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Exploring Software Approaches for the Design and Simulation of Bending Active Systems


Abstract and Figures

Emerging directly from a masterclass held by the authors at IASS 2017, this paper presents a quantitative and qualitative benchmark comparison between three distinct software environments, namely SOFiSTiK, Kangaroo and Kiwi3d, framed specifically within the context of designing and simulating bending-active structures. The three environments differ significantly not only in their numerical methods and implementation but also in their stages of software development, licensing structure and design intent and so their comparison represents a timely and valuable insight into the status quo for the design of bending-active hybrid structures.
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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 Anna M. BAUER, Philipp LÄNGST, Riccardo LA MAGNA, Julian LIENHARD, Daniel
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Exploring Software Approaches for the Design and Simulation of
Bending Active Systems
Anna M. BAUERa, Philipp LÄNGSTb, Riccardo LA MAGNAb, Julian LIENHARDb, Daniel PIKERc,
Gregory QUINN*, Christoph GENGNAGEL, Kai-Uwe BLETZINGERa
*Department for Structural Design and Engineering (KET), Berlin University of the Arts
Hardenbergstrasse 33, 10623 Berlin
aChair of Structural Analysis, Technical University of Munich
bstr.ucture GmbH, Stuttgart
c Robert McNeel & Associates, England
Emerging directly from a masterclass held by the authors at IASS 2017, this paper presents a quantitative
and qualitative benchmark comparison between three distinct software environments, namely
SOFiSTiK, Kangaroo and Kiwi3d, framed specifically within the context of designing and simulating
bending-active structures. The three environments differ significantly not only in their numerical
methods and implementation but also in their stages of software development, licensing structure and
design intent and so their comparison represents a timely and valuable insight into the status quo for the
design of bending-active hybrid structures.
Keywords: bending-active, hybrid, finite elements, IGA, Kangaroo, SOFiSTiK, Kiwi3d
1. Introduction
The three software environments explored in this paper (SOFiSTiK, Kangaroo, Kiwi3d) employ
different methods in their implementation of numerical solvers, pre- and post-processing of geometry,
element formulations and user interfacing. Our findings reveal how the mechanical accuracy, speed and
interactivity can vary between the environments and detail the pros and cons between discrete and
NURBS-based finite elements as well as between numerical solvers based on local or global stiffness.
The previous decade has seen a surge of academic interest in and construction of bending-active hybrid
structures. This has led to the emergence of numerous software environments which address questions
on the form-finding and evaluation of bending-active structures. The software environments presented
in this paper represent a selection of the most common approaches currently in use. There are however
alternative software solutions which are commercially available or currently under development in the
field of bending-active structures, which are not considered here.
2. Methods
The following subchapters aim to describe each of the three methods concisely but with sufficient
technical detail to highlight their distinct compositions.
2.1 Method 1: SOFiSTiK (discrete elements, global stiffness-based solver)
The Finite Element Method is a general numerical method for the solution of partial differential
equations. FEM has become the de facto standard in the field of structural analysis, and it is commonly
used as the tool of choice for a wide variety of engineering problems. Similar to other numerical
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
methods, the Finite Element Method discretises a continuum with a certain number of elements, hence
its name. The method approximates a continuous domain into a finite set of elements.
The Finite Element Method is based on a variational formulation of the principle of virtual work. The
principle of virtual work states that the sum of work done by external forces applied on a system must
be balanced by the sum of internal work in an arbitrary (but small) virtual displacement. The Finite
Element Method is a matrix-based approach, and for static and quasi-static problems it uses implicit
integration schemes which solve a system of algebraic equations where the unknowns are represented
by the displacements. The Finite Element Method is exemplified in the well-known relationship:
𝑲𝒅 = 𝒇
where K represents the stiffness matrix of the system, d the vector of unknown displacements and f the
vector of external forces. Typically, the stiffness matrix is derived by considerations of virtual work,
although other derivations are also possible.
The commercial software SOFiSTiK is a general-purpose Finite Element based program with a strong
focus on structural applications. Besides modules for linear static analysis, SOFiSTiK also implements
geometrically non-linear solving schemes for the simulation of large deflections. Benchmarks can be
found in [1], [2]. Recently, an Active Bending module (ACTB) was implemented which automatically
calculates the internal stress state from a curved beam under the assumption that it was initially straight.
