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Proceedings of the IASS Symposium 2018
Creativity in Structural Design
July 16-20, 2018, MIT, Boston, USA
Caitlin Mueller, Sigrid Adriaenssens (eds.)
Copyright © 2018 by Peter VON BUELOW, Omid OLIYAN TORGHABEHI, Steven MANKOUCHE, Kasey VLIET
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Combining parametric form generation and design exploration to
produce a wooden reticulated shell using natural tree crotches
Peter VON BUELOW*, Omid OLIYAN TORGHABEHI, Steven MANKOUCHE, Kasey VLIET
*University of Michigan
Ann Arbor, Michigan
pvbuelow@umich.edu
Abstract
LIMB is a project recently carried out at the University of Michigan, Taubman College to explore the
potential use of natural tree crotches as bifurcation elements in the construction of a reticulated, wooden
shell. The use of these natural tree elements offers advantages of both economy in using waste material (the
crotches) as well as an aesthetic offered by the organic elements which have been formed over time by the
flow of bifurcating forces. The project explores replacing mortise and tenon joinery methods common in
historic heavy timber construction with a single bifurcated piece of wood. Because of their low economic
value, tree crotches are often not harvested for commercial purposes. This project proposes using these
natural pieces to design connections in timber construction. Through the design and fabrication of a full-
scale reticulated shell, this research shows how organic variations in tree limb bifurcation can bring about
valuable and sustainable opportunities for generative, architectural timber design. ParaGen, a design
exploration method developed at the University of Michigan, was used to develop the form of the final shell.
The method combines form generation based on a parametric model with analysis using simulation software,
and stores all solutions in a Structured Query Language (SQL) database. The database can then be explored
using a variety of data acquisition methods. New solutions can be generated to target desired criteria using
genetic algorithm techniques. An example of a realized design is presented.
Keywords: wood structures, timber joinery, reticulated shells, form exploration, topology optimization
1. Introduction
Historic precedents for the use of tree crotches in wood structures can be found in both 17th century framing
for naval vessels as well as joinery in timber barn construction [1]. Presumably, this technique offered
angular joints without complex mortise and tenon details. In addition, a degree of moment resistance could
be achieved that exceeded other joining techniques. Figure 1 shows examples of the described use of natural
tree bifurcations. In these cases, the wood grain naturally follows the shape of the piece. More recently Claus
Mattheck at the University of Karlsruhe has carried out extensive physical testing of the behavior and
strength of natural forked tree sections [2]. In his work he also gives guidelines for the selection and defect
detection in these pieces in nature.
The goal of the work presented here is to make use of these naturally forked tree sections as joining elements
in architectural, structural systems. In this effort we focus on the design of reticulated dome structures. The
raw tree crotches are cut to size and milled to final form and dimensions in a 5-axis CNC router (see Figure
2.). The design intent is to produce standardized nodal elements that can be joined easily to connective strut
elements. By using the CNC router, exact final angular and linear dimensions can be precisely attained.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
2
Figure 1: Example bent and bifurcated elements taken from natural tree sections. [1]
Part of the design intent is to limit the number of different joint elements in order to achieve a standard set
of parts that could be produced and used in different circumstances.
Figure 2: left) Component parameters and assembled parts right) Milling jig.
2. Design process
The form generation model is constructed using Rhino/Grasshopper. The model executes the following steps
in the generation of each solution:
1. Selection of a base topology grid
2. Dynamic relaxation of the grid to find a compression shell (with Kangaroo)
3. Analysis of the shell under gravity loading (with Karamba)
4. Export of images (with Ladybug)
In addition, as a post process, the chosen form can be adjusted to use a preselected set of joints. This allows
for economy using either fewer different pieces or pieces from an available stockpile.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
3
2.1. Selection of a base topology grid
Because tree crotches generally join three members, a hexagonal grid is chosen for the shell mesh. Also, for
this initial study, it is desired to limit the total number of joints and members so as to reduce fabrication
time. For this reason the grid topologies are limited in overall size and complexity. In addition, some
topologies contain a central oculus that further reduces the number of joints and members. Figure 3 shows
the seven topologies included in the form finding search.
Figure 3: The seven different topologies included in the form finding search.
2.2. Dynamic relaxation of the grid
The next step is to use the Grasshopper plugin Kangaroo [3] to apply dynamic relaxation coupled with an
upward force to find a compression controlled shell. The force level (rest/length ratio) which drives the
height extension is taken as a variable, and spring tensions are set over three ranges of the surface – the
supporting legs, the edges and the central portion. This has an influence on the final curvature in the different
regions. The examples in Figure 3. all show an uplift force of 1. Figure 4 shows topology 3 with upward
forces applied ranging from 0.5 to 1.8.
