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Assembly-aware design of masonry shell structures: a computational approach

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This paper proposes a workflow for Assembly-Aware Design (AAD) of masonry shell structures and introduces an interactive tool in a CAD environment to assist the design process while simulating the step-by-step assembly of masonry blocks. Thus designers can explore the design space of masonry shell structures and be aware of structural performance before the assembly phase, at the early design stage. Masonry shell structures are an old construction technique, which has recently received a lot of attention due to new computational methods. Even though the form of such a structure is optimised for structural performance, its incomplete form during construction often requires the support of falseworks, which can be extensive, costly and time-consuming. To tackle this unsolved problem, we developed an assembly strategy that significantly reduces the falsework usage while still maintaining the equilibrium of the incomplete shell at each assembly step. The key idea is to compute a disassembly strategy inspired by the Jenga game and then reverse it to obtain the actual assembly sequence of the masonry blocks. Rather than using discrete element methods to predict the structural behaviour of the masonry blocks, we employed the GPU-based rigid-body dynamic solver from the engine NVIDIA PhysX, this allows very fast computation speeds while still offering sufficient accuracy for our purposes. Finally, we verified our method using small-scale 3D printed models.
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Proceedings of the IASS Annual Symposium 2017
“Interfaces: architecture.engineering.science”
25 - 28th September, 2017, Hamburg, Germany
Annette Bögle, Manfred Grohmann (eds.)
Copyright © 2017 by <G. Kao, A. Körner, D. Sonntag, L. Nguyen, A. Menges, J. Knippers>
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
architecture . engineering . science IASS 2017 hamburg
September 25th - 28th, 2017
Assembly-aware design of masonry shell structures: a
computational approach
Gene T.C. KAO*,a,b, Axel KÖRNERa, Daniel SONNTAGa, Long NGUYENb, Achim MENGESb, Jan
KNIPPERSa
*University of Stuttgart, Keplerstrasse 11, 70174 Stuttgart, Germany
*e-mail: kao.gene@gmail.com
a Institute of Building Structures and Structural Design (ITKE)
b Institute for Computational Design and Construction (ICD)
University of Stuttgart, Keplerstrasse 11, 70174 Stuttgart, Germany
Abstract
This paper proposes a workflow for Assembly-Aware Design (AAD) of masonry shell structures and
introduces an interactive tool in a CAD environment to assist the design process while simulating the
step-by-step assembly of masonry blocks. Thus designers can explore the design space of masonry
shell structures and be aware of structural performance before the assembly phase, at the early design
stage. Masonry shell structures are an old construction technique, which has recently received a lot of
attention due to new computational methods. Even though the form of such a structure is optimised for
structural performance, its incomplete form during construction often requires the support of
falseworks, which can be extensive, costly and time-consuming. To tackle this unsolved problem, we
developed an assembly strategy that significantly reduces the falsework usage while still maintaining
the equilibrium of the incomplete shell at each assembly step. The key idea is to compute a
disassembly strategy inspired by the Jenga game and then reverse it to obtain the actual assembly
sequence of the masonry blocks. Rather than using discrete element methods to predict the structural
behaviour of the masonry blocks, we employed the GPU-based rigid-body dynamic solver from the
engine NVIDIA PhysX, this allows very fast computation speeds while still offering sufficient
accuracy for our purposes. Finally, we verified our method using small-scale 3D printed models.
Keywords: Masonry structure, shell structure, assembly sequence, disassembly sequence, discrete structures, construction
with less falsework, discrete element modelling, game engine, rigid body dynamics, physical simulation.
1. Introduction
Shell structures play an important role both in architecture and engineering due to their aesthetic
qualities and their efficient load bearing behaviour, the latter being the result of a double curved
geometry.
Although only a few masonry shells exist nowadays, there has been a revived interest in masonry shell
structures over the last few years. This is largely due to the introduction of new computational
methods for design and analysis coupled with significant advancement in digital fabrication methods.
Ongoing research such as Panozzo et al. [8] continues to extend the design space of masonry shell
structures. The load bearing behaviour of masonry structures severely constrains the potential design
space, a solution to which is the appearance of new computational design tools. Specifically, the issue
of fabricating double curved masonry shells with individually shaped blocks can be tackled with
modern computational fabrication tools. However little attention has been given so far to the issue of
assembly, and extensive falsework is usually necessary during the construction stage to temporarily
support the unfinished structure. This necessity of falsework is still a major drawback of this
construction technique. Deuss et al. [5] proposed a different approach by using a sparse set of chains
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Interfaces: architecture.engineering.science
2
to maintain the stones in equilibrium during construction, while another method mentioned in Fitchen
[6] uses tensioned ropes instead of dense falsework to hold blocks in place. These methods, however,
can still be time consuming and result in extra structures that are required to hold the supporting
elements in place.