2.2 Method 2: Kiwi3d (NURBS-based elements, global stiffness-based solver)
Kiwi3d, a new plugin for Grasshopper, is based on Isogeometric Analysis (IGA) as introduced by
Hughes et al [3] in order to directly integrate structural analysis into CAD. IGA is a subgroup of Finite
Element Methods. Its special characteristic lies in the usage of Non-Uniform Rational B-Splines
(NURBS) as basis functions for the Finite Elements, which are commonly used for the geometry
description in CAD. Hence, a complete reparametrization (meshing) of CAD models for analysis is
avoided. The degrees of freedom do not lie on the surface of the element but on the control points of the
geometry. The refinement can be done at every stage before and during the analysis without changing
the geometry. The applied FEM-kernel is Carat++, which is proprietary research from the Chair of
Structural Analysis at the Technical University of Munich. It is available in combination with Kiwi3d
as a work-in-progress version. The plug-in Kiwi3d generates a text file in order to communicate with
the solver. In turn the plug-in reads the results provided in a further text file for the visualization and
evaluation. The text-based interface would also allow the linking of other IGA-enhanced solvers with
only small effort. However, Carat++ has advanced features for the non-linear simulation of construction
stages and form-finding process, including cutting pattern, which is very beneficial in the design of
bending-active hybrid structures. Application examples in this context can be found in [4][6].
Further advantages of using IGA in the design of these kind of structures can be seen in the independence
of the parametrization for boundary conditions such as loads, supports and coupling entities. All CAD
features are available e.g. for the derivation of additional structural members. The method-inherent
ability to consistently represent the whole sequence of construction stages during the design process,
without losing or having to approximate stresses or displacements, enable a detailed evaluation and
enhanced design. The continuous basis functions allow a smooth representation of geometry and results.
But this implies as well that discontinuous deformations and stresses within the domain cannot exactly
be represented.
2.3 Method 3: Kangaroo (discrete elements, local stiffness-based solver)
The dynamic relaxation (DR) method for iteratively solving structural problems was first developed in
the 1960s [7] and has since become well established in many fields. In the built environment, DR is
commonly associated with stiffness-independent membrane form-finding [8] or with the distribution of
architectural grids over curved surfaces [9]. The form of DR used in Kangaroo differs somewhat from
the standard force-based approach, where forces acting on each node are summed to calculate
accelerations (from which velocities, then positions are updated), instead making use of projections.
“Goals” are defined as functions acting on a set of points, which can describe geometric constraints,
elastic material elements, applied loads and other energies. Each goal returns a set of target positions for
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
each point it acts on, projecting them to their closest zero energy state. This can result in multiple target
positions for each point, depending on the number of goals acting on it, and these are then combined in
a weighted averaging step. The solver alternates between these two simple local steps to minimize the
global energy - a form of the alternating direction method of multipliers (ADMM)[10].
Since the strengths of the goals relative to one another are given by the scalar weighting factors in the
averaging step, this keeps the new position for each point within the convex hull of its target points,
avoiding the problem of ‘overshooting’ which can occur in the force based DR method, where elements
with high stiffness can result in large acceleration vectors, leading to instability, and reducing the
timestep sufficiently to mitigate this can be difficult or lead to impractically slow convergence. Another
simple projection-based constraint satisfaction technique which has been widely used in games and
animation is to apply local constraints sequentially [11], iterating over them with a Gauss-Seidel method.
However, this is not suitable where quantitatively correct physical deformations are sought, since the
ordering of the constraints and number of iterations performed all affect the result, making it difficult or
impossible to tune for real material stiffness parameters. By contrast Kangaroo performs all the
projections for one step independently and in parallel, and the energy minimised is exactly the sum of
the squared distances of the points from the target positions of all the goals, each multiplied by the
weighting factor for that goal. This allows for quantitative simulation of deformations with real material
stiffness parameters.
Finite elements can be used here as goals, the key difference with the more common form of FEM being
that the global stiffness matrix does not need to be computed, since only local stiffness is used. This
technique is also closely related to that described in [12], but there the step in which the projections are
combined involves a global solve. By contrast both steps in the Kangaroo solver are local, meaning
topology can be freely modified during simulation, and making the definition of new goals simple and
flexible, since they need only return a target position and scalar weighting. Furthermore, in Kangaroo
the projection method is combined with a modified version of the ‘drift damping’ described in [13]
technique to accelerate convergence more effectively than the usual kinetic or viscous damping.
