Design, Analysis and Fabrication of Expressive, Efficient Shell Structures: A Prototype exploring synergy between architecture, engineering and manufacture

Abstract

The research-prototype is a 4 x 5 x 2m, “topologically optimized” concrete shell that was designed and
built in ten days. The prototype and this ensuing paper aim to extend the rich legacy of form-finding to
adequately represent the complexities of scale, digital design systems and delivery mechanisms of contemporary architectural practice. They explore synergies in early design between architecture, structural engineering, and manufacturing.

Full text

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
15 to 19 September 2014, Brasilia, Brazil
Reyolando M.L.R.F. BRASIL and Ruy M.O. PAULETTI (eds.)
Copyright © 2014 by the authors.
Published by the International Association for Shell and Spatial Structures (IASS) with permission. 1
Design, Analysis and Fabrication of Expressive, Efficient Shell
Structures: A Prototype exploring synergy between
architecture, engineering and manufacture
Alicia NAHMAD VAZQUEZ*, Shajay BHOOSHANa, Asbjorn SONDERGAARDb,
Chikara INAMURAc, Joshua ZABELd , Mustafa EL–SAYEDa,
*Populous, London
17 Majestic Court, Portland Rise N4 2UT, London, UK.
ali_nahmad@hotmail.com
a Zaha Hadid Architects, London
b Aarhus University, Aarhus
c Sasaki and Partners, Tokyo
d Kreysler & Associates, San Francisco
Abstract
The research-prototype is a 4 x 5 x 2m, “topologically optimized” concrete shell that was designed and
built in ten days. The prototype and this ensuing paper aim to extend the rich legacy of form-finding to
adequately represent the complexities of scale, digital design systems and delivery mechanisms of contemporary
architectural practice. They explore synergies in early design between architecture, structural engineering, and
manufacturing.
Keywords: conceptual design, form finding, topology optimization, concrete shell structures,
computational design tools, structural design and analysis, CNC routing, digital fabrication, emergent economy
1. Introduction
Contemporary architectural design and construction, operates under extreme pressures of time and
resource management. Design-development times are progressively being reduced while the complexity of
spatial, structural and manufacturing parameters – are constantly increasing. Significantly, a majority of design
decisions with regard to the overall geometry of the project are made within a compacted early-design phase.
Subsequently, down-stream production and delivery processes post-rationalize such geometries whilst
attempting to retain the design intentions from the early-phases. Such a process comes at a high premium of
resources – time and personnel. Thus, there is increasingly a need to inform architectural design with critical
aspects of structural design and fabrication processes from the early stages. This paper presents the specifics of
one such time-bound collaboration, including: an examination of computational geometry and design tools and
their use in a multi-stage, collaborative design phase, application of topology optimisation methods for design
and form-finding of concrete shell structures; incorporation of structural design in early-design; and strategies to
describe complex geometry (i.e. form-work and steel reinforcement layout) onsite in a labour intensive economy
and the teaching thereof.
2. Computational geometry and design technologies
2.1. Subdivision surfaces
2.1.1. Tacit Knowledge & iteration

