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Proceedings of the International Association for Shell and Spatial Structures (IASS)
Symposium 2015, Amsterdam
Future Visions
17 - 20 August 2015, Amsterdam, The Netherlands
SmartNodes: ‘Light-weight’ parametric structural design
process with BESO
Daniel PROHASKY*, Nicholas WILLIAMSa, Kristof CROLLAb,
Jane BURRYa
*Spatial Information Architecture Laboratory (SIAL)
RMIT University, Melbourne 3000
[email protected]
a
b
RMIT University, Melbourne
The Chinese University of Hong Kong, School of Architecture
Abstract
This paper includes the documentation of research to overcome the challenges of coordinating
architectural and structural initiatives for complex structures in the research project SmartNodes. The
technique documented here utilises parametric finite element analysis (FEA), which updates in realtime with qualitative and quantitative structural feedback relayed to the designer. The system is
documented with reference to a case study pavilion design, which exemplifies its ability to
accommodate freeform flexibility in structures while incorporating complex design tasks such as
applying the bidirectional evolutionary structural optimisation (BESO) process to uniquely loaded and
hence uniquely shaped nodes. This novel approach was demonstrated through the fabrication of a 1:5
scale prototype of the pavilion. The prototype is composed of 207 standard rectangular section timber
beams and 144 3D printed structurally optimised nodes or ‘SmartNodes’. To mass produce the
structurally optimised nodes, the multidimensional coordination of structural data such as spatial,
force and restraint variables needed careful manipulation through two scales, at the level of the beam
network and within each ‘smart node’.
Keywords: BESO, structural optimisation, smartnodes, parametric.
1. Introduction
The developments in additive manufacturing (AM) techniques and topological structural optimisation
tools have led to the exploration of the concept of ‘SmartNodes’ – structurally optimised nodes using
the BESO algorithm [1], [2] which connect standard structural elements to create a structural network.
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
The complexity of the structure is concentrated within each node – allowing increased geometric
flexibility for the manipulation of the built form. The use of AM techniques reduces challenges which
freeform and organic geometries present to manufacture. Two AM technologies were used for parallel
studies in the project: Fused Deposition Modelling (FDM) for plastic parts at scale 1:5, and Selective
Laser Melting (SLM) for stainless steel prototypes at full scale [3].
This paper covers a portion of the ‘SmartNodes’ project [4] workflow which includes the utilisation of
parametric tools which aid in the conceptual design of a prototype pavilion with a functioning BESO
solution for the nodes for the 1:5 scale prototype pavilion. The parametric operations that were used in
succession were:
1. The vaulted form generation algorithm
2. Structural analyses
3. BESO processes
4. Mesh smoothing operations
This paper focuses on the parametric structural analyses, BESO processes and briefly touches on the
mesh smoothing operations used. An integrated system was developed to analyse the structural
performance/behaviour of the overall form while monitoring critical structural actions at locations
along the beams and the node/beam connections. The parametric link between the geometry and
structural analysis with a visual representation of the critical structural actions created a seamless
informative workflow between architect and engineer. Suggestions for the improvement of the form
for structural integrity could be made very quickly. Multiple iterations were possible over a period of
a few days.
The vaulted form of the pavilion went through three main stages of structural interrogation – iterative
design and structural feedback - with implicit architectural intentions:
1. Macro scaled manipulation of the beam network to improve the structural rigidity of the
overall form
2. Structural optimisation of the overall form through material reduction of the beams
3. Micro scaled coordination of loads and geometry for the BESO of the nodes
Figure 1: Smart Nodes Pavilion
Future Visions
2. System Workflow
The ‘SmartNodes’ project functioned through two parallel workflows: 1. Conceptual design and
realisation of the 144 nodes with light weight parametric tools; 2. The detailed design and generation
of full scale ‘SmartNodes’ using more robust and precise structural software. This paper focusses on
the former case (highlighted in red in Fig.2). This was undertaken through a single software package
McNeel Rhinoceros 5.0, with parametric modeling platform Grasshopper3d and a number of further
plugins: Kangaroo, Karamba [5] and Millipede.
Figure 2: Workflow diagram
3. Structural analysis and local design changes
The structural behaviour of a shell is heavily dependent on its curvature and continuity of structural
elements. An approximate shape for a funicular surface was generated through a simple form-finding
process using Kangaroo, a plugin for Grasshopper. A beam network was created using a custom
designed sphere packing method, creating a ‘porous’ shell where the linear beams approximate the
curvature of the shell.