Generally, a prerequisite for implicitly integrated methods more common with FEM is that the systems
must be statically determinate or indeterminate. Mechanisms can cause numerical instability and are
more difficult to solve. Kangaroo however is insensitive to the static determinacy of a structural system
such that mechanisms and large deformations are not an issue, provided the solver is able to remain
stable (as is usually the case). This insensitivity to static determinacy and large deformations is highly
suited to experimental and interactive design environments.
3. Benchmarks
While the subject matter presented in this paper merits in-depth and comprehensive technical
benchmarking covering many aspects relating to software and engineering performance, this paper
presents one quantitative and one qualitative benchmark for a concise overview.
3.1 Inextensible Cantilever
Large deformations feature heavily in bending-active hybrid structures. Therefore, a classical
benchmark for very large deformations is chosen for the comparison of the three methods with an
analytical solution derived by Mattiasson [14]. A cantilever with length L=10, bending stiffness EI=100
and axial stiffness EA=1e9 is loaded by increasing load increments with a maximum value Fmax = 10 at
the tip as shown in Figure 1. For each software environment several discretization resolutions, i.e.
number of elements n, are compared and plotted against the analytical solution in Figure 2. Note that for
IGA the term ‘element’ corresponds to a non-zero knot span of the underlying NURBS geometry.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
Figure 1: Deformed cantilever under tip loading with 8 discretized elements for all 20 load steps.
Figure 2: Relative displacement u/L and v/L of the cantilever’s tip computed with SOFiSTiK, Kiwi3d and
Kangaroo for different numbers of elements n and load steps.
This benchmark test aims to evaluate exclusively the accuracy of method’s bending stiffness with an
effectively inextensible beam (extremely high value for axial stiffness EA). The results are valuable,
particularly within the context of bending-active structures. However, it should be noted that the Finite
Element formulations from each method are not the same. Kangaroo’s bending formulation is based on
Barnes simplified model of three sequential vertices with 3 DOF [15]. SOFiSTiK makes use of
Timoshenko’s beam theory and IGA uses Euler Bernoulli beam. As such the results from this benchmark
represent only one aspect (accuracy) within the context of designing and building bending-active
As is to be expected, the simulations with the lowest number of discretized elements return the largest
errors. For the u/L deflection, IGA shows a deviation of -13.5% from the analytical model and Kangaroo
features a deviation of 19.1% whereas SOFiSTiK features only 4.6% error. At a discretisation of 20
elements, all methods feature high precision with errors for v/L deflection at -0.001% for IGA, -0.003%
for SOFiSTiK and 4.305% for Kangaroo. It may be noted, that in real terms 4.305% error for a 10m
cantilever equates to 24mm.
3.2 Complex Shape: Elastica Tetrahedron
A key objective for bending-active structures is to achieve high stiffness and low weight from very
slender beams. This usually involves forming and then constraining the bending-active elements such
that they occupy a large volume which, if executed well, will provide the high stiffness and low weight
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
sought after. The second benchmark presented here was performed as part of the 2017 IASS workshop
and comprises two slender beams which are bent in multiple axes and fixed to one another at three
locations approximating a tetrahedron. Such a system may be stabilised and stiffened by the addition of
tensile membrane or cable elements. To achieve this complex shape, each of the three methods adopt
substantially different processes (described below) with distinct advantages and disadvantages relating
to accuracy, speed, user interfacing and design interactivity.
Figure 3: Elastica tetrahedron: complex 3D form from slender and actively-bent GFRP rod. From left to right:
SOFiSTiK, Kangaroo, Kiwi3d and mock-up.
3.2.1 SOFiSTiK
The most common approach in SOFiSTiK for the simulation of bending-active structures is by using
contracting cables [16]. The cables are given an arbitrary and low axial stiffness so that under a prestress
load they contract rapidly by transferring this prestress load directly to the ends of and aligned to the
cable. The rate of contraction can be defined by the user to follow a polynomial relationship per iteration
or it can be linked to load results from the cable from the previous iteration step. In this way the rate of
contraction adapts to accommodate the nonlinearities of the form finding process. As the deformation
path of the elements is dependent on intermediate stages of changing equilibrium, contracting cables
have the advantage of reducing inelegant or artificial restraining forces during the form-finding process.