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
The production of simulation - friendly geometries is not a novel or relatively unresolved process in itself, as
digital simulation using particle-spring simulation frameworks is fairly well established especially following the
work of early (architectural) exponents such as Axel Killian (Kilian and Ochsendorf, 2005). However, this
section describes the production of geometries that not only satisfy that criteria but also a number of others, such
as fulfilling certain design intentions and the achieving of a desired structural performance.
This early design workflow stresses an intuitive and qualitative knowledge aided by feedback generated
between early design methods and downstream validation processes such as structurally-based topology
optimization and fabrication constraints. This feedback loop is improved by the utilization of rapid iteration and
the evolution of the design geometry aided by the trial and error, volume dependant nature of information.
2.1.2. Designing for a convergence solution
Generating these resultant geometries leads to the requirement of managing expected high resolution,
simulation-friendly meshes, met by working primarily though a proposed low resolution, designer-friendly
(Shepherd P. and Richens P. [1] and Bhooshan S. and El Sayed M [2]) Hierarchical Subdivision Surface (HSS)
. This workflow generally begins with a designer’s sketch solution to a spatial design problem, typically
manifested as a pre-dominantly quad-faced, low resolution mesh. This mesh is constructed to accommodate
design features such as topological conditions and directionality, holes and/ or boundary conditions, touchdown
points, clearances, etc. Given that these morphological developments rely both on the iterative nature of the
process and quick time-span of each iteration, ease, intuition and speed of manipulation become crucial. This
makes the low resolution nature of the design mesh quite important, as it creates a freeform, manipulation
friendly geometry used to explore design possibilities and limitations. A low resolution mesh also facilitates the
intuitive tracking of important technical details such as the presence of singularity points and eventual pre
simulation details, such as holes or fixed boundaries. This is possible due to the ability to manipulate the
geometry’s through adjusting a few vertices and/ or the addition/ subtraction of a few faces (Fig. 1)
Figure 1: Multiple resolutions of design mesh, showing relatively low number of faces (6 faces) used to create
complex surface.
Furthermore, by taking advantage of the recursive refinement structure of subdivision surfaces the low-
resolution mesh is easily converted into a high-resolution mesh. This higher resolution mesh has nice attributes
such as majority of its vertices of having equal valence, relatively even spacing of vertices etc. These features are
beneficial for downstream processes as conversion to NURBS surfaces, even Finite Element Meshes etc.
2.1.3. Structural performance intuition
The manipulation friendly aspect of the workflow also allows for another major advantage, namely that
of using a qualitative and intuitive understanding of structural principles of complex topologies to shape the base
geometries. This is achieved primarily through two avenues, the first being the ability to describe relatively
large curvature areas in the geometry’s topology with a fairly small and easy to manage amount of geometric
information, typically three to four mesh faces. The second is the aforementioned ability to control and influence

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
the presence of singularity points (Fig. 2) in the overall tessellation of the inherited high-resolution mesh. These
are crucial as they usually describe points at which curvature inverts or drastically changes in the geometry. Such
areas typically correlate with areas of weaker structural performance. These points are easy to spot and predict in
the low-resolution mesh as they tend to occur when the mesh valence varies from the predominant quad-based
subdivision, at a particular vertex.
Figure 2: High-resolution mesh with highlighted singularity points
2.1.4. Downstream benefits
A HSS based workflow as described, allows for the explorative evolution of multiple design resolutions through
rapid iterative processes. This then, develops both an intuition for structural performance and also resultant
geometries that are suited for downstream verification and analysis (as described previously). Additionally, the
resultant geometries of the topology optimization processes (described in next section) needed to be rebuilt in a
similar low-resolution manner. This is mainly due to the fact that the Finite Element mesh is subdivided to a
resolution suited to the optimization process but neither conducive to other downstream processes nor design
manipulation. The rebuilding process is aided by the discrete nature of describing a subdivision mesh through
vertex placement and edge connections, which in this case was guided by the primary curvature lines of the
optimized mesh. The benefits of the rebuilt mesh were most clearly observed in the structural analysis stage,
where the mesh resolution and topology were easily edited to suit the process.
Figure 3: Left to Right : High resolution mesh FEM mesh ~50000 vertices ; multi-patch, medium resolution
mesh ~6200 vertices ; low resolution, predominantly-quad, mesh ~ 275 vertices;
2.2. Topology Optimization

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
The application of topological optimization (TO) as a constitutive design tool has obtained widespread adoption
within aeronautic, automotive and naval industries (Bendsøe, M. P, and Sigmund O. [3]). While initial research
on the application of TO to architectural structures indicate the possibility for both significant performance gains
- in terms of reduction of material consumptions – and the infusion of particular design qualities specific to the
process (DOMBERNOWSKY, P, and SØNDERGAARD, [4], DOMBERNOWSKY, P, and SØNDERGAARD, [5],
STROMBERG, L. L. et al.[6]), the topic in its relation to architectural construction remains widely unexplored.
The prototype presented in this paper explores a bi-directional, generative modus of design application, in which
the result of topological optimization not only serves to reduce the self-weight of the concrete body through the
generation of structurally efficient rib patterns, but also to significantly affect the appearance and effect of the
final architectural object.
Figure 4: Shell design space FE model (top left), Shell design space FE model (top right), Material density
distribution after topology optimization (bottom left), displacements of post-optimized concrete body (bottom
right)
This was achieved through the following optimization process: the shell geometry, designed following the steps
documented in the previous chapters, was approximated in the FE-solver, HyperMesh 11.0, to a tetrahedric
Finite Element-mesh of 100 x 100x 100 mm units. Assuming a reinforced C35 concrete of 6.5e+9 elasticity
module, a tensile strength of 3 MPa, and a compressive strength of 34 MPa, the mesh was subjected to a uniform
load of 2.92 kN/m2 on the outer surface in the –z direction – representing the dead load and wind load of the
structure - and fully supported along the bottom shell edge. Using the optimization solver, Optistruct 11.0, this
setup was topologically optimized for a minimization of compliance with a volume fraction of 25%.

