Scanning in 3D and analysing the models of Heinz Isler,
the preliminary results
Andrew BORGART
1and Peter EIGENRAAM
21
Faculty of Architecture, Delft University of Technology, Delft, The Netherlands,
a.borgart@tudelft.nl
2
Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands, peter.eigenraam@gmail.com
Summary
During his live Heinz Isler built around 1400 shell structures, until he deceased in 2009. Heinz Isler is part of a Swizz tradition of structural art in the 20th century, which includes engineers such as Robert Maillart, Othmar Ammann und Christian Menn [1].
During his live Heinz Isler developed several methods for physical form finding of his shell structures [2, 3]. Methods such as hanging models, inflated membranes etc. The physical scale model where used for determining the strains and stresses in the shell structure. This was done by loading the scale models and measuring the strains and consequently calculating the stresses. The geometry of the scale models was used for the actually build shell structures by precisely measuring the scale models and scaling these up to the real size shell. Analysing Isler’s shells has always been impossible because Isler never published the precise geometry of his shell structures. Isler’s model where scanned for the first time ever in 2011, the results where used to construct NURBS (Non Uniform Rational B-spline) surfaces which describe the exact geometry of Isler’s scale models. The results are used for all kinds of analysis, such as finite element (FEM) calculations, curvature analysis etc. This means that for the first time a qualitative investigation can be made of Isler’s shell structures. This paper will present the first results. Hopefully it will give us a greater insight in the relation between geometry and the structural behaviour of shell structures.
Keywords: Heinz Isler: concrete shells: structural art: models: 3D scanning: finite element and
curvature analysis
1. Introduction
Shell structures designed by Heinz Isler became famous for their structural efficiency and beauty. The method of designing shells by Heinz Isler was different from that of most shell designer. Where others choose mathematically defined surfaces Isler choose a different approach. In his paper 'New shapes for shells' [4] he shortly described the specific design methods used for form finding his shell structures. He also developed his own methods for recording the geometry of his form fined physical models; Isler measured thousands of points on a surface of a model (Fig. 1) as to be able to describe the precise geometry of the shell and then used railway model tracks to create smooth curves.
Fig. 2: Precision measuring equipment used by Heinz Isler.
Technology has developed and the manual work done by Heinz Isler to capture the geometry of his models would these days be done in a different more computational way. Nowadays we can measure millions of points on the surface of his models by using full automatic 3D scanners and create NURBS surfaces to digitally describe the geometry.
It would seem technology made his job a lot easier, but unfortunately this is not entirely true. We still face the same challenge Isler was facing. Despite modern technology transforming all the scanned points into really smooth surfaces still requires a lot of effort.
Fig. 3: Isler’s models in his workshop and Bellinzona model, 2011
Mid 2011 the ETH Zurich, who became the beneficiary of Isler’s legacy, started taking inventory of his scale models in his previous office and workshop in Lyssachschachen, near Bern, in Switzerland. His office was cleared in 2011 and his scale models and archive where taken to the ETH Zurich. In July a group of researchers from the Delft University of Delft, namely Andrew Borgart, Peter Eigenraam, Jaco Timmers and Bas Altena went to Isler’s office to make 3D scans of his scale models in high resolution. This was done with a FARO laser scanner during two days. The larger than his most models, the Bellinzona scale model in the grounds outside the office was also scanned (Fig. 2). This produced lots of data (point clouds) waiting to be analyzed. This paper describes way we used to convert the point clouds into NURBS surfaces which can be imported into FEM software for structural analysis or into 3D modelling software for curvature analysis.
Fig. 4: FARO Photon scanner, scanning Isler’s models in his workshop, 2011
The Isler models where scanned with a FARO Photon 120 3D scanner (Fig 3). The results from the scan, cloud points, are saved in a file produced by the FARO scanner software. Several models where scanned in one run, after which all models are to be converted separately cutting out the unnecessary background (Fig. 4). The scans are then exported individually to the cloud point editing programme Cyclone cleaning up the scan by removing the redundant points.
Fig. 5: Scanned result FARO software, cleaned-up scan in Cyclone
The cleaned-up point clouds are converted into NURBS surface by using the RhinoResurf programme. The for each models created NURBS surface can now be imported into a FEM or 3D modelling programme for respectively structural and curvature analysis (Fig. 5).
The accuracy of the created surface is reported in RhinoResurf or Rhino (Fig. 6). It is important to find a good accuracy but also to create a smooth surface. The smoothness of the surface can be controlled in two ways; by smoothness settings or number of control points of the NURBS surface. The number of control points is the most influencing parameter. Fewer control point means a smoother surface, but results is larger deviations from the point cloud. A good optimum has to be found.