This is achieved by making the structure follow the deformation path that it would naturally occur from
the gradual contraction of the cables.
In the case of the tetrahedron, the structural system is modelled with the same dimensions, units, material
properties and cross-section values as in reality. This is necessary when simulating bending-active
systems with SOFiSTiK, as the software tends to be sensitive to non-realistic and off the charts values.
The simulation process follows in two stages. In the first step the straight rod is iteratively bent into a
loop until the end points meet. For the second step a transversal contracting cable is added to bend the
loop out of the plane and achieve the spatial tetrahedron. For the second step, a small imperfection in
the form of a vertical force is needed to induce the initial buckling of the system. For the import/export
of CAD geometry between Rhino and SOFiSTiK the official SofRhino plugin by SOFiSTiK as well as
the Rhino/Grasshopper interface STiKbug were used [17].
Figure 4: Different stages of the simulation process for the elastica tetrahedron in SOFiSTiK. From left to right:
The rods are bent using a series of contracting cables, the loops are formed and secured together with coupling
elements and finally a new series of contracting cables pull the rods together.
3.2.2 Kiwi3d
Contracting cables are also used in Kiwi3d in order to model the elastica tetrahedron similar to
SOFiSTiK. In a first step the beam is bent to a loop with two cables for aligning the ends. In the second
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
step the result can be mirrored and be used as initial geometry, which is still aware of the first bending
process. Forces are used in the first load step to push the beams out of the ground plane. Two cables
connect the upper part of the loops. Note that the lower parts are not blocked against torsion as a torsional
connecting of the real GFRP model was neither possible. A torsional support would slightly modify the
result. Alternatively, the automatically derived pre-stress (similar to SOFiSTiK’s ACTB module) can
be used to directly model the structure if torsional moments are not expected. The whole analysis data
is available and can be evaluated in the CAD environment. Consequently, also other functions are
callable and e.g. an optimization w.r.t. the final structure gets possible by changing the geometry and
analysis parameters simultaneously.
Figure 5: Design process of the elastica tetrahedron within Kiwi3d: Left: rod is bent by two cables in its first
construction stage to a loop. Right: two clamped loops are connected and pulled together by cables in order to
derive its final shape.
3.2.3 Kangaroo
A custom computational pipeline [18] developed, primarily by Anders Holden Deleuran, for the
SmartGeometry conference in 2016 was introduced at the IASS 2017 workshop and was used in order
to generate the tetrahedron benchmark geometry with Kangaroo. The computational pipeline harnesses
Rhino and Grasshopper’s many geometric strengths (via the RhinoCommon library) to allow users to
design polygonal topology assemblies (comprised of beams, cables, intersections thereof and supports).
The pipeline discretises the geometry, assigns topology logic, part indexing, material properties and then
sends this data to Kangaroo to solve, on the fly. Since the target angle between sequential polyline
segments in the Kangaroo goal for bending stiffness can be freely defined, both linear and polygonal
initial geometries which result in curved elastica can be solved. This novel approach allows users to
create a design, explore topological variations and modify accordingly based on real-time feedback on
structural performance. It also meant that the complex form in this benchmark could be sketched and
solved within a matter of minutes.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
Figure 6: Custom computational pipeline for Rhino / GH in which the user draws a polygonal topology
representation of a design (left) which is solved for equilibrium on the fly by Kangaroo (right) allowing for rapid
design exploration & evaluation.
4. Conclusion
This paper offers a timely insight into one established and two emerging software environments each
capable of modelling, shaping and simulating bending-active structures: a feat that not many FE
packages can achieve due to their large deformations, complex geometries and geometrically non-linear
effects. The first benchmark compares deformations from an inextensible tip-loaded cantilever and
reveals how SOFiSTiK is rightly celebrated as one of the industry’s most precise and dependable FE
packages. The second benchmark models a geometrically complex elastica tetrahedron and reveals much
about the, often overlooked, aspects of topology generation and user interfacing. Despite improvements
from plugins, SOFiSTiK’s FORTRAN and CAD-based data input methods are showing their age in a
world of parametric modelling. The Carat++ solver behind Kiwi3d is reaffirmed as highly robust and
precise while the bold new world of isogeometric analysis offers a tantalizing leap of progress for FEM
in seamlessly combining NURBS modelling with physical simulations by eluding (or at least greatly
simplifying) discretisation. Kangaroo offers users an unparalleled freedom to script geometric
constraints or FE formulations to suit their own requirements. The stability of Kangaroo’s novel
projection-based dynamic relaxation solver introduces a completely fresh level of interactivity,
accessibility and customizability to the world of Finite Element Modelling.