Figure 4: Topology 3 shown with an upward force ranging from 0.5 to 1.8.
2.3. Analysis of the shell
Two basic categories of data are collected on each shell solution: geometric parameters and structural
parameters. Key geometric values that are useful in choosing a solution include: clear height of the side
arches, center maximum height, number of joints and members, longest and shortest members, defining
crotch angles, as well as the base topology type. Since the member sections and wood density are preset, the
overall weight is also calculated. With the geometry of the shell determined, a structural analysis is
performed using Karamba [4]. Values recorded from the analysis include maximum axial force, moment
and deflection as well as utilization factors of members in tension and compression. All quantitative values
are uploaded to a SQL server as well as images of the geometry and structural plots. In addition, a catalog
view showing each joint with all defining angles is included (see Figure 5).
2.4. Export of images
A selected range of images is generated and exported from Grasshopper using Ladybug. All of the generated
images can be viewed along with the quantitative data, and printed as a one-page description for any
solution. Figure 5. shows such a description sheet for one solution. These summary sheets are very useful
in making a design selection among a specified set of solutions. Using ParaGen a final selection set can be
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
4
defined by solutions that meet chosen criteria. Then the final selection can be made based on both visual
quality and a combination of other criteria. Quantitative data can of course be graphed and compared (e.g.
with Pareto sets), but qualitative aspects are often best shown by visual depictions.
Figure 5: Detail summary sheet for one solution showing both quantitative data and visual form.
3. Design generation/exploration with ParaGen
The generation of the solution space, along with the exploration to find the best solutions is accomplished
using ParaGen, a design aid developed at the University of Michigan. Details of the ParaGen method have
been discussed in several previous IASS papers [5]. Basically, the system couples some parametric form
generation, (in this effort the Rhino/Grasshopper combination was used with Kangaroo), with a simulation
and analysis tool, (for this Karamba is being used). The results are uploaded to a SQL server, which uses a
genetic algorithm (GA) to search for more solutions that fit specified criteria. The process is cyclic and can
run on a single machine or on any number of clients in parallel. All that is required is for the clients to be
able to each access the software and the SQL server through an interactive web page. Figure 6. shows the
basic ParaGen cycle as well as the steps in the process.
ParaGen is based on a Non-Destructive Dynamic Population GA (NDDP-GA) [5]. It is non-destructive in
the sense that every solution generated is saved in a SQL database. The breeding populations are then drawn
from this database dynamically at the moment breeding takes place. This offers several advantages over
conventional GAs. Whereas traditional GAs remove unfit solutions from a population, the NDDP-GA stores
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
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Figure 6: The basic ParaGen cycle showing the steps used to generate a range of solutions.
all solutions permanently in a database. One advantage in this approach is that as each new child is generated,
a check can be made in the database to ensure that the child has not already been developed. This is not
possible in a traditional GA, and as a result, the same solution is often repeated causing wasted
computational effort. Also in a traditional GA, the population evolves slowly and progressively with each
new cycle of breeding. This means that if the breeding criteria (the fitness or objective function) changes,
the entire process must be restarted to again slowly evolve a fit population. A dynamic population, however,
is drawn immediately from the database of all solutions so far. So rather than starting over entirely, the
criteria are merely redefined, and the best population for the new criteria is drawn from the database of all
solutions found to that point. This gives an NDDP-GA a great deal more flexibility in exploring a large
solution space for multiple criteria.
Figure 7: SQL filters for search and breeding criterion.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
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The use of an NDDP-GA gives ParaGen a distinct advantage in solution exploration as opposed to
traditional optimization. Classic optimization generally searches for a single best solution for some given
criteria. ParaGen, on the other hand, is focused more on exploration. It searches for a range of pretty good
solutions for differing criterion. This might be a traditional Pareto set (ParaGen can perform Pareto
optimization too) or it might simply be a set of solutions that respond well to different criteria. Because
ParaGen also provides images of the solutions, it is possible to consider qualitative considerations as well
which include form, aesthetic appearance or spatial qualities.
Figure 8: A plot showing the relation of dome topology set 7 (red dots) to the other topologies with respect to
entrance height vs. total weight.
Exploration in ParaGen is further facilitated by a set of post-processing tools. First, since all of the defining
data for each solution is maintained in the SQL database, the full range of SQL queries can be employed in
searching for different combinations or ranges of criteria.
In Figure 7., a search is made for domes with an entrance height of at least 2 meters (6.5 feet) but with a
peak center height limited to 2.7 meters (9 feet). The search set is restricted to topology type 7, and the
results are displayed in ascending order of displacement (from least to greatest). Since the results are all
contained in the database, they will be displayed instantly, thus making the search truly interactive and
visual.