This research aims to investigate possible solutions to saving falsework during the design process, by
trying to find assembly sequences, where intermediate construction stages are already in equilibrium
and therefore require only minimal falsework. This requires the development of a digital design
environment, where the structural behaviour of various construction stages can be digitally predicted
and fed back in order to modify the assembly sequence or potentially have influence on overall form
and tessellation. Furthermore, the necessity to investigate large amounts of possible configurations
requires the finding of time-efficient analysis methods for those intermediate construction stages, all
of which are discussed in the following sections.
2. Related works
2.1. A freeform stone shell
One of the latest examples of freeform masonry shells was the Armadillo Vault for the Architecture
Biennale in Venice, which shows the design possibilities of masonry shells through the development
of modern design and construction technologies. This project shows the potential of designing more
complex shell geometries using the Thrust Network Analysis (TNA) method developed in the last
years at the Block Research Group (Block [2]), where users can interactively explore the design space
of masonry shells. The method allows us to form-find feasible geometries for compression only
structures, which is a necessary design constraint for masonry shells. The vault was built using CNC
cut limestone blocks, which were then assembled without any additional joints such as mortar or
mechanical fasteners. Rippmann et al. [9] presents the design and construction process of freeform
masonry shells and provides a workflow for the Armadillo Vault from design to production.
The vault was assembled using principally the same techniques as traditional masonry constructions,
with each individual block being fully supported by custom-made falsework.
2.2. Assembly and disassembly
To predict a feasible assembly sequence, Tai [12] uses the assembly-by-disassembly
approach to find a solution for interlocking frames. The procedure is to recursively divide the
assembly into subassemblies, until no part can be removed from the subassembly. Beyeler et
al. [1] explore the sequence of deconstructing an object pile one by one without comprising
its stability. However, these two approaches are not sufficient enough in practice for masonry
shell structures due to its complexity of potential disassembly sequence which leads to huge
calculation times. Therefore, simplification possibilities of the disassemble strategy must be
explored.
South [11] develops a spring-based physics simulation to simulate the Jenga game, which is a game
created by Leslie Scott where players take turns removing one block at a time from a tower then put
the removed block back on the top of the tower. One of the strategies to remove a block from the
tower without compromising its stability is to choose the loosest block. The asymmetrical
redistribution of elements makes some blocks more important to the overall stability of the tower than
others, this looseness allows us to predict a potential disassemble sequence of masonry shell by
reducing the amount of possibilities in each disassemble step. After a feasible disassemble sequence is
found, Backward Assembly Planning (BAP), which formalised by Lee [7], can be used to reverse the
disassembly step to obtain a feasible assembly sequence.
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3. Discrete modelling vs GPU based game engine
In general, masonry structures have been analysed mechanically using graphic methods or simplified
analytical calculations to assess the overall stability of the structures. Finite element methods are often
problematic, due to discontinuities at the joints and difficult interpretation of the results. Lately
Discrete Element Methods (DEM) have received more attention as an alternative way to model the
behaviour of masonry shells. However, they are computationally very expensive.
Van Mele et al. [13] simulates the mechanical behaviour of masonry shells with the commercial
software 3DEC (ITESCA, 2016) and compares the results to a physical model. The results show that
the collapse sequence of the blocks is remarkably similar in both models.
Rigid Body Dynamic (RBD) as commonly used in the game industry also allows us to approximate
the behaviour of discrete particles in a very time-efficient manner. The restriction is that they require
certain simplifications, such as considering all elements as rigid bodies. In the following chapter both
methods are compared in order to assess if RBD can be used to predict the structural behaviour of
masonry shells for form-finding purposes.
In this research, the open source and GPU based RBD platform PhysX from NVIDIA is integrated in
the CAD software Rhinoceros and made available inside the plug-in Grasshopper. It is compared to
the commercial DEM software 3DEC, which is based on formulations from Cundall [3].
Both methods are based on explicit formulations of Newton’s three laws of motion and Coulomb’s
friction model, however DEM takes into account the elastic deformation of the distinct elements and
joints. Below, two simple cases comparing the equilibrium of two blocks using similar parameter
settings are further investigated.
(a) (b)
Figure 1: Block on block rotating and sliding parameters.
In the first experiment, one block A is laid on top of another block B. As shown in figure 1a, d is the
distance between the vertical projection of Block A’s centre of gravity and the edges of Block B, with
d being positive when the vertical projection of the centre of gravity is inside the projected boundaries.
The goal of the experiment is to test if tiling failure is correctly represented. Both methods provide
similar results in the first experiment, and the boxes fall down once d becomes negative, see figure 2a.
In the second experiment the angle between both blocks is progressively increased in order to simulate
sliding failure, see figure 1b. It can also be seen, that both methods provide similar results. In both
experiments the computation using PhysX is approximately 10 times faster compared to 3DEC.