The first prototype test of the project’s complete workflow included the exploration of the
architectural potential of the system. The project opted for shell structures rather than deep spaceframes in order to reduce the complexity of the structure and the nodes. The curvature of the shell was
designed for the structural actions imposed on it (funicular in nature). The designed shell structure
included a wide range of surface conditions with properties ranging from synclastic to anticlastic
curvature, and load systems going from vaulted arches to semi-cantilevering/vaulted overhangs. In
order to arrive at this shape the setup started from an input mesh in which colour coding defined
boundary and foundation points. A sphere packing algorithm was used to define centre-points for the
panels that were primarily hexagonal and were derived using a Voronoi tessellation. These shapes
primarily had three members per node which greatly facilitated 3D printing and assembly. Kangaroo
was then used to derive the inverted funicular shape. Nodes and panel edges were brought into a
spring-particle system in which certain points were fixed as anchors and an upward force was applied
Future Visions
onto the interconnected network. The spring-particle system was utilised to morph the form into a
state of equilibrium based on virtual material/spring stiffness – similar to the structural hanging chain
models designed by Gaudi [6] - this is a virtual equivalent [7]. The curvature of the form which
followed the logic of a complex vault performs best under gravitational load actions. The prototype
pavilion was designed with only gravitational loads applied and an approximated 0.1kN point load
which simulated the weight of each node since the mass of the nodes will change depending on the
BESO output for each node. The structural actions were scaled to suit the prototype pavilion scale
(1:5) for the structural analysis and BESO generation for the prototype pavilion. However, the
structural actions were applied at full scale during the conceptual design of the full scale pavilion
(which was important for the structural optimisation of beam sizes).
3.1. Structural feedback
Figure 3: Example diagram of parametric qualitative and quantitative structural feedback diagram to
share key observations between architect and engineer.
The above diagram (Figure 3) displays an example visualisation of the structural actions for a design
iteration of the pavilion. The diagram was simplified to include the maximum shear forces, axial
forces, bending moments and deflections rather than each of their minor and major axes components.
They were translated into visual non-dimensional representations of the maximum structural actions
for each beam – where a circle’s radius represents the magnitude of the structural action. The
document was circulated with graphical layers in-tact (interactive pdf) so the designer could hide or
unhide the segments of the diagram. The flattened version of this diagram (Figure 3) was
Future Visions
parametrically generated from the 3D model - which automatically updated the diagram on the ground
plane when a node was moved (see Figure 5).
The applied panel sizes in the first iteration of the prototype were rather large with respect to the
curvature of the surface. In certain areas, where the curvature was greater, isolated node peaks broke
the visual continuity of the surface shell and required manual smoothing. The manual smoothing
process was the manipulation of the beam network for structural improvements (architecturally
considered). The position of the nodes, and hence the beam lengths, were precisely positioned within
the constraints of the vaulted curvature and fabricated to their correct dimensions to avoid a loss in
structural rigidity.
Figure 4: a. Structural improvements of the form through manual manipulations of node positions
(top); b. original wireframe from form generator (bottom left); c. example graphical representation of
critical loads from the overhanging region shown in ‘a.’; d. structurally improved beam network with
three beam sizes shown in varying colour tones (dark = large section; mid-tone = mid-section; light =
small section).
Future Visions
The structural stiffness of the arched or dome-like regions could be drastically improved by careful
manipulation of the network to achieve a more continuous gradient of curvature. The cantilevering
regions were the most difficult to manage to within the structural limits. However, by manipulating
the alignment of beam elements to extend back spans, heightening the vaults, repositioning the ground
supports and creating a continuous flowing perimeter string of beams from ground supports to the
cantilevering regions the deflections of the structure were able to be reduced to within workable limits
(this step used one standard rectangular timber section that was within the structural limits of the
maximum bending moment). The structural manipulations were then communicated to the architect
and the pavilion design team through qualitative diagrams that were directly generated from the
structural analysis of the form (Figure 3).
Figure 5: a. Three diagrams showing the vertical manipulation of one node. The orange circles show
the relative displacement at each node - values of the nodal displacements are also shown (top); b.
Parametric qualitative and quantitative structural feedback interface (bottom)
Future Visions
3.2. Beam section distribution
The structural analysis and local design changes workflow included the ability to distribute different
sized beams throughout the wireframe based on the relative stress within each beam. Once the form
was within reasonable limits from the careful manipulation of the structural form, multiple beam sizes
could then be distributed amongst the structure to reduce the amount of material used. This involved
using a parametric engine which used critical structural actions of each beam to create a beam size
mapping hierarchy. The larger beams were distributed to high stress regions and smaller beams to
lower stress regions. Inevitably the deflections of the structure increased through this process - but
were balanced through further minute tweaking of the form. The new distribution of the beam sizes
inevitably altered the distribution of weight within the structure so further manipulation of each node
within the form was required to increase the structural stiffness. Since the amount of material was
reduced – the mass of the structure was reduced. Hence, the structural forces also reduced – which
lead to a reduction in the forces applied to the nodes for the optimisation process. This further
optimises the material reduction of the nodes (for a structure under only self-weight). This final design
reduced the material mass of the structure by about 0.74 tonne of timber (MGP12) at full scale.