Each of the three methods discussed in this paper offer unique and significant strengths with respect to
the modelling of bending-active structures.
The support by "Zentrales Innovationsprogramm Mittelstand" of the Bundesministerium für Wirtschaft
und Energie (BMWi) under grant number ZF4066102BZ6 is gratefully acknowledged.
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Creativity in Structural Design
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... Maya, 3DS Max, Cinema4D, Blender) and, more recently, popular CAD environments such as Rhinoceros. The Kangaroo plug-in for Rhinoceros is a good example of this type of software, and its dynamic relaxation type (more specifically, projective constraint-based) solver makes use of projections (''goals'') as defined as functions acting on a set of points, which can describe geometric constraints, elastic material elements, applied loads and forces [12]. These goals include components such as stiffness, stretch and shear, which are then applied to geometry, describing how they will behave in a relaxed state. ...
Woven textiles are typically designed with methods and software that demonstrate the graphical aspects of fabric but are limited in their representation of fabric behavior. The category of textiles that undergo shape changes in the finishing phase are well suited to alternate design approaches that incorporate predictive modeling. In this paper, we describe a methodology that uses parametric modeling and simulation to ideate, refine and inform physically produced woven fabrics with specific dimensional qualities, shifting the iterative work inherent to textile design into a digital space.
... The deformation of material in bending-active structures can usually be described by analytic geometry following the rules of the elastica (Lienhard, 2014), which offers a mathematical basis for its form-finding regardless of materiality. In the digital age, form-finding simulation methods are actively developed to accommodate architectural designers' interest in bending-active structures in the design stage (Bauer et al., 2018). For instance, by reducing the degree of freedom of a spatial node from 6 to 3 (Adriaenssens and Barnes, 2001), Kangaroo Physics, a plug-in for the digital modeling software Rhinoceros, applies dynamic relaxation method to simulate bending-active behavior of an elastic rod (Piker, 2013;Cuvilliers et al., 2018). ...
... Researches on tension, compression, pneumatic, grid shells and mobile structures passed the boundaries of the field [1,2,3]. Recent advances on space structures as form-finding, computational morphogenesis, numerical analysis and robotic fabrication are reported in literature [4,5,6]. Despite these advances, the current industrial materials applied are still pollutant, demand for high-energy consumption and requires centralized processes. ...
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Self-supporting bamboo structures are ultralight architectural modules applying bamboo round poles, tensile pantographic grids and textile membranes. The structural system applies articulated flexible joints in polyester ropes and locking bio-composite bandage rings, keeping bamboo bars free of torsion stresses. An experimental 1:3 scale prototype and a full-scale structure were fabricated to make previsions about the physical and mechanical behavior of the structure. The experimental results were verified applying a numerical model for the structure. In turn, the flexible joints were analyzed theoretically. The computer model was analyzed using the finite element SAP2000 program. The numerical results were in close agreement with the experimental results specifically for the structural behavior of the flexible joints.
... The interactivity and responsiveness afforded by this method is also what allows it to be embedded within fast, iterative design processes for architectural structures (Senatore and Piker 2014). This approach is particularly applicable to the overall form-finding of meso-scale architectural components, such as in the design of timber grid shells (Quinn 2018) and other bending active assemblies such as described by Bauer et al. (2018). ...