Close to the instability situation the DEM simulation provides higher accuracy by taking deformation
of the building blocks into account. Nevertheless, the results of the RBD method are close enough to
make less time-consuming approximations to filter out a high number of impossible solutions. Once
an assembly sequence is found, DEM can be used for verification.
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Interfaces: architecture.engineering.science
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(a)
(b)
Figure 2: 3DEC (left) and Rhino (right) viewport of two experiments. (a) See figure 1a. (b) See figure1b.
4. Introducing assembly-aware design of masonry shell structures
Based on the workflow of the Armadillo Vault, this research proposes an extended workflow for
Assembly-Aware Design (AAD) of masonry shell structure with four steps as shown in figure 3.
First, a form-found surface that works structurally as a compression-only shell is generated. In the
second step the surface is tessellated and generated to three-dimensional blocks geometry, the
tessellation being a design choice guided also by fabrication constraints, structural behaviour and in
our case assembly as well. Finally, the assembly sequence will be generated based on backward
assembly planning (BAP), formalised in Lee [7]. If no single assembly sequence can be satisfied, then
it is necessary to return to the previous steps by following the flowchart and repeat the process until a
feasible solution is found.
Figure 3: Workflow of assembly-aware design of masonry shell structures.
4.1. Collapse behaviours of different tessellations
Rippmann [10] addresses that the tessellation is crucial for the construction of a masonry shell
structure. For plate structures, Wester [14] shows for patterns with valency-3 nodes the structures are
always stable, which gives indications about geometric constraints on suitable tessellation patterns.
Hence, we verify the results using PhysX simulation to compare different tessellations.
First, three terms are defined here:
assembly absolute coverage
(
nabC
),
assembly coverage
(
naC
) and
assembly area coverage
(n
aaC
):
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{
n
abC
= ni / nm , n
ÎN
} (1)
{
n
aC
= np / nm , n
ÎN
} (2)
{
n
aaC
= np / (nmne), n
ÎN
} (3)
Where n
i
represents the amount of blocks which can be assembled individually, n
p
represents the amount of blocks which can be assembled in pairs or individually and n
e
represents the amount of falsework which is needed on the open edge, while n
m
represents
the amount of all blocks on the shell structure. Therefore, the higher the
nabC,
naC
and n
aaC
value the less falsework is needed, and n
aaC
represents the case which does not count the
block on open edge area that need falsework.
In this section we compare three different tessellations; triangular, quadrilateral and
polygonal, based on the same thrust surface with circular projection plane, to analyse which
tessellation has higher n
abC
and n
aC
values.
The same block generation rule is applied to three different tessellations. The tessellation of the
surface needs to be extruded to three-dimensional blocks, which is done by extruding the edges of the
blocks according to each vertices normal direction by the same distance. This extrusion method does
not guarantee the planarity of the interfaces between the blocks, therefore the constraint-based
optimization scheme presented by Deuss, et al. [4] is used to planarise the interfaces, so that the
fabrication methods proposed by Rippmann et al. [9] can be applied.
In all models identical physical parameters are assigned to the PhysX simulation models.
For all models the amount of blocks is comparable (triangular 121, quadrilateral 122,
polygonal 121), the static and dynamic friction coefficients are set to 0.65 and the density of
the blocks are 2000 kg/m3.
In the simulation, the disassembly approach is used and each block is removed one by one
in order to observe whether equilibrium is still maintained. If all the blocks can be
disassembled without causing the neighbouring blocks to collapse, then there is a chance
that if the process is reversed, the structure can be assembled using minimal falsework. The
choice of the removing blocks sequence is based on the logic of the Jenga game as
presented previously; where in each step the first attempt is to remove the loosest block.
(a) (b)
Figure 4: (a) Algorithm of removing blocks. (b) Comparison of tessellation and stabilities.
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The basic block removal algorithm is described in the pseudocode in figure 4a. Whenever
all blocks are stable (V(Bn) = 0)), the block with the biggest displacement from the original
position (the loosest) is removed.
The results of the PhysX simulations of the three tessellations at various stages are shown in
figure 5. The triangular tessellation was the most vulnerable and after several blocks were
removed, the structure collapsed, showing that the triangular pattern is not stable in general.
When the connection is observed in detail, see figure 6a, it can be seen that in the triangular
tessellation, the two blocks support each other by only a point-like connection. In addition,
it can be seen that in general the structure is very sensitive to imperfections at all stages.
While the quadrilateral tessellation is relatively stable, see chart 4b, the removal of certain
blocks leads to instability of entire rows since the integrity of arches within the shell has
been compromised.
(a) (b) (c)
Figure 5: Screenshots of three tessellation collapse behaviour. (a) Triangular. (b) Quadrilateral. (c) Polygonal.
(a) (b) (c)
Figure 6: Screenshots of three tessellation collapse behaviour.