Further improvements can be made by increasing the number of beam sizes to be distributed and by
varying the beam dimensions to suite the major and minor axis structural actions. The optimisation
criteria were predominantly based on the maximum bending moments and shear forces within each
beam (see Karamba manual for details of the optimisation algorithm).
Beam Section(s)
Beam
Qty
Mass of
Structure
Max
Deflection
Max
Moment
Max
Shear
Max
Axial
140mm x 80mm
207
1870kg
20mm
0.75kNm
0.83kN
2.0kN
140mm x 70mm;
120mm x 60mm;
90mm x 45mm
45;
48;
114
1130kg
25mm
0.90kNm
0.77kN
1.7kN
Table 1: Beam distribution for weight minimisation output
4. Node details and topology optimisation
The coordination of structural data for each of the nodes required multiple data types i.e. meshes,
breps, spatial coordinates, orientation vectors, force vectors and planes. Nodes were designed to have
standardised connections to beams, using simple flitch plate connections (see figure 7). The size of the
multidimensional array varied with the number of connections to the node and the type of connection
(flitch plate or ground connection). Breps (solid 3D geometries) were utilised for the definition of
regions within the node for BESO support, load action, void and design regions. Meshes were used for
post BESO solid boolean operations and smoothing. Spatial coordinates and orienting vectors position
and orient the node in the world coordinate system. The force vectors were coordinated from the
structural output of the beam network to the nodes. Moments were also simulated with force vectors
and careful manipulation of the brep load action regions (see figure 7). Planes were used to orient
brackets, connection details and orient force vectors within local beam coordinate systems.
Future Visions
Figure 6: BESO data flow diagram
4.1. Structural actions on nodes
The SmartNodes pavilion was optimised for its self-weight. Uniformly distributed loads across entire
beam lengths (beam mass) and node point loads (node mass) were applied to the wire frame. Hence,
the bending moment diagrams (BMD) have a 2nd order polynomial function. Therefore, 3 points along
each beam chord were needed for the bending moment function derivation (Equation 1) which was
differentiated for shear (Equation 2). The moments, shear and axial forces were extracted from the
locations of bolted connections with nodes (at position ‘ ’ along each beam).
2
3
∙
2
∙
4
3
∙
4
(1)
(2)
Future Visions
There were 3 levels of indices needed to coordinate the actions for each beam-node connection point:
1. The node index denoted by ‘ ’ where |0
and ‘ ’ is the total number of nodes
(
144 in our case study pavilion)
The connection details and BESO restraint inputs were different for nodes located on the
ground and nodes only connecting to beams. However, it was possible to maintain the same data
structures within the structural analysis and force transposition processes for the BESO engine
sketch/algorithm (refer to figure 6).
and ‘ ’ is the total number of
2. The flitch plate index denoted as ‘i’ where |0
connections to the
node.
3. The index of the bolted connection regions with the
flitch plate denoted as ‘ ’ where
and ‘ ’ is the total number of connection points on the
flitch plate (for the
|0
prototype pavilion presented here
4). There is a requirement for at least 4 defined connection
regions located within each quadrant of the local ′ ′ axes (see figure 7) to simulate all moments
with their equivalent force regions.
Figure 7: Sign conventions: a. Axonometric local beam sign convention (top); b. Node connection
detail section y’x’ (bottom left); c. Node connection detail section z’x’ (bottom right)
Future Visions
The following assumptions were made to simplify the BESO process:
- The axial and shear forces can be combined and distributed evenly amongst the flitch plate
connection points (the location of the bolts)
- The moments can be transposed to equivalent forces located at the centroids of the bolted
) shown in figure 7
connection points which are the force regions (
-
All forces can be converted to volumetric forces to be applied within ‘force regions’ to create
the necessary input into the Millipede BESO engine (these are defined by the 4 bolt
connection regions located on each flitch plate as shown in figure 7)
The following general formula defines the forces (
region:
) located at the centroid of each bolt connection
(3)
The solutions to equation 3 result in 4 force vectors (one for each bolt within the connection plate) for
each beam connection to their respective node. The forces at the force region centroids are then
translated into ‘volumetric forces’ (
/ ) to suit the BESO engine input requirement for
force regions (see equation 4).
