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A case study on the influence of multiscale modelling in design and structural analysis

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The current paper discusses the role of multi-scale modelling within the context of design and structural analysis. Depending on the level of detail, a design model may retain, lose or enhance key information. The term multi-scale refers to the breakdown of a design and analysis task into multiple levels of detail and the transfer of this information between models. Focusing on the influence that different models have on the analysed performance of the structure, the paper will discuss the advantages and trade-offs of coupling multiple levels of abstraction in terms of design and structure. To illustrate the concept of multi-scale modelling, the prototype of a bridge structure that was realised making use of this information transfer between models will be presented. The prototype primarily takes advantage of the geometric and material stiffening effect of incremental metal forming. The local features of the formed panels guarantee a proper load transfer between the elements, otherwise impossible to achieve in the planar, underfomed state of the aluminium panels. In terms of structural analysis, each successive level of detail dramatically increases the computational effort required to assess the performance of the structure. By adopting the multi-scale modelling approach, the level of model refinement can be adapted to the requirements of the analysis and therefore relieve the simulation complexity especially in the early stages of design.
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Proceedings of the IASS Annual Symposium 2017
“Interfaces: architecture . engineering . science”
September 25 - 28th, 2017, Hamburg, Germany
Annette Bögle, Manfred Grohmann (eds.)
Copyright © 2017 by <name(s) of the author(s) as listed above>
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
A case study on the influence of multiscale modelling in design
and structural analysis
Riccardo LA MAGNA*, Paul NICHOLASa, Mateusz ZWIERZYCKIa, Esben NORGAARDa,
Scott LEINWEBERa, Mette RAMSGAARD THOMSENa, Christoph GENGNAGELb
* Konstruktives Entwerfen und Tragwerksplanung (KET), UdK Berlin, Hardenbergstr. 33, Berlin,
r.lamagna@udk-berlin.de
a Centre for Information Technology and Architecture (CITA), KADK Copenhagen
b Konstruktives Entwerfen und Tragwerksplanung (KET), UdK Berlin
Abstract
The current paper discusses the role of multi-scale modelling within the context of design and structural
analysis. Depending on the level of detail, a design model may retain, lose or enhance key information.
The term multi-scale refers to the break-down of a design and analysis task into multiple levels of detail
and the transfer of this information between models. Focusing on the influence that different models
have on the analysed performance of the structure, the paper will discuss the advantages and trade-offs
of coupling multiple levels of abstraction in terms of design and structure.
To illustrate the concept of multi-scale modelling, the prototype of a bridge structure that was realised
making use of this information transfer between models will be presented. The prototype primarily takes
advantage of the geometric and material stiffening effect of incremental metal forming. The local
features of the formed panels guarantee a proper load transfer between the elements, otherwise
impossible to achieve in the planar, underfomed state of the aluminium panels. In terms of structural
analysis, each successive level of detail dramatically increases the computational effort required to
assess the performance of the structure. By adopting the multi-scale modelling approach, the level of
model refinement can be adapted to the requirements of the analysis and therefore relieve the simulation
complexity especially in the early stages of design.
Keywords: multi-scale modelling, design, structural analysis, metal forming,
1. Introduction
Most physical phenomena can be described at different scales of resolution. Depending on the level of
detail, certain aspects may lose relevance as others gain importance according to the specific scale of
observation. In general, at higher scales certain abstractions can be operated that simplify the description
of the phenomena under examination. These simplifications rely on observations at a lower scale along
with the individuation of recurrent patterns and their formal description. These descriptive frameworks
are then employed at the macroscale to model the behaviour of the phenomena and simplify the
complexity of the system’s model. It could well be possible to model a whole bridge at atomistic level,
but the complexity arising by doing so would not be justified by the added insight on the global
behaviour of the structure. Taking into account the explicit microstructure at the coarse scale model is
practically not feasible due to the prohibitive computational cost that it would lead to. The reduction of
computational models to simplified versions is typical in science and engineering. The phenomena that
rule the behaviour of the system at a lower scale of observation are normally safely disregarded.