On the other hand, in polygonal tessellation, almost all the blocks can be removed one by
one without causing its neighbours to collapse (figure 4c, figure 5c). The polygonal
tessellation allows more interfaces to effectively transfer loads and form arches in more than
one direction, see figure 6c. It can be seen that the polygonal tessellation in most situations
allow for the formation of arches in secondary directions which help stabilize the overall
structure (figure 6c).
4.2. Assembly strategy inspired by Jenga
Based on BAP, this research proposes the Masonry Jenga Backward Assembly Planning (MJBAP),
which tests all blocks in the current state for their looseness and by this logic identifies possible
candidates for further disassembly.
If due to the removal of this block (block A, figure 7a) the equilibrium of neighbouring blocks (such
as block B) is compromised, several strategies to modify the disassembly pattern are possible;
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disassemble with falsework, i.e. temporarily support the other blocks (figure 7b), disassemble different
items first such as block B (figure 7c), or disassemble several items as subassembly (figure 7d).
(a) (b) (c) (d)
Figure 7: Disassemble options. (a) Removing A cause B collapse. (b) Using falsework before removing A. (c)
Alternative removal of B. (d) Remove A and B together.
During the disassembly, the selection of the loose items can also be based on different priority
settings. In figure 8b, all blocks with red colour indicate they are the first priority set of disassemble
items because they have more edges exposed to the open area, which is easier to be removed than grey
areas. The algorithm, which was implemented for the disassembly of items with priority settings, is
shown in figure 8a.
(a) (b)
Figure 8: Algorithm to remove blocks with priority settings.
By following this idea, an assembly sequence can be generated by reversing the disassembly sequence
which results in similar options: assemble with another block, assemble a group of blocks all at once
or assemble blocks using falsework on neighbours, then remove the falsework after the blocks are
stable together.
In the figure 9a, a masonry shell structure with 10 blocks is labelled from A to J. MJBAP disassembly
graph reduces a lot of possibility branches and only considers removing either the loosest block or the
block around the open area. The removal of branches considered unsuitable significantly reduces the
complexity of searching for a feasible assembly sequence among the branches, so the assembly graph
of MJBAP is closer to a linear path instead of a complicated graph with numerous branches.
In the disassembly graph figure 9b, the colour red indicates the subassembly with the loosest item that
can be safely removed. The colour orange indicates the collapse of some blocks after the removal of
an item or multiple items. Square shapes mean the subassembly has more than one item while circle
shapes mean only one item remains in the subassembly.
After the feasible disassembly graph is found, an algorithm simply reverses the graph to generate an
assembly sequence.
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(a) (b)
Figure 9: Simple dome diagram and disassemble graph.
5. Results: Interaction simulation models and physical models
Three simulation results with corresponding physical models are shown in this chapter to demonstrate
the possibilities of the AAD process using the assembly strategy presented in this paper, and their
potential to be used in real world projects.
In the first result, a simple dome with 21 blocks where 11 boundary blocks are fixed to the ground and
an assembly sequence for 10 blocks is generated through MJBAP.
Figure 10 shows both simulation results and the test with a physical model, with the same assembly
sequence at intermediate steps. The physical model was 3d printed with the ABS (acrylonitrile
butadiene styrene) thermoplastic through the filament printer UP Plus first generation from UP3D.
And in order to increase the interface static friction coefficient value, finishing paper P100 from
Klingspor AG was attached to joint interfaces.
Figure 10: Simple dome disassembly process, simulation and physical model.
In the second result, a simple vault with three open edges is successfully constructed using limited
amount of falsework, which is only needed for the open edges naaC = 40/40 = 100%, and nearly 50%
of falsework is saved compared to the construction methods using common scaffolding elements.
Only 18 blocks used falsework among 58 dynamic blocks. naC = 40/58 = 68.9%, nabC= 32/58 = 55.1%
(only four of them need to be assembled as two sets).
17 ground blocks are fixed among 75 blocks. PhysX parameter settings are similar to the first result:
static friction 0.65, kinematic friction 0.65, density 2000 kg/m3, block thickness 0.295m, structure
span 10m.
The strategy of disassembling an open edges vault is that all blocks on the open edges must be
supported first. Figure 11 shows the numerical and physical model at different steps from disassembly
to assembly.
For the model making some registration notches are used in order to increase the alignment precision.
In our research, we used the same notch approach system used by Deuss, et al. [5]. In the real
construction, even the notches do not transfer the load, the possibilities of some form of joints would
be necessary.
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Figure 11: Open edges vault disassembly process, simulation and physical model.
In the last result, a more sophisticated vault geometry as described in Rippmann [10] is shown in
figure 12 to demonstrate the potential usage of AAD workflow and MJBAP with a larger amount of
discrete blocks. PhysX parameters are described here: static friction 1.0, kinematic friction 1.0, density
2000 kg/m3, block thickness 0.295m.
Only 36 open edge blocks use falsework among 175 blocks, this helps the construction of masonry
shell save most of the falsework. NaC = 139/175 = 79.4%, nabC = 109/175 = 62.2%, naaC = 139/139 =
100%.