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Integrated material practice in free-form timber structures is a practice-led research project at CITA (Centre for IT and Architecture) that develops a digitally-augmented material practice around glue-laminated timber. The project is part of the InnoChain ETN and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642877. The advent of digital tools and computation has shifted the focus of many material practices from the shaping of material to the shaping of information. The ability to process large amounts of data quickly has made computation commonplace in the design and manufacture of buildings, especially in iterative digital design workflows. The simulation of material performance and the shift from models as representational tools to functional ones has opened up new methods of working between digital model and physical material. Wood has gained a new relevance in contemporary construction because it is sustainable, renewable, and stores carbon. In light of the climate crisis and concerns about overpopulation, and coupled with developments in adhesives and process technology, it is returning to the forefront of construction. However, as a grown and heterogeneous material, its properties and behaviours nevertheless present barriers to its utilization in architecturally demanding areas. Similarly, the integration of the properties, material behaviours, and production constraints of glue-laminated timber (glulam) assemblies into early-stage architectural design workflows remains a challenging specialist and inter-disciplinary affair. Drawing on a partnership with Dsearch – the digital research network at White Arkitekter in Sweden – and Blumer Lehmann AG – a leading Swiss timber contractor – this research examines the design and fabrication of glue-laminated timber structures and seeks a means to link industrial timber fabrication with early-stage architectural design through the application of computational modelling, design, and an interrogation of established timber production processes. A particular focus is placed on large-scale free-form glulam structures due to their high performance demands and the challenge of exploiting the bending properties of timber. By proposing a computationally-augmented material practice in which design intent is informed by material and fabrication constraints, the research aims to discover new potentials in timber architecture. The central figure in the research is the glulam blank - the glue-laminated near-net shape of large-scale timber components. The design space that the blank occupies - between sawn, graded lumber and the finished architectural component - holds the potential to yield new types of timber components and new structural morphologies. Engaging with this space therefore requires new interfaces for design modelling and production that take into account the affordances of timber and timber processing. The contribution of this research is a framework for a material practice that integrates processes of computational modelling, architectural design, and timber fabrication and acts as a broker between domains of architectural design and industrial timber production. The research identifies four different notions of feedback that allow this material practice to form.
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Double-curved surfaces are increasingly being designed and fabricated in contemporary architecture and engineering. However, the fabrications are always time-consuming and costly. Inspired by traditional weaving handicrafts, we propose a bending-active weaving structure, which consists of continuous elastic rods and standard joints for the fabrication of large-scale freeform surfaces. Uniform rods with circular cross sections were used to avoid torsion and simplify fabrication. The advantage lies in its convenience in construction, adaptability of spatial forms, and structural efficiency. We introduced the geometric principle of weaving structures, its generation algorithm based on remeshing, structural simulation by dynamic relaxation, and lattice optimization to reduce rod curvature. Structure simulation of lattices were performed to demonstrate its potential in architectural scale construction, and the extended kagome lattice was found more efficient with less stress concentration. Fabrication methods were also discussed. Furthermore, several experimental fabrications were performed to demonstrate the advantages and potentials of the system.
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The R&D project ADAPTEX showcases a material-driven and computationally informed design approach to adaptive textile facades through the integration of shape memory alloy (SMA) as an actuator. The results exhibit thermally responsive and self-sufficient sun-shading solutions with innovative design potential that enhance the energy performance of the built environment. With regard to climate targets, an environmentally viable concept is proposed that reduces the energy required for climatization, is lightweight, and can function as a refurbishment system. Two concepts-ADAPTEX Wave and ADAPTEX Mesh-are being developed to be tested as full-scale demonstrators for facade deployment by an interdisci-plinary team from architecture, textile design, facade engineering, and material research. The two concepts follow a material-driven, low-complexity design strategy and differ in type of kinetic movement, textile construction, integration of the SMA, reset force, and scale of permeability. In this paper, we describe the computational design process and tools to develop and design current and future prototypes and demonstrators, providing insights on the challenges and potentials of developing textiles with integrated shape memory alloys for architectural applications.
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Hybrid, bending-active structures constitute a challenging task for structural design due to the high dependency between shape and forces. Isogeometric analysis suggests itself in this context because of several advantages. Model conversion with concomitant corruption of the simulation results can be overcome. All stages of the construction, which are necessary for the correct simulation of such structures, can be modeled and correctly linked. Moreover, the parameter space of the NURBS description provides a perfectly suited, additional design space for embedded entities, which can be defined independently of the parametrization. The contribution of this paper is a presentation of the basics for embedding within isogeometric analysis and reveals beneficial aspects of nested NURBS descriptions in the context of staged construction. A case study of a staged simulation is carried out and another one for the form-finding procedure of hybrid structures.
