of 1650 hexaeder
elements for the uid domain (10 quadrilaterals on the interface, Fig. 7) a

Computational engineering for wind-exposed thin-walled structures 5
250
CFD
18 nodes,
10 elements
CSD
15 nodes,
8 elements
Fig. 5. Discretization of the interface
displacement upper boundary [mm]
200
150
100
50
0
−50
−100
−150
t 1 = 0:025 s
t 2 = 0:0125 s
t 3 = 0:00625 s
−200
0 0.5 1 1.5 2 2.5 3 3.5
time [s]
Fig. 6. Displacement for dierent t
uniform renement was performed in two levels which leads to 13,200
and 105,600 hexaeder elements and 40 or 160 quadrilaterals for the interface,
respectively. The coarsest grid for the CSD simulation consisting of only 2
elements is also shown in Fig. 7. Uniform renement yields surface meshes of
8 or 32 quadrilateral elements for the structure simulation, respectively.
CFD
18 nodes,
10 elements
CSD
6nodes,
2 elements
Fig. 7. Initial interface discretization
displacement upper boundary [mm]
300
250
200
150
100
50
0
−50
−100
−150
CFD10=CSD 2
CFD40=CSD 8
CFD160=CSD 32
−200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
time [s]
Fig. 8. Displacement for dierent interface
discretizations
Fig.8points out the insucient accuracy of the results corresponding to
the initial interface discretizations and the good agreement of the transient
displacements achieved with the rened meshes. In particular the CSD mesh
consisting only of 2 elements for the y-direction is too coarse to obtain useful
results.
4.2 Vertical plate under a sudden wind gust
The geometry and material properties of the second test case are the same
as before. Fig. 9 shows a cutting plane through the uid domain which is
open with an inlet (left boundary), an outlet (right boundary), and symmetric
boundary conditions at the top as well as in z-direction. At the beginning
of the coupled simulation the uid suddenly accelerates and adopts

6 Ansgar Halfmann et al.
immediately a constant inowvelocity
ofU1 = 10 m/s being equivalent
to a Reynolds number of Re L =50.
As a consequence the structural oscillations
are induced by the saltus
of the uid velocity and reach a
stationary deformation state after a
certain time. Fig. 10 shows again the
displacement of the upper boundary
of the plate for various timestep
sizes. The interface discretizations
comply to the grids pictured in
Fig. 5. Only minor distinctions could
be identied for the dierent time
discretizations. Furthermore, the in-
uence of the spatial interface discretization
was investigated using
the grids shown in Fig.11 and performing
an uniform renement of
two levels for the CSD grid whereas
the mesh for the uid domain remains
unchanged. It is again obvious
displacement upper boundary [mm]
U
8
70
60
50
40
30
20
10
y
1111111111111111111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000000000000000000
A
Fig. 9. System conguration
0
0 0.5 1 1.5 2 2.5 3 3.5
time [s]
B
L
t 1 = 0:025 s
t 2 = 0:0125 s
t 3 = 0:00625 s
t 4 = 0:003125 s
t 5 = 0:0015625 s
Fig. 10. Displacement for dierent t
that the bending oscillations of the plate cannot be represented suciently
accurate by a CSD mesh with only two elements in y-direction, see Fig. 12.
x
CFD
18 nodes,
10 elements
CSD
9nodes,
4 elements
Fig. 11. Initial interface discretization
displacement upper boundary [mm]
60
50
40
30
20
10
CFD10=CSD 4
CFD10=CSD 6
CFD10=CSD 8
0
0 0.5 1 1.5 2 2.5 3 3.5
time [s]
Fig. 12. Displacement for dierent CSD
interface discretizations
4.3 Tent roof
Fig. 13 shows a screenshot of the CAD-environment representing the geometric
model of a real-life structure as a starting point for the simulation.