Figure 12: Complex vault disassembly process, simulation.
6. Conclusion:
This research demonstrates the basic knowledge of Assembly-Aware Design’s application for
masonry shell structure. Even though this approach is still a work in progress and in the very early
stages of development, it can potentially assist the designers in reducing extensive falsework during
the construction phase of masonry shell construction.
In future research the following factors should be addressed. First, imperfections due to manufacturing
of the components are currently not considered in the simulations. Although, registration marks such
as notches or spheres can reduce tolerance issues, during the construction phase fabrication and
assembly inaccuracies accumulate to larger deviations. Therefore, scanning and adjusting the
fabrication of each stone after each step could be one possibility to minimize the tolerances of
masonry shells.
Second, safety value and stabilities should be applied in order to construct the structure safely. For
example, after a block has been added to the assembly, we can quickly test its stability by applying a
“disturbance” force, pointing downward with magnitude proportional to the block’s weight, at an
unsupported corner point, and verify if the block still manages to maintain equilibrium
Third, the current approach assumes planar interfaces between the building blocks. By adjusting the
interface geometry in direction or adding interlocking shapes such as wedges while considering the
assembly sequence and direction, the stability can be increased. Fourth, some more accurate
comparisons between simulation and physical model, even with different methods such as Limit
Analysis, can be further explored. Last but not least, a complete AAD workflow can include the TNA
methods with feedback and evaluation methods between all steps to act on all stages of the assembly,
from the global underlying shell geometry, to mesh topology and tessellation and adjustment of
interface geometry.
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Acknowledgements
The research was realised as a master thesis as part of the Integrative Technologies and Architectural
Design Research M.Sc. programme (ITECH) at the University of Stuttgart, led by the Institute of
Computational Design (ICD) and the Institute of Building Structures and Structural Design (ITKE).
Special thanks to Dr. Rippmann and Prof. Dr. Block from BRG at ETH Zurich for providing digital
models which were used as a case study.
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... L'ordre d'assemblage ainsi qu'une conception différente (incliner les briques) permettent donc de faciliter une construction sans cintres. D'autres recherches plus récentes explorentégalement cette possibilité d'éviter ou limiter les cintres en jouant sur l'ordre d'assemblage (Deuss et al., 2014;Kao et al., 2017). ...
... Pour calculer la stabilité d'une structure maçonnée lors de l'assemblage, Kao et al. (2017) utilise le moteur physique en temps réel PhysX de NVIDIA, traditionnellement utilisé dans l'industrie du jeu vidéo. Ce moteur physique se base sur la dynamique des corps rigides et peut simuler un frottement de type Coulomb. ...
... Il serait intéressant de comparer PhysX et 3DEC sur une structure hyperstatique, comme par exemple dans Godio et al. (2018), pour avoir une idée de la validité des résultats, d'autant plus que l'industrie des jeux vidéos privilégie souvent la rapiditéà la précision. Néanmoins, l'article de Kao et al. (2017) nous montre que c'est un outil utile pour des tests rapides. Grâceà la rapidité de la simulation via PhysX, on peut ainsi filtrer les configurations d'assemblages impossibles avant de vérifier avec 3DEC. ...
Thesis
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Ce travail de thèse s'inscrit dans le contexte du développement de la robotique dans la construction. On s’intéresse ici à la construction robotisée de structures maçonnées complexes en ayant recours à de la vision artificielle. La construction sans cintre étant un enjeu important en ce qui concerne la productivité sur un chantier et la quantité de déchets produits, nous explorons, à cet effet, les possibilités qu'offre la rigidité en flexion inhérente aux maçonneries topologiquement autobloquantes. La génération de ces dernières, classique dans le cas plan, est généralisée ici à la conception de structures courbes, à partir de maillages de quadrangles plans et de manière paramétrique, grâce aux logiciels Rhinoceros 3D / Grasshopper. Pour cela, nous proposons un ensemble d'inégalités à respecter afin que la structure obtenue soit effectivement topologiquement autobloquante. Ces inégalités permettent, par ailleurs, d'introduire un résultat nouveau ; à savoir qu'il est possible d'avoir un assemblage de blocs dans lequel chacun des blocs est topologiquement bloqué en translation, mais un sous-ensemble — constitué de plusieurs de ces blocs — ne l'est pas. Un prototype de maçonnerie à topologie autobloquante est finalement conçu. Sa conception repose sur une découpe des joints d'inclinaison variable qui permet de le construire sans cintre. En parallèle, nous abordons des aspects de vision artificielle robuste pour un environnement chantier, environnement complexe dans lequel les capteurs peuvent subir des chocs, être salis ou déplacés accidentellement. Le problème est d'estimer la position relative d'un bloc de maçonnerie par rapport à un bras robot, à partir de simples caméras 2D ne nécessitant pas d'étape de calibration. Notre approche repose sur l'utilisation de réseaux de neurones convolutifs de classification, entraînés à partir de centaines de milliers d'images synthétiques de l’ensemble bras robot + bloc, présentant des variations aléatoires en terme de dimensions et positions du bloc, textures, éclairage, etc, et ce afin que le robot puisse apprendre à repérer le bloc sans trop de biais d’environnement. La génération de ces images est réalisée grâce à Unreal Engine 4. Cette méthode permet la localisation du bloc par rapport au robot avec une précision millimétrique, sans utiliser une seule image réelle pour la phase d'apprentissage ; ce qui constitue un avantage certain puisque l'acquisition de données représentatives pour l'apprentissage est un processus long et fastidieux. Nous avons également construit une base de données riche, constituée d’environ 12000 images réelles contenant un robot et un bloc précisément localisés, permettant d’évaluer quantitativement notre approche et de la rendre comparable aux approches alternatives. Un démonstrateur réel intégrant un bras ABB IRB 120, des blocs parallélépipédiques et trois webcams a été mis en place pour démontrer la faisabilité de la méthode
... Slightly inclined to help cohesion, the arches are achieved one by one and rest on one another (Fig.2b). Other more recent researches propose to limit the use of formwork by changing also the erection strategies [8,9]. ...