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Figure 5: Optimization results density studies
The resulting topology, analysed in Hyperview 11.0, exhibited a 5.67 mm of displacement and maximum tensile
stress value of 0.08 kN/cm2; well within the accepted properties of the material. Applying a density filtering of
0.29 the optimized mesh was re-exported and remodelled in the Rhinoceros 5.0 CAD-modeller. The post-
processed interpretation of the optimization result held a volume of 1.219 m3 by comparison to initiating starting
volume of the original shell of 1.85 m3, representing a 34.1 % reduction of volume through optimization.
Through this operation, the self-load of the concrete body was reduced, hereby rendering visible the principal
load trajectory pattern of the structure as perforations of the input design space volume
Figure 6: Remodelled geometry in McNeel Rhinoceros
3. Structural design
The structural context of the design and the envisaged methods of construction, required us to include various
considerations and make appropriate responses in the structural engineering of the proposed design. This section
describes them.

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Figure 7: Deflection analysis
3.1 Governing lateral load : Seismic or wind loads.
Given that Mexico City is in a seismically active area, we had to consider whether to use seismic loads or wind
loads as the governing lateral load. Following are the key assumptions we made, and subsequently decided to
use seismic loads of 300gal as the governing one.
1. DL (Self-Load) = 24kN/m3 x 0.08m = 1.92 kN/m2
2a. EX (Seismic Load, 300gal) = DL x 0.3 = 0.576 kN/m2
2b. EX (Seismic Load, 200gal) = DL x 0.2 = 0.384 kN/m2
3. WX (Wind Load) = 0.44 kN/m2 (Based on the wind-code tables)
3.2 Foundation design.
3.2.1 Stiff beam versus counter-weight approaches.
The above assumptions had a substantial impact on the design of the foundation. Given that we were attempting
to amount of concrete used via TO, we were conscious not to lose those savings in the design of the foundation
of the structure. This section describes the various considerations and the final choice of foundation design
made. (Figure 8)
Figure 8: Foundation design as a stiff beam.
Under self-load, the reaction uplift, due to the geometry of the structure, were 200Kg (both sides) in the front leg
and 60 Kg (both sides) at the rear. These could have easily been countered with the weight of foundation.
However the foundations had to consider the lateral loads mentioned above. Under 300 gal lateral loads, the shell
was found to be very sensitive against the side way (Y-axis) forces. We needed a foundation beam of about
20cm x 30cm rectangular section at both front and rear touchdown areas. Further, these foundations required that
they have wider footings (40cm to 60cm width) to spread the overall weight evenly to the supporting ground.
Additionally, the primary arcs of the touchdown areas of the geometry, come very close toward the front leg,
allowing rather limited stance between each touchdown point to act against bending action. Thus, even though
the overall weight was about 2 tonnes, the concentration of compression and tension at each touchdown point
would have become about 5.5 ton. It would have been rather uneconomical to try to cancel this heavy tonnage

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
with counterweight of concrete. Instead, we thought of designing a foundation beam with sufficient stiffness and
sectional area to act against the induced bending moment and shear.
3.2.2 Toppling.
Another issue to be considered was that of toppling given the tall and narrow proportions of the design.
However, we found that the geometry was on the safe side given the following: i) Centre of Gravity, upon which
the lateral force acts, is 1.78m from the ground, much lower than 3.0m ii) Weight of the shell is 23.5 kN,
including the steel, and much lower than 30.0 kN. Considering the factors above, we decided to design the
foundation as a stiff beam of 20cm x 30cm box with 40cm x 10cm footing for the front legs. The tail was
supplied with the foundation beam of the same profile as the geometry. We then connected these two isolated
foundations together by a pair of concrete beams on either side. Connecting beam was found not to require a
footing. This foundation was estimated to weight about 0.5 ton, significantly less than the counter-weight
strategy.
3.3 Bending moments.
Upon analysis, it was found that the highly curved geometry of the shape induced considerable bending action in
the structure. The compressive stress values used for analyses, were reduced to the approximately 2/3rd the
design strength of the concrete as concrete could fail at lower than its compressive stress due to such bending
effects.
3.4 Distance of apertures from boundary.
The topological optimisation process produced long thin elements at the rear of the structure. These however,
had to be reduced due to the possibility of buckling given the very small distance from the edge to the
perforation. A minimum distance of 120mm from the edges was established all around the piece and not any
concrete element was less than 120 x 120 mm in cross section.
3.5 Manual installation of steel bars.
Free-form nature of the geometry of the shell meant that the principal moment vector changed drastically across
the shell. On the other hand, considering the practicality of manual installation, rebar placement would not be as
flexible as we would need it to be. Therefore, we needed to make somewhat redundant rebar placement on both
U and V directions of the shell, so that each can cover both upward bending and downward bending by
themselves. Additionally, analyses performed after increasing safety factor to 5, to account for construction
errors and concrete creeping, also indicated the prudence in this strategy. Lastly, 8mm diameter steel bars was
specified, since at that thickness, it could be manually bent to conform to the geometry.
Figure 9: Principal moment vector field.