Nonetheless, in certain situations a concurrent modelling approach at multiple scales might be necessary
to correctly describe the object of study. For this reason, a transfer of information must then occur at
different levels of resolution to achieve the best trade-off between scales of observation.
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Interfaces: architecture.engineering.science
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Modelling approaches that actively rely on the exchange of information between different levels are
termed multiscale. They originate on the base of the following observations: 1) that no single model or
framework is adequate on its own to capture the full behaviour of a system, since the information and
models that we have about the world are partial and bounded; 2) That modelling efficiencies can be
gained by exploiting different levels of resolution; and 3) that high resolution models quickly becomes
intractable at larger scales (Elliot [1]). Multiscale approaches assemble a multiplicity of models, each
capable of describing an important feature using a particular framework. By transferring information
between frameworks, these models are linked together so that the output of a given model becomes the
input for another. Multi-scale modelling is therefore the identification and construction of suitable
models and frameworks, together with the application of modelling techniques that relate or ‘bridge’
these models and frameworks (Elliot [1]) by coupling together different kinds of description. Multiscale
models aim to describe a problem by separating it into discrete models, typically of different type and
nature. They leverage that, for some applications, a model does not require the full complexity of the
object. Each model addresses a particular feature of the design problem and can therefore focus
exclusively on the correct representation of that specific feature. These models parameterize one
another, either sequentially or simultaneously. A key concern is therefore those techniques which enable
the information generated within each of these models to flow to others.
In engineering, and especially material science, multiscale models have been widely developed to
capture the physics of microstructures to be able to efficiently predict the macroscopic behaviour of
materials. Identifying the relationships between microstructure and macroscopic properties is an
essential problem in material science as well as computational mechanics (Nguyen et al. [2]). Multiscale
methods have been successfully employed in the simulation of composite structures, masonry, fluids,
polymers and more. Such models are well suited in the case of heterogeneous and multiphase materials.
The transfer of information between levels of observation typically occurs through numerical and
computational homogenization methods. Homogenization is a method to determine the properties of a
heterogeneous material at microscale, thereby allowing one to substitute this material with an equivalent
homogeneous material or its descriptive information. Mainly used and developed in the field of material
science, multiscale approaches are also attractive in other research contexts where multiple levels of
resolution are involved in the analysis of the system.
Modelling in architecture is a typical example of hierarchical organisation of multiple scales that focus
on one level at a time, gradually refining and adding detail from the larger to the smaller scale. The
exchange of information between scales typically follows a simplified process, as the relationships are
often linear among multiple levels of design. Architectural structures can be thought similarly: as nested
organizations from which features, behaviours and properties emerge based on interactions across scales
and systems (Nicholas et al. [3]).
Within architecture and structural design, one approach to multiscale modelling is to link a macro scale
structural domain with a micro scale material domain. With either design generation or optimization as
a goal, each level is varied so as to achieve a specific global effect. In the simplest case, this involves
the iterative solution of one problem at the macro level (stability, for example) and several problems
(which together inform the best local configuration) at the material level (Coelho and Guedes [4]). Some
multi-scale models, including the approach described in this paper, include an intermediate meso scale
level, in this case related to an architectural component and its detailing. But because the type and level
of detail of information is different for the different levels of description, multi-scale models can easily
be constrained by the need to translate information. For this reason, bridging techniques and
communication techniques which translate, coarsen or refine information as they pass it between models
are central to the multiscale modelling process. The mesh-based techniques described in this paper
directly address this issue.
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Figure 1: View of the bridge prototype
2. Case study: A Bridge Too Far
Thin panelised metallic skins play an important role in contemporary architecture, often as a non-
structural cladding system. Strategically increasing the structural capacity of this cladding layer can
offer significant savings for secondary and primary structural systems, but requires a modelling
approach that guards against instabilities due to buckling at three distinct scales: buckling of the
structure, buckling within panel elements, and buckling and tearing that can occur during the sheet
forming process itself. This deep entanglement of macro and micro necessitates a multiscale approach.