The quantitative parameters can also be searched using interactive graphing functions. Additional
information can be displayed through the use of color. For example in Figure 8., the red dots show the
relation of topology 7 as compared to the other topologies regarding entrance height and overall weight.
Again because all data is stored in the database, the results are displayed instantly, making interactive
comparisons quick and easy. Also, by running the cursor over any of the dots, the solution id and data is
displayed, and by clicking on any dot, the solution image is immediately displayed. All of these post-
processing options combine to make ParaGen a versatile design exploration tool.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
7
Using the ParaGen exploration tools a final design was chosen from the generated options. Due to limits of
space, time and resources the criteria for the initial prototype were set to give a smaller dome that still
maintained a minimum entrance height of 2 meters. The number of nodes was also minimized which resulted
in topology 7. The other factor considered was the range of crotch angles which was chosen to match the
range of sizes that was available. The selected dome is shown in Figure 5. Also due to time constraints, the
initial prototype was constructed from one third of the total dome. The constructed prototype is shown in
Figure 9.
Figure 9: The constructed prototype of one third of the full dome
4. Prototype construction
The fabrication of the dome segment had three parts: the nodes, the members and the joining element
between them.
4.1. Grid nodes (tree crotches)
The nodal points between members were fabricated from tree bifurcation pieces or crotches. The process
included seven steps:
1. Collecting the crotches – sawn from waste timber
2. Scanning the crotches – photogrammetry with cameras using Agisoft Photoscan.
3. Fitting the desired finished geometry within the raw crotch
4. Producing the CNC mill path – using Mastercam
5. Milling the piece
6. Sealing the piece to retard drying and cracking
7. Milling the connection (hole for peg)
Figure 2 shows a piece mounted in the milling jig at the conclusion of the 3D routing operation. Each piece
went through this process which takes several hours per piece. The milling time alone took about 2 hours.
4.2. Member pieces
The straight, strut elements between nodes were fabricated using 70 mm (2-3/4 inch) diameter billets. For
these, rough turning maple blanks were used (commonly used to produce baseball bats). These are knot free
pieces, and should have a strength comparable to select mixed maple (NDS allowable compressive stress of
6000 kPa (875 psi)).
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
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4.3. Pegged connections
The connecting element between the crotch node and the straight struts was a simple 25mm (1 inch) wood
dowel as a peg. In the original design the intention was to glue the peg in place with casein (wood) glue.
The joint was tested in this form in flexure, and was found to develop the full tensile strength of the dowel,
which was 276 Nm (204 ft-lbs). However, because the prototype needed to be disassembled, the pegs were
fixed in place with screws rather than glue, which reduced the flexure capacity to about 100 Nm (73 ft-lbs).
The allowable compressive capacity would still be based on the net section and was about 20 kN (4500 lbs).
5. Discussion
The erection process was easily accomplished with temporary bracing of the nodes. Due to a time limit to
produce the prototype, only one third of the designed dome was fabricated and erected. Although the
erection of the shell took less than one day, the production of the joints through the seven step process
described above proceeded at a rate of about two per day. In the prototype, because disassembly would be
necessary, the pegged joints were screwed and not glued which compromised the strength. This resulted in
some joint slippage during erection. After a few weeks standing in the dry indoor environment, some
cracking of the crotch pieces was also observed. As a means of crack prevention, tests are currently being
run using Polyethylene Glycol (PEG) injection under pressure. Also, kiln drying techniques using controlled
pressure, temperature and humidity to dry the lumber without cracking are being pursued.
6. Conclusion
The concept of repurposing the waste product of tree crotches did succeed, and a section of a dome was
fabricated. Problems encountered include the time required to scan and mill each piece. This could be
improved by standardizing the angles used, which would minimize the number of different sizes needed.
Also, the grading of the wood was a concern. One approach would be to pre-shape pieces with a band saw,
thus exposing potential defects in the wood, reducing milling time and expediting drying.
Acknowledgements
This project was made possible by a grant from the Taubman College of Architecture and Urban Planning
at the University of Michigan.
References
[1] Honoré Sébastien Vial de Clairbois, l’Encyclopédie méthodique Marine, Paris 1783.
[2] C. Mattheck, Design in Nature, Learning from Trees, Springer Verlag, Berlin, 1998.
[3] G. Senatore and D. Piker, "Interactive real-time physics: an intuitive approach to form-finding and
structural analysis for design and education," Computer-Aided Design, vol. 61, pp. 32-41, 2015.
[4] C. Preisinger, and M. Heimrath, “Karamba—A Toolkit for Parametric Structural Design”, Structural
Engineering International, vol.24, no.2, pp.217-221, 2014.
[5] P. von Buelow, "ParaGen: Performative Exploration of generative systems," Journal of the
International Association for Shell and Spatial Structures, vol. 53, no. 4, pp. 271-284, 2012.