Fig. 7 Report on the accuracy of the fit between the point cloud and the NURBS surface
The results of a first FEM calculation of an imported NURBS surface showed the scanned models are not symmetric, which is a consequence of using physical models for form finding. Isler
addressed this issue by only used a symmetric part of the models for measurements. This part is later mirrored or rotated to form the entire surface. This could also be done in 3D modelling programme used, Rhinoceros. This would result in symmetrical results. It does show that the
calculated structure could be sensitive to shape imperfections. The second observation revealed that the distribution of internal forces is influenced by the smoothness of the surface. Therefore attention should be given to the smoothness when creating a NURBS surface from a point cloud. It is a challenge to find a smooth and accurate surface.
3. First results of analysis
Fig. 8 The construction of Isler shells in Norwich Sports Park, Norwich England, 1991 The first results presented in this paper of the finite element and curvature analysis concerns a shell design Isler made for sports halls. This shell was built in different places in Switzerland and also in
England (Fig. 7). Isler form fined this shell by using a hanging model; he made several models of this particular shell (Fig. 8). The results shown here is the scan of one of these models. In a further paper the results will be compared to each other of all the results in this scanned series.
Fig. 9: Several hanging models made by Isler of the sports hall
From this scanned model presented in this paper a NURBS surface was extracted from its point cloud (Fig. 9), which was consequently imported into a Rhino for curvature analysis and into a finite element programme (DIANA) for structural calculations.
The first results of the analysis will be presented and preliminary discussed here, as they have been recently obtained. In further studies these and other, yet to be achieved, results will be studied more in-depth. These results, apart from the curvature and finite element analysis, will also be used to test several exciting and newly developed (analytical) theories concerning shell structures. With the aim to make these theories more insightful and to be able to truly understand the physical behaviour of shell structures, which will give the (structural) designer a better understanding for designing effective and beautiful shells.
Fig. 10: NURBS surface of the sports hall model, showing coordinate reference and sections used for analysis
The results of the curvature and finite element analysis are shown in figures 10, 11 and 12. As mentioned before these results are preliminary. The load case for the finite element calculation is the self weight of the shell. Additional load cases, such as wind and snow, will follow in further
x
y
publications. The results will be briefly commented on.
The mean curvature is equal to half the sum of the principal curvatures, if the mean curvature is zero the surface is a minimum surface, like that of a soap film. The Gaussian curvature is equal to the product of the principal curvatures, a positive value of the Gaussian curvature represent of synclastic curvature and a negative value of the Gaussian curvature an anticlastic curvature. In the image below one can observe that large part (expect the edge zones) of this shell has a mean curvature of nearly zero, which would suggest this part is much like a soap film (Fig. 10). This is also confirmed be inspecting the distributed internal normal forces, which are for the most part constant, much like that in a soap film (Fig. 11).
By observing the Gaussian curvature is can be clearly seen that the edge zones have anticlastic curvature (bleu zones), and the mid part of the shell has synclastic curvature (green zones).
Fig. 11: Curvature analysis of the sports hall; top image the Mean curvature, bottom image the Gaussian curvature
Fig. 13: The distributed internal normal force in y-direction as contour plot, the distributed internal bending moments is x-direction, in cross section 1 and the principle stress trajectory
The curved sides on the short sides act like arches (top image Fig. 12).
Also one can be observed that the distributed bending moments (middle two images Fig. 12) at the curvature change between the synclastic top part of the shell and the anticlastic long edges of the shell increase. This would imply the edges have a stiffening effect.
The principle stress trajectories (bottom image Fig. 12) suggest confirming the “rain flow” analysis [5]; “like a rain flow loads will flow along curves with the steepest ascent on the shell surface to its
supports”.
4. Conclusions
Getting all the relevant results from the scans of the models of Heinz Isler will take more work, investigations and research. It may prove to be essential for further understanding his methods for designing shells which could help future architects and engineers to develop new types of shell structures. Ekkehard Ramm once called shells the prima donna of structural design. The outcome of this research could at least tame this elusive lady.
In papers to come we will publish the next steps in uncovering the work of Heinz Isler.
The authors would like to warmly acknowledge to invaluable support of John Chilton, Toni Kotnik and Duks Koschitz for their support in making the scanning of the models of Heinz Isler possible.
References
[1] Billington, D.P., The Tower and the Bridge: Ten New Art of Structural Engineering, Princeton University Press, 1985
[2] Chilton, J., Heinz Isler (Engineer’s contribution to Architecture), Thomas Telford Publishers, 2000.
[3] Ramm, E., Schunck, E., Heinz Ilser Schalen: Katalog zur Austellung, Vdf Hochschulverlag Ag Publishers, 2002.
[4] Isler, H., Heinz Isler as Structural Artist, Exhibition book, Princeton University, 1980
[5] Borgart A., Leuw de, M., Hoogenboom, P., The Relationship of Form and Force in (irregular) Curved Surfaces. Proceedings of the 5th International Conference on Computation of Shell and Spatial Structures, Salzburg, 2005