... If the sign of the four angles α 1 , α 2 , α 3 and α 4 (0 • < |α i | < 90 • ) alternate between positive and negative values, meaning (α i · α i+1 ) < 0, then, sin (α1 + α3) · sin (α2 + α4) = − sin (|α1| + |α3|) · sin (|α2| + |α4|) < 0 (9) Hence, Eq. 6 is verified and a general result is that a block generated from a parallelogram quadrangle with angles α i whose signs alternate between positive and negative is translationally interlocked. ...
Article
The paper presents new results about the geometry of topological interlocking masonries and some possibilities they present to build without formwork. Construction without the use of formwork may be an important issue concerning both productivity increase and decreasing of waste generated on a construction site. Due to the development of computational design and robotics in the construction industry, it makes sense to (re)explore innovative design and process of complex masonry structures. The design of this kind of masonry is standard for planar structures, and in this paper, a generalisation is proposed for the parametric design of curved structures. To achieve this, a criterion for translationally interlocked structure based on quadrilateral meshes is exhibited. The application of this criterion is then extended to masonry structures derived from other patterns. Physical prototypes of topological interlocking masonry are also presented. One of these designs seems to allow construction without formwork.
... Form-finding methods from graphical statics are used for compression only shells [22] that can be manufactured and joined from relatively small individual parts [23]. The same research group also comes up with proposals for the fitting of concrete ceilings by means of curved edge shapes based on the principal force flow [24]. As a result, all of these approaches have structural efficient constructions and some planar modules, but are not focused or do not have much control over the local properties of the elements for the particular production process: size, shape, geometry of interfaces between connections, etc. ...
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Although they are very efficient structures, concrete shells have lost popularity due to the complexity of the traditional construction process using cast-in-place concrete. A key concept to overcome the labor-intensive formwork in situ is the segmentation of the shells into prefabricated parts. In order to avoid individual formworks during prefabrication as well, the authors rely on extrusion-based 3D printing of strain-hardening cement-based composite (SHCC). The goal is a highly automated, scalable, and adaptable flow-prefabrication of modules controlled by a holistic digital design process. Such the creation of modular free-form shell structures can be accelerated significantly, resulting in structures comparable with gridshells. Starting with the problem statement and the elaboration of the technology used, the main contribution of this research is the development of geometrical methods for modularization based on given production conditions. The challenge lies in the free-form geometry discretization with respect to the structural analysis and within the defined constraints such as planar quads, no edge torsion, and minimal material consumption. Methods of discrete differential geometry for circular PQ (planar quad) mesh generation are combined with Response Surface Methodology (RSM) for multi-objective optimization of the global parameterized shape. The results were illustrated in a study case where the geometrical and structural production parameters of starting and final shell are compared.
... Blok [12] also comes up with pro-posals for the fitting of concrete ceilings by means of special edge shapes. These are geared towards additive manufacturing methods [13]. With regard to curved patches for discretization, in particular hyperbolic paraboloids (HP), the work by Pottmann on ruled surface strips and by Kotnik on the statics of HP patches should be men-tioned [14] [15]. ...
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Shell-like, double curved and thus above-average performance structures, are usually produced monolithically on site. For industrial advancement, however, they must be divided into transportable modules which can be assembled on the construction site (design for assembly). Models are lattice shells made of steel and glass, in which predominantly flat sub-surfaces (modules) are used. Therefore, the main question is: Which modularizations are suitable for flow production with mineral building materials? In this paper designed free-form surface is going to be discretized as PQ circular mesh system, suitable modules for 3D concrete printing. Moreover, the multi-criteria optimization is done with Response Surface Methodology (RSM) in order to get optimal final shape. The goal is to start from the arbitrary shape, that can be generated from two curves, with possible two-way division into modules and compare it with the resulted discretized PQ circular mesh system, realized with new algorithm. The comparison can be defined through two main criteria: geometrical and structural.