Conference Paper
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Form-active hybrid structures (FAHS) couple two or more different structural elements of low self weight and low or negligible bending flexural stiffness (such as slender beams, cables and membranes) into one structural assembly of high global stiffness. They offer high load-bearing capacity at a fraction of the weight of traditional building elements and do so with a clear aesthetic expression of force flow and equilibrium. The design of FAHS is limited by one significant restriction: the geometry definition, form-finding and structural analysis are typically performed in separate and bespoke software packages which introduce interruptions and data exchange issues in the modelling pipeline. The mechanical precision, stability and open software architecture of Kangaroo has facilitated the development of proof-of-concept modelling pipelines which tackle this challenge and enable powerful materially-informed sketching. Making use of a projection-based dynamic relaxation solver for structural analysis, explorative design has proven to be highly effective.
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This paper proposes and validates a three degrees of freedom element formulation that accounts for torsion and transverse bending of three-dimensional curved elements in explicit numerical analyses methods such as Dynamic Relaxation. Using finite difference modeling, in-plane distortions and moments, the increment of twist (and hence torsion) and out-of-plane bending deformations are determined. Numerical stability and convergence limits of the element are discussed. Two sets of circular arc test cases validate the accuracy of the element against theoretical and six degrees of freedom finite-element results. This element is widely applicable and found in strained grid shells and spline stressed membranes.
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This paper explains the basic elements of an approach to physically-based modeling which is well suited for interactive use. It is simple, fast, and quite stable, and in its basic version the method does not require knowledge of advanced mathematical subjects (although it is based on a solid mathematical foundation). It allows for simulation of both cloth; soft and rigid bodies; and even articulated or constrained bodies using both forward and inverse kinematics. The algorithms were developed for IO Interactive's game Hitman: Codename 47. There, among other things, the physics system was responsible for the movement of cloth, plants, rigid bodies, and for making dead human bodies fall in unique ways depending on where they were hit, fully interacting with the environment (resulting in the press oxymoron "lifelike death animations"). The article also deals with subtleties like penetration test optimization and friction handling. 1 Introduction The use of physically-based modeling to produce nice-looking animation has been considered for some time and many of the existing techniques are fairly sophisticated. Different approaches have been proposed in the literature [Baraff, Mirtich, Witkin, and others] and much effort has been put into the construction of algorithms that are accurate and reliable. Actually, precise simulation methods for physics and dynamics have been known for quite some time from engineering. However, for games and interactive use, accuracy is really not the primary concern (although it's certainly nice to have) – rather, here the important goals are believability (the programmer can cheat as much as he wants if the player still feels immersed) and speed of execution (only a certain time per frame will be allocated to the physics engine). In the case of physics simulation, the word believability also covers stability; a method is no good if objects seem to drift through obstacles or vibrate when they should be lying still, or if cloth particles tend to "blow up".
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Numerical evaluations of elliptic integral solutions of some large deflection beam and frame problems are presented. The values are given in tabular form with up to six significant figures. The numerical technique used for evaluating the elliptic integrals is described.
We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuum-based potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation.
The paper describes numerical procedures, based on the method of dynamic relaxation with kinetic damping, for the form finding, analysis and fabrication patterning of wide-span cable nets and grid shells, uniform or variably prestressed fabric membranes and battened membrane roofs. The historical development of the method is briefly reviewed and a full description is then given which accounts for cable or strut elements, membrane elements and spline beam elements. All of these elements are implemented in their natural stiffness form allowing for gross geometrical and material non-linearities, with automatic controls to ensure stability and convergence of the method.
The concept of isogeometric analysis is proposed. Basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite element h- and p-refinement schemes are presented and a new, more efficient, higher-order concept, k-refinement, is introduced. Refinements are easily implemented and exact geometry is maintained at all levels without the necessity of subsequent communication with a CAD (Computer Aided Design) description. In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented. Standard patch tests are likewise satisfied. Numerical examples exhibit optimal rates of convergence for linear elasticity problems and convergence to thin elastic shell solutions. A k-refinement strategy is shown to converge toward monotone solutions for advection–diffusion processes with sharp internal and boundary layers, a very surprising result. It is argued that isogeometric analysis is a viable alternative to standard, polynomial-based, finite element analysis and possesses several advantages.
The Potentials of Isogeometric Analysis Methods in Integrated Design Processes
  • P Längst
  • A M Bauer
  • A Michalski
  • J Lienhard
P. Längst, A. M. Bauer, A. Michalski, and J. Lienhard, "The Potentials of Isogeometric Analysis Methods in Integrated Design Processes" in Proceedings of the IASS Annual Symposium 2017 "Interfaces: architecture. engineering. science," 2017.