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Figure 10: Reinforcement distribution diagram
4. Fabrication
Following an iterative process of structural analysis and design refinement, the optimization result was
remodelled in Rhinoceros for achieving a final topology optimized geometry that satisfied all the conditions of
the seismically active environment of Mexico City and with the adequate size to be built in 10 days using
manual labour. Given the complex geometry of the shell and the existence of a CNC router on site a the Tec de
Monterrey we decided to contour the shape and cut it out of EPS Foam panels to be assembled on site and serve
as a guide for the workers to layout the rebar and pour the concrete. An inverted negative of the shape was
remodelled on Rhino establishing all the edges at 90 degrees normal to the original surface to avoid the need of
perimeter tubes and be able to create a continuous curvature on the edges (Figure 11). This model was divided in
12 pieces that could fit the bed of the CNC machine and contoured at one-inch segments, a interval that
corresponds to the thickness of the low density polystyrene sheets that were locally available; subsequently the
contours were nested to achieve the maximum material efficiency while reducing the cutting time. As the model
is symmetrical in one axis it allows us to cut some pieces of foam together and then rotate them 180 degrees to
get their final position (Figure 12). The contours were glued utilizing polystyrene solvent free industrial adhesive
on 12 blocks of contour, to allow them to be transported on site; utilizing a contour approach to the shape
generated another layer of texture to the geometry, accentuating the curvature of the shell.
4.1. Construction on the building site
Once on site the construction of the formwork was organised in 12 blocks of contours, of in all 160 polystyrene
sheets. External scaffolding towers were deployed on site comprised of standard 2000 x 600 mm modules to
allow the workers to walk and move around the prototype (Figure 13). The formwork was only going to be
utilised as guide work for the workers on site so it didn’t need to be sanded to reduce the texture of the contours
or coated with any releasing agents. The polystyrene blocks were assembled and reinforcement bars placed by
hand following the curvature of the surface. A double sided wire mesh slip was created around all of the
perforations of the piece to ensure geometric fidelity as the rebar proved to be difficult to bend on this closed
angles accurately and using thinner wire would not strong enough to receive the concrete (Figure 14). After
placing the reinforcement bars a double layer of wire metal mesh was applied on both sides of the rebar to
receive the concrete mixture. The edges of the piece as well as the perimeter edge of each of the perforations had
to be covered with a double layer of wire mesh enclosed in a slip of plastic to ensure that the concrete mix
remains perpendicular to the surface all around the edges, as doing a perpendicular edge in a traditional manner
would have been extremely complex given the curvature of the piece.
A low water concrete mixture was cast into this double layer of metal mesh; to avoid the need of vibration the
concrete was poured and compacted in 4 step sequence –back bottom areas, front bottom areas, middle and top -
the foam guide work had to be removed immediately after casting to be able to take it out without damaging the
surface and without having to destroy or further cut it.

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
A layer of high water cement paste was applied to the piece after finishing the cast to even the surface and
prepare it to receive subsequent painting treatment. The prototype is in a public park in the Santa Fe area of
Mexico City and was opened to the public on the 20th of September.
The process from 3d modelling and preparation of formwork files to on-site casting took 10 days and the
concrete was left to cure for 2 more weeks.
Figure 21: Typical section of the formwork guide (left) and contoured negative model of the geometry (right)
Figure 12: CNC routing of contours (left) and contours ready to be glued and transported on site (right)

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Figure 13: On site assembly of the formwork with scaffolding towers to the sides and placing of the
reinforcement bars
Figure 14: (left to right) Perimeter edges cover with reinforced wire plastic slip. Piece after concrete was poured
and formwork removed.