Computational engineering for wind-exposed thin-walled structures 7
The shape of the structure is a result of the formnding process sketched
in Section 2 and species a textile roof being positioned in front of an oce
building. A material of glass-bre synthetics with a thickness of 1.5 mm, a
modulus of elasticity ofE =3000MPa, and a shear modulus of G =1500
MPa is assumed. The structure is 24 m long and shows a width between 3
m and 8.5 m. The boundary of the block-structured three-dimensional CFD
grid on the interface and the CSD surface grid are shown in Fig. 14 and 15.
Due to the fact that the k- model produces non-physical results for such
complex geometries the CFD simulations were performed neglecting turbulence
in this rst step. The velocity distribution of the assumed wind gust and
the displacement as structural response are pictured for four dierent timesteps
in Fig. 16. The gust leads to a maximal displacement in z-direction of
z max =31cm.
3536 nodes,
3400 elements
Fig. 14. CFD interface discretization
1409 nodes,
1311 elements
Fig. 13. Geometry of the tent roof
Fig. 15. CSD interface discretization
Fig. 16. Velocity distributions and diplacements of four dierent time-steps
(t 1 =2:0 s,t 2 =3:0 s,t 3 =4:36 s and t 4 =4:46 s)

8 Ansgar Halfmann et al.
5 Conclusions
The partitioned solution approach has been investigated for the simulation of
uid-structure interaction of light civil engineering constructions under wind
load. Before the outlined concept could be a practically used procedure, it will
be necessary to incorporate more elaborate turbulence modeling such as largeeddy
simulation, perform more numerical tests and compare the numerical
results with veried experimental data. If thus sucient condence is gained
in this simulation technique, it can be an application of high-performance
computing with signicant impact on engineering practice.
Acknowledgements
The work was nanced by the Bayerische Forschungsstiftung in the Bavarian
Consortium of High-Performance Scientic Computing, FORTWIHR (III).
The simulations were partially carried out on the Hitachi SR8000-F1 at the
LRZ Munchen [8]. This support is gratefully acknowledged.
References
1. Ahrem, R., Hackenberg, M.G., Post, P., Redler, R., Roggenbuck, J. (2000)
MpCCI { Mesh Based Parallel Code Coupling Interface. Institute for Algorithms
and Scientic Computing (SCAI), GMD, http://www.mpcci.org/
2. Bellmann, J. (1998) Membrantragwerke und Seifenhaut { Unterschiede in der
Formndung. Bauingenieur, 3/98, 118{123
3. Cebral, J.R. (1996) Loose Coupling Algorithms for Fluid-Structure Interaction.
Ph.D.-Thesis, George Mason University Fairfax, Virginia
4. Durst, F., Schafer, M. (1996) A Parallel Block{Structured Multigrid Method
for the Prediction of Incompressible Flows. Int. J. Num. Methods Fluids 22,
549{565
5. EUROCODE 1 (1995) Basis of Design and Actions on Structures Part 2-4: Actions
on Structures - Wind Actions. European Committee for Standardization
Ref. No. ENV 1991-2-4
6. Gluck, M., Breuer, M., Durst, F., Halfmann, A., Rank, E. (2000) Computation
of Fluid-Structure Interaction on Lightweight Structures. Proceedings of
Fourth International Colloquium on Blu Body Aerodynamics & Applicastions,
Bochum, To appear in J. of Wind Engineering and Industrial Aerodynamics
7. Halfmann, A., Rank, E., Gluck, M., Breuer, M., Durst, F. (2000) A Partitioned
Solution Approach for the Fluid-Structure Interaction of Wind and
Thin-Walled Structures. Proceedings of IKM 2000, Weimar
8. http://www.lrz-muenchen.de/services/compute/hlrb/.
9. Rank, E., Halfmann, A., Rucker, M., Katz, C., Gebhard, S. (2000) Integrierte
Modellierungs- und Berechnungssoftware fur den konstruktiven Ingenieurbau:
Systemarchitektur und Netzgenerierung. Bauingenieur, Februar 2000, 60{66
10. Sonderkonstruktionen und Leichtbau GmbH (1993) The Work of SL.
Leinfelden-Oberaichen
11. SOFiSTiK AG (2000) ASE{Handbuch. Munchen