The case study discussed in the following paragraphs made use of multiple modelling scales to handle
the increasing geometric complexity arising at higher levels. The structure consists of 51 unique planar,
hexagonal aluminium panels, arranged into an inner and outer skin (Figure 1, Figure 2). The thickness
of each panel varies locally, though it is at maximum 1mm thick. Excluding buttresses, the bridge spans
3m and weighs 40kg. Geometric features for resisting local footfall, buckling within each panel and
structural connections – for managing shear forces across inner and outer skins – are produced through
the custom robotic forming of individual panels.
Figure 2: Hierarchical multiscalar nesting of hexagonal elements
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Interfaces: architecture.engineering.science
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Figure 3: Scheme of the adopted multiscale approach
The computational design approach uses a data tree structure to allow different computational operations
including shape discretization, planarization, structural analysis, generation of rigidisation patterns,
calculation of material properties, and optimization (Figure 3). These operations occur on the scale that
is best suited or most efficient. A particular class, the HNode Class (Nicholas et al. [5]), was developed
to connect these operations by creating and supporting bidirectional information transfer across data
trees. This process happened at the lowest level of the tree, and is passed to a medium level resolution
to inform the structural analysis. An example of downstream data propagation is the distinction between
panels and seams. The bidirectional workflow tied multiple scales together in a consistent and
manageable way. Ability to process and reference data in parallel to other levels made an element on
one level aware of information at any other level of the tree. This enabled adaptation of any particular
element based on higher or lower level information within an automated feedback loop, which includes
fitness criteria from multiple scales of the model.
Figure 4: Incremental sheet forming process
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Figure 5: Double sided robotic approach
This project used robotic Incremental Sheet Forming (Jeswiet et al. [6]) to introduce rigidising and
connection geometries into a panelised structure (Figure 4). The Incremental Sheet Forming (ISF)
method imparts 3D form on a 2D sheet, directly informed by the 3D CAD model. A simple tool
facilitates mould-less forming by moving over the surface of a sheet to cause localized plastic
deformation. In this research, a double sided robotic approach was used that supported forming out of
plane in opposing directions (Figure 5) (Nicholas et al. [7]). Geometric features that locally stretch the
sheet out of plane increase structural depth, prevent lines of bending, and also provide architectural
opportunities for connection and surface expression. Depending on the geometric transformation,
properties are locally introduced into the material to different degrees, according to the depth and angle
attained. At the material scale, local thinning of the stretched metal can lead to buckling or tearing when
approaching zero thickness. The metal also undergoes cold working during the fabrication process,
introducing local variations in hardness and yield strength. Aluminium 5005H14 was chosen as it
provided a good balance between formability, forming speed, initial thickness and initial hardness.
3. Structural analysis
Extensive analysis accompanied the development of the bridge to assess its main features and global
structural behaviour. As the modelling approach was mesh-based since the early stages of design, it
made sense to employ the same base geometry to perform in parallel the structural analysis. In this way,
a direct exchange of information between the architectural development and the structural analysis was
established. The same models could be easily transferred between domains and be used directly without
further required adjustments. For this reason, the usual pre-processing steps for Finite Element Analysis,
namely the meshing of the continuous surface elements, could be skipped. Besides the immediate
consequence of time saving, the possibility of working on the same geometrical model meant that a
direct feedback between the architectural and the engineering working environments could be
established without further manipulation of the input data. By doing so the input for the structural
analysis corresponded to the output of the architectural design. In turn, the results of the structural
analysis could be fed directly into subsequent design iterations of the bridge. The seamless exchange of
information enabled the efficiency of the process, therefore saving time and computational effort during
the development of the design.
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Figure 6: View of the structural model
3.1. Information flow and scale aspects
Despite the advantages mentioned in the previous section about the fusing of the architectural and
structural models, the extreme level of detail of the highest mesh hierarchy posed an inherent problem
for the agile analysis of the bridge. The third and highest level of mesh refinement quickly approached
a number of elements which became intractable for preliminary structural analysis iterations. The model
in Figure 5 shows the level of mesh detail that was used during the development of the project for the
assessment of the structural behaviour. The model iteration displayed in Figure 5 corresponds to the
second level of mesh refinement out of three total levels that were employed during the development of
the prototype. Compared to the full resolution mesh, at this scale many geometric features were
inevitably lost. As can be seen in the model above, the rigidisation pattern of each panel is only slightly
outlined. The principle characteristic and main feature that donated stiffness to the panels and the global
structure was therefore erased from the model.