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Figure 15: Topology optimized shell prototype 4 x 5 x 2m, 8 cm thick
5. CONCLUSIONS
We presented the specifics of a time-bound design collaboration, including computational geometry and design
tools and their use in multi-stage collaborative design phase, incorporation of structural design in early-design,
strategies to describe complex geometry – form-work and steel layout – onsite in a labour intensive economy.
5.1 Computational geometry and design technologies.
5.1.1 Subdivision surfaces
Growth in the role of simulation in conceptual design and evaluation of building performance is coupled with
need for architects to manage the dichotomy between high resolution geometries used in simulation and lower
resolution, free-form manipulation friendly, CAD geometries. We argued for the benefits of Hierarchical
Subdivision surfaces in this process, concentrating specifically on its uses in:
i. Design and collaboration workflow, enabling multiple resolutions of design and analysis, rapid iteration
and evolution of design geometry.
ii. Developing an intuition for structural performance of geometries due to the nature of the smooth
curvature flows produced by subdivision geometries and the correlation of the curvature with
structural performance.
5.1.2 Topology optimisation and shell structures.
Incorporation of structural analysis within the rapid, iterative and free-form nature of early design is quite a
challenge. The methods and software are neither easily accessible to architects nor easily incorporated within
methods and software they use. Further they are time-consuming and defy easy integration of architectural
constraints. In this context, recent developments with regard to development and availability software to

Proceedings of the IASS-SLTE 2014 Symposium
“Shells, Membranes and Spatial Structures: Footprints”
Copyright © 2014 by the author(s).
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
optimise material layout within a given design space is a welcome development. We specially argued for the
benefits of such topology optimisation in:
i. Reduction in material quantities, and thus reduction of economic and environmental costs.
ii. Reduction in the design iteration time.
5.2 Structural design
We also discussed the difficulties in developing details of structural design in the context of free-form
geometry, seismically-active physical environment and labour-intensive economic environment in which the
prototype was built, focussing specifically on:
i. Development of reinforcement fibre layout in the geometries developed by the processes above.
ii. Design of foundation for such unusual geometries, with the explicitly design intention to minimise the
size and complexity of the same.
5.3 Fabrication.
Further we presented our strategies to enable a straight-forward translation of the design to physical reality
including:
i. Description of geometry complex geometry on-site, given the constraints of time and labour intensive
economy.
ii. Development of guide-work / Form-work for concrete negotiating requirements of pouring/compaction
with the complexities of the geometries produced by topology optimisation.
In conclusion, we hope to have made a case for a more holistic design practise – from collaborative design to
fabrication, and a thus a more holistic reduction of costs – design time and resource, material savings via
topology optimisation and the need to include fabrication costs in such evaluations.
ACKNOWLEDGEMENTS
We would like to thank the director of Zaha Hadid Architects, Mr. Patrik Schumacher for his guidance and
support of this research prototype. We would like to thank Tom Newby of Expedition Engineers, London for his
professional, timely and invaluable advice regarding the structural performance of the proposed design.
REFERENCES.
[1] Shepherd P., Richens, P., Subdivision Surface Modelling for Architecture, in IASS 2009 Proceedings of the
International Association for Shell and Spatial Structures Symposium. Valencia 2009
[2] Bhooshan S. and El Sayed M., Use of Sub-division Surfaces Architectural Form-Finding and Procedural
Modelling, Proceedings of the international conference on simulation in Architecture and urbanism, simAUD
2011, Boston, USA.
[3] Bendsøe, M. P, and Sigmund O. 2003 Topology Optimization - theory, methods and applications. Springer
[4] DOMBERNOWSKY, P, and SØNDERGAARD, A. 2011. Unikabeton prototype. In FABRICATE: Making Digital
Architecture. Riverside Architectural Press.
[5] DOMBERNOWSKY, P., and SØNDERGAARD, A. 2012. Design, analysis and realization of topology optimized
concrete structures. International Association for Shell and Spatial Structures 53, 209-216.
[6] STROMBERG, L. L., BEGHINI, A., BAKER, W. F., and PAULINO, G. H. 2012. Topology optimization for
braced frames: combining continuum and beam/column elements. Engineering Structures 37, 106-124.