/
(4)
The vector translations to create a unified sign convention for each bolt connection region are handled
with the array shown in Equation 5.
, ,
(5)
Where ,
and
are all either -1 or +1 to simulate the equivalent force vectors for moments in
their correct respective directions – these vary through ‘ ’.
Where:
/
Table 2: General structural and node indexing parameters.
Provided that the node-beam connection design has 4 symmetrical locations for bolt connections
equation 3 can be applied. Equation 3 can possibly be expanded for non-symmetrical arrangements of
bolts and a variable number of bolt connections given that there remains (in general) at least one
connection point in each quadrant in the local y’z’ plane. It is possible to design a cleat plate that
morphs to the desirable geometry based on the forces applied to the node, however this was not
applied to the pavilion design – this could be incorporated into the node optimisation process (within
the “node connection design” block (see figure 6) in future designs).
Future Visions
4.2. The BESO engine
Relatively low resolution results were achievable within a very short time (5-10 minutes per node)
with the BESO engine used for the pavilion design (Millipede). Some difficulties with the BESO
engine inputs were encountered. For example: A Brep of a ‘perfect’ sphere did not work, however an
approximation of a sphere was successful; sensitive to cylindrical geometric inputs; BESO engine
sensitive to Rhino3D unit settings; resolution of combined BESO regions was restricted to a 40 x 40 x
40 ‘voxel’ mesh; resolution is calculated within bounding box of all defined BESO regions; the
volume fraction is based on the initial volume of the bounding box not the initial volume of the
combined regions, hence accurate volume fractions could not be predefined. However, for a
conceptual design at the scale chosen, the BESO engine used was adequate.
4.3. Node smoothing and boolean operations
The raw output from the BESO engine was a ‘voxelated’/disjointed mesh that needed cleaning and
smoothing. The cleaning process involved removing detached voxels from the main voxel cluster and
the unification of mesh normals for successful application of solid mesh Boolean operations for the
connections (see figure 6 and 8). The smoothing process was handled with a combination of mesh
edge and verticy beveling and Laplace smoothing. There were instances where this process was
unsuccessful - this resulted in a rerun of the BESO engine with a different volume fraction (figure 6).
Figure 8: Example prototype ‘SmartNode’ at 1:5 scale: a. smoothed virtual mesh output (left); b.
physical 3D printed output (right).
8. Conclusion
The link between the structural manipulation of the beam network (macro structural considerations),
the architectural intentions for the structure, and finally, the parametric BESO process for the nodes
(micro structural considerations), was strengthened by integrating them within a single parametric
model. This is a prime example of how 3D virtual modelling information between architect, engineer
and advanced manufacturer enhances and expands the possible realities of freeform structures. The
documentation of this novel process will contribute to the developing improvements of the
‘SmartNode’ parametric system towards further automation and understanding.
Future Visions
Acknowledgements
This template was adapted from the one used for IASS-IACM 2008 / IASS 2009.
References
[1] A. Aremu, I. Ashcroft, R. Hague, R. Wildman, and C. Tuck, “Suitability of SIMP and BESO
topology optimization algorithms for additive manufacture,” in 21st Annual International Solid
Freeform Fabrication Symposium (SFF)–An Additive Manufacturing Conference, 2010, pp. 679–
692.
[2] X. Huang and M. Xie, Evolutionary topology optimization of continuum structures: methods and
applications. John Wiley & Sons, 2010.
[3] S. Galjaard, S. Hofman, and S. Ren, “New Opportunities to Optimize Structural Designs in Metal
by Using Additive Manufacturing,” in Advances in Architectural Geometry 2014, Springer, 2015,
pp. 79–93.
[4] K. Crolla and N. Williams, “Smart Nodes: A System for Variable Structural Frames with 3D
Metal-Printed Nodes,” ACADIA 14 Des. Agency Proc. 34th Annu. Conf. Assoc. Comput. Aided
Des. Archit. ACADIA ISBN 9781926724478, pp. 311–316, 2014.
[5] C. Preisinger and M. Heimrath, “Karamba-A Toolkit for Parametric Structural Design,” Struct.
Eng. Int., vol. 24, no. 2, pp. 217–221, May 2014.
[6] S. Huerta, “Structural Design in the Work of Gaudí,” Archit. Sci. Rev., vol. 49, no. 4, pp. 324–
339, Dec. 2006.
[7] A. Kilian, “Linking digital hanging chain models to fabrication,” Proc. AIAACADIA, pp. 110–
125, 2004.

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