... Assembly-aware design or stability during assembly is a new research area that has received much attention recently. Kao et al. [46] proposed a design process with a heuristic strategy to assemble discrete shell structures stably without using falsework. They utilised an existing game engine as a stability analysis tool, which is not guaranteed to be reliable. ...
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The rigid-block equilibrium (RBE) method uses a penalty formulation to measure structural infeasibility or to guide the design of stable discrete-element assemblies from unstable geometry. However, RBE is a purely force-based formulation, and it incorrectly describes stability when complex interface geometries are involved. To overcome this issue, this paper introduces the coupled rigid-block analysis (CRA) method, a more robust approach building upon RBE’s strengths. The CRA method combines equilibrium and kinematics in a penalty formulation in a nonlinear programming problem. An extensive benchmark campaign is used to show how CRA enables accurate modelling of complex three-dimensional discrete-element assemblies formed by rigid blocks. In addition, an interactive stability-aware design process to guide user design towards structurally-sound assemblies is proposed. Finally, the potential of our method for real-world problems are demonstrated by designing complex and scaffolding-free physical models.
... The assembly process is a critical stage in the fabrication of compressive-only structures (Beyeler, Bazin, and Whiting 2015;Kao et al. 2017) since elements are designed to bear scale pavilion was designed and fabricated that inscribes a 5 x 4 x 3 cube as its bounding box (Fig. 9). ...
Conference Paper
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Net structures, because of their minimal material waste and intuitive aesthetics, are gaining more interest recently. There are various efforts to redesign the tensile- and compression-only structures, as the computational tools and novel materials have broadened the scope of geometries possible to construct. However, the fabrication process of these structures faces different challenges, especially for mass construction. Some of these challenges are related to the technology and equipment utilized for materializing these complicated forms and geometries. Working with concrete as a quickly forming material for these irregular forms seems promising. Nevertheless, using this material has difficulties, including the preparation of formworks and joints, material reinforcement, structural behavior in the fresh state, and the assembly procedure. This paper introduces a method based on computational design and geometrical solutions to address some of these challenges. The goal is to shift the complexity of construction from the high-tech equipment used in the fabrication stage to integrating design and fabrication through a hierarchical system made entirely by affordable 2D CNC laser cutters. The stages of developing the method and the process of designing and building an architectural size proof-of-concept prototype by the proposed method are discussed. The efficiency of the method has been shown by comparing the designed prototype with the Con-Create Pavilion.
... Several subprojects have identified assembly on the construction site as a critical design factor and consequently place the last step of the production at the beginning of their considerations (design for assembly). 21 Technically, joints, especially dry joints, are weak points in traditional concrete construction and should be avoided if possible. ...
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Building in heavy rain is seldom beneficial, but common practice on site. It promotes inaccuracies and impairs the use of modern but sensible high-performance materials and costs time, since disruption in construction frequently causes complicated returns to the planning process. Nevertheless, a handcrafted production process is still considered the one and only alternative since all buildings are unique and thus must be manually constructed on site. Indeed? The priority program entitled “Adaptive modularized constructions made in a flux” funded by the German Research Foundation follows a completely new approach. Buildings are divided into similar modular precast concrete elements, prefabricated in flow production, quality assured, and just-in-time assembled on site. Comparable to puzzles with many pieces, the uniqueness of the structure is maintained. The motto is: “Individuality on a large scale - similarity on a small scale”. The contribution presents approaches of modularization, production concepts, and linking digital models. Serial, stationary prefabrication enables short production times and resource-efficient modules that are assembled to load-bearing structures with low geometrical deviations. Stringent digitalization ensures high quality of all intermediate steps. These comprise fabrication, assembly, and the whole service life of the structure. The result is a lean production process. This article is protected by copyright. All rights reserved.
... Mehrere Teilprojekte haben den Zusammenbau auf der Baustelle als entwurfskritischen Faktor identifiziert und setzen folgerichtig den letzten Schritt an den Anfang ihrer Überlegungen (design for assembly)[20]. Eigentlich sind Fugen, insbesondere Trockenfugen, im traditionellen Betonbau Schwachstellen und möglichst zu vermeiden. ...