In Figure 6 an analysis of individual panels at each level of resolution was conducted to evaluate the
trade-off between the different models. The panels are analysed under self-weight and the deformation
is displayed with a 300x magnification factor. Each panel is simply supported around the edges and is
modelled with the same 5005-H14 aluminium material of the bridge. The aluminium has a stiffness of
69000 MPa for a specific weight of 27 kN/m3. The analysed panels were part of the bridge’s deck and
measure roughly 0.5m x 0.7m. From the front view and perspective, the strong influence that the
rigidisation pattern has on the stiffness of the panels can be noted. In the third iteration of refinement
the deflections of the panel are noticeably less visible in comparison to the previous two levels. This
suggests that the stiffening effect of the pattern is not entirely negligible when evaluating the global
performance of the structure. At each level of refinement, the analysed behaviour of the bridge changes
dramatically, as the bending stiffness of the panels increases exponentially with respect to the geometric
details embedded in the mesh model.
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Interfaces: architecture.engineering.science
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Figure 7: Deflections (300x) of panels at different levels of resolution
The compromise between accuracy and agility of analysis is extremely relevant in cases like this one.
The trade-off operated by over-simplifying the computational model may not be adequate when the
estimation error overwhelms the advantage of speed. Although the choice that was made in the
development of the prototype favoured a safe approach by underestimating the stiffness of the panels,
it has been shown that the geometric stiffening effect of the incrementally formed pattern is not
negligible. The test case discussed here suggest that other methods should be sought that ease the transfer
of information between the design and structural domain. A possible approach that lends itself well to
this type of design investigations would be homogenisation techniques that were briefly introduced at
the beginning of the paper. Rather than approaching the problem in a brute-force manner by feeding the
raw mesh data into the structural analysis, the stiffness of single pattern portions could be evaluated
beforehand and used as numerical input for the local stiffness of the individual finite elements. In this
way, the bulk of data can be reduced to a single piece of information rather than having to deal with an
explicit and heavy description of geometric features.
4. Conclusions
This paper discussed the application of a multi-scale modelling approach developed for the design and
fabrication of a prototypical bridge structure. Different levels of model resolutions offered a seamless
transfer of information between the modelling frameworks. The multiscale process was tested and put
into practice within the design environment of the bridge. The information transfer between the design
environment and the structural analysis ran through the same mesh models, therefore reducing the need
of translating working files from one platform to the other. Nonetheless, the high level of resolution of
the design working models rendered the structural calculations not efficient enough for quick design
explorations. Investigations on the mesh sensitivity showed that at lower levels of detail the accuracy of
the simulation was partially compromised. Drawing from existing research in the field of multiscale
modelling for material simulation, further developments and ongoing research will be focusing on the
implementation of alternative methods of information transfer such as homogenisation techniques. In
this way, an efficient and seamless link between design and structural simulation could be achieved.
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References
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Heterogeneous Materials: A Review on Recent Developments, in Journal of Multiscale Modelling,
2011, 3, 4, 1–42.
[3] Nicholas P., Zwierzycki M., Stasiuk D., Norgaard E. and Ramsgaard Thomsen M., Concepts and
Methodologies for Multi-scale Modeling A Mesh-based Approach for Bi-directional Information
Flows, in ACADIA 2016. Posthuman Frontiers, 2016.
[4] Coelho F. and Guedes R., A Hierarchical Model for Concurrent Material and Topology
Optimisation of Three Dimensional Structures, in Structural and Multidisciplinary Optimization,
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[5] Nicholas P., Zwierzycki M., Stasiuk D., Norgaard E., Leinweber S. and Ramsgaard Thomsen M.,
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