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This paper proposes a strategy for constructing unreinforced segmented shells with the aspiration to bring together several related research fields. By incorporating data from structural analysis and digital simulations into a continuous workflow, an automated building system is introduced. The research aims to provide a methodology of translation between digital form-finding, optimisation strategies and physical materialisation by persisting through the interdependent stages of design and robotic assembly. Through an integration of structural analysis data, a force- driven form-finding process is determined, accompanied by a custom tessellation pattern. System stereotomy is developed as an integrated interlocking system, derived from material properties and robotic fabrication constraints. Assembly process is developed as an automated construction 'pick and place system' capable of customized, on-site fabrication of architectural-scale structures. The system consists of multiple six-axis robotic arms, carried on mobile platforms with scissors lifts. The complexity of robotic manufacturing is addressed through developing a custom robotic toolpath. Correlations between these steps of the process are verified through developing a large-scale prototype, tested with proposed robotic assembly logic.
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This paper describes the development of an unreinforced, freeform vault consisting of 399 discrete limestone blocks with thicknesses ranging from 5 to 12 cm. The vault covers an area of 75 m2 and spans more than 15 m in pure compression, without mortar between the blocks. We discuss how the design of the vault and its individual pieces was entirely driven by constraints related to the fabrication process and to the architectural and structural requirements and timeline of the project. Furthermore, we describe the form-finding process of the shell’s funicular geometry, the discretisation of the thrust surface, the computational modelling and optimisation of the block geometry, and the machining process. Finally, we discuss some of the strategies that were developed for dealing with tolerances during fabrication and construction.
Thesis
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Addressing both architects and engineers, this dissertation presents a new framework for the form finding and design of fabrication geometry of discrete, funicular structures in the early design phase. Motivated by ongoing debates about digital architecture and funicular shell form finding, it introduces a new methodology for structurally-informed design of curved surface architecture through the use of geometrical rather than analytical or numerical representations of the relation between form, forces and fabrication. Based on Thrust Network Analysis (TNA), new algorithms are presented that enable an interactive exploration of novel funicular shapes, enriching the known formal vocabulary of shell architecture. Using TNA, the framework adopts the same advantages of techniques like graphic statics, providing an intuitive and educational approach to structural design that ranges from simple explorations to geometry-based optimisation techniques. Complementary to this structurally-informed design process, the work reflects on the latest building technologies while also revisiting historic construction techniques for stereotomic stone masonry and prefabricated concrete shells to develop efficient fabrication design strategies for discrete funicular structures. Based on architectural, structural and fabrication requirements, several tessellation approaches for given thrust surfaces are developed for the design of informed discretisation layouts of any funicular shape. The flexibility and feasibility of the form-finding framework is demonstrated in several case studies employing the new structural design tool RhinoVAULT, which implements the developed form-finding methods. The use of fabrication design strategies is discussed in a comprehensive case study that shows project-specific tessellation design variations and first fabrication results for a complex stone masonry shell.
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We present ShapeOp, a robust and extensible geometric modelling paradigm. ShapeOp builds on top of the state-of-the-art physics solver (Bouaziz et al. in ACM Trans Graph 33:154:1–154:11, 2014). We discuss the main theoretical advantages of the underlying solver and how this influences our modelling paradigm. We provide an efficient open-source C++ implementation (www. shapeop. org) together with scripting interfaces to enable ShapeOp in Rhino/Grasshopper and potentially other tools. This implementation can also act as a template for future integration of computer graphics research. To evaluate the potential of ShapeOp we present various examples using our implementation and discuss potential implications on the design process.
Chapter
The aim of object pile deconstruction is to safely remove elements one by one without compromising stability. The number of combinations of removal sequences increases dramatically with the number of objects and thus testing every combination is intractable in practical scenarios. We model the deconstruction sequencing problem using a disassembly graph, and investigate and discuss search strategies for discovery of stable sequences in an architectural context. We run and compare techniques in a large-scale experiment, on various virtual scenes of architectural models composed of different shapes, sizes and number of elements.
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The distinct element method has advanced to a stage where the complex mechanical interactions of a discontinuous system can be modelled in three dimensions. An important component is the formulation of a robust and rapid technique to detect and categorize contacts between three-dimensional particles. The technique, described in Part I of this paper, can detect the contact between blocks of any arbitrary shape (convex or concave) and represent the geometrical and physical characteristics prescribed for the contact (e.g. three-dimensional rock joint behaviour). The method utilizes an efficient data structure which permits the rapid calculation on a personal computer of systems involving several hundred particles.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2009. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 145-153). This dissertation presents Thrust Network Analysis, a new methodology for generating compression-only vaulted surfaces and networks. The method finds possible funicular solutions under gravitational loading within a defined envelope. Using projective geometry, duality theory and linear optimization, it provides a graphical and intuitive method, adopting the same advantages of techniques such as graphic statics, but offering a viable extension to fully three-dimensional problems. The proposed method is applicable for the analysis of vaulted historical structures, specifically in unreinforced masonry, as well as the design of new vaulted structures. This dissertation introduces the method and shows examples of applications in both fields. Thrust Network Analysis, masonry, historic structures, compression-only structures, limit analysis, equilibrium analysis, funicular design, form-finding, structural optimization, Gothic vaults, reciprocal diagrams. by Philippe Block. Ph.D.