Pneulastics_pneumatically activated differentiated elastic membranes

*pneumatically activated differentiated elastic membranes.

Master of Parametric Design in Architecture Thesis

ANNA RIZOU / September 2018

Supervisors : RAMON SASTRE, ENRIQUE SORIANO

MPDA BarcelonaTech School of Professional & Executive Development

MasterĘźs degree Parametric Design in Architecture

Pneulastics Pneumatically activated differentiated elastic membranes.

Anna Rizou

.2

Pneulastics *pneumatically activated differentiated elastic membranes.

Anna Rizou

Master Thesis September 2018

MPDA Master’s Degree Parametric Design in Architecture Thesis direction Prof. Ramon Sastre Thesis advisors Enrique Soriano, Pep Tornabell, Gerard Bertomeu

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.4

INDEX

00.00 ABSTRACT

.00

01.00 INTRODUCTION

.00

01.01 AIM .10 01.02

CONTEXT : PNEUMATICS

.20

BASIC PRINCIPLES ORIGINS 01.03 PNEULASTICS

.30

02.00 STATE OF THE ART

.40

02.01

.50

CURRENT RELATED WORK

03.00 RESEARCH HYPOTHESIS

.60

03.01 MATERIAL SYSTEM .70 03.02 FABRICATION POTENTIAL .80 03.03

FORM FINDING WORKFLOWS : A. BOTTOM UP

.90

B. TOP DOWN

.100

04.00 RESULTS EVALUATION

.110

05.00 CONCLUSIONS & FURTHER RESEARCH

.120

06.00 ACKNOWLEDGEMENTS .130 07.00 REFERENCES .140

.5

.6

00.00 ABSTRACT

We present a computational approach for designing pneulastics, initially flat, novel pneumatically activated elastic membranes of differentiated elasticity along their surface. They consist of areas of differentiated thickness, and therefore elasticity, that respond with a different expansion rate and create complex tension conditions on their surface when sealed and pneumatically inflated. The uniform stress applied by the air pressure differential acts upon zones of different material properties and results in rich doubly curved forms along the membrane.

Following the confirmed hypothesis that pneulastics can provide a wide range of doubly curved, pre-stressed shapes, the design process starts with a target shell shape. Our method translates curvature and topology into flat membrane thickness, and optimizes thickness differential, shape and zone boundaries, to obtain the best approximation of the initial shape when the flat but complex membrane is pneumatically activated.

The

method

is

developed

first

by

empirical

experimentations

and

hypothesis,

with a series of physical experimentations in order to decipher and describe material algorithm,

behaviour and

into

finally

digital a

simulation,

demonstration

of

proceeding

to

effectiveness

calibration of

the

of

the

approach

by

a wide range of shapes, that is validated with a series of physical prototypes.

Keywords: elasticity, auxetic material, pneumatic activation, computational design, target shape approximation. .7

01.00 INTRODUCTION

Pneumatic mechanisms: [from top left and clockwise] Sailboat [Figure 01.01], Soap films[Figure 01.02 & 03], Pufferfish[Figure 01.04], Hot-air baloons[Figure 01.05]. .9

01.01 AIM

The object of this thesis is to investigate the potential of elastic membranes in inflatable structures in adapting to

complex

geometries,

when

their

elasticity

rates

vary on one single pneumatically distended surface.

This research is based on the hypothesis that elastic membranes of differentiated cross sections (and therefore elasticity rates) on their surface may distend to consequently differentiated extents when sealed and

inflated, and

therefore produce a wider range of geometries and topologies, than the ones provided by plain, non-expandable membranes.

The object is the control of pneumatic activation, that is, of the expansion rate of surface elements when subjected to internal air pressure,

in order to be able

to translate geometries into flat uninflated elements with a mapping of elasticity-depending cross section thickness that derives from an inversion of the inflation process. .10

Liquid Printed Pneumatics,Self Assembly Lab, MIT, 2018[Figure 01.06], Digital Matter Intelligent Constructions, MAA,Iaac 2015 [Figure 01.07], Liquid Actuated Elastomers: Soft Architectural Systems,ACADIA, 2018[Figure 01.08].

When dealing with elastic membranes, we can count on an iterative pneumatic activation of the material, within their limits of tolerance, that can also be reversed. That is, a raise in air pressure will have as a consequence a raise in the deformation of the surface elements, according to their elasticity, and when the air is no longer provided, the membrane shall recover its original configuration.

Another argument in favour of this strategy is to simplify the

production

sequence

of

membranes

for

inflatable

structures, by replacing patterning and cable-stiffening procedures by a tool that translates topology into case Frei Otto’s model study for the different shapes achieved by trussing a pneumatic dome with cablenets[Figure 01.09] Model study for containers for grain or cement[Figure 01.10].

specific local thickness of a flat membrane, that when inflated transforms into a tensile doubly curved surface. .11

01.02 CONTEXT

Basic Principles Pneumatic structures consist of membranes stressed by the differential pressure of a gas (or liquid). A pneu is a structural system consisting of a ductile envelope which is capable of supporting tensile stress, is internally pressurised and surrounded by a medium. The pneu allows forces to be transferred over considerable distances with a minimum use of materials, and extremely wide span

M = 0.5 P*R

structures to be erected.

R

Their structural capacity lies in the balance between the self-weight of the unstressed membrane and the pressure applied. This pressure needs to be sufficient under action

P

of all loading conditions to prevent compressive membrane stresses. Meanwhile, membrane stresses that develop need to be smaller that the stress limit of the material of the membrane.

The pressure differential can be no greater than that of ordinary barometric fluctuations, in order to consider the inflatable structure inhabitable.

Under the equally distributed pressure forces applied vertically to the surface of the membrane, pneumatics tend

P > W + Wind +Anchonring

W

WIND

to adopt a spherical uniformly stressed shape. The inner pressure automatically seeks to find its own form, the outer surface assuming the minimum surface area by maximum volume. This natural consequence means that even though we might meet planar zones on an inflatable structure, double curvature on single membranes will most probably be exclusively positive. Single curvatures and negative ones are not an expected result on an inflated plain membrane. .12

P ANCHORING Pneumatic envelope, distended when subjected to internal pressure P, surrounded by air, under weight and wind loads. M = max membrane stress[Figure 01.11]

Each

biological

object

consists of Pneus, For every living cell is a pneu.

Origins The term “pneu” first appears in the works and publications of the research team of Biologie und Bauen, directed by Frei Otto and the anthropologist Johann-Gerhard Helmcke, who composed a cosmology of objects, both living and manmade structures, to construct the development and history of form.

According to them, pneu is “the most extreme form of lightweight construction”, one of the most efficient technical structural systems, where objects transferring large forces while having a relatively low self-weight are considered “lightweight”.

The objects of inanimate nature are essentially formed by four processes through flow and movement of fluids and gases, especially water and air; This growth of living organisms is only made possible within an elastic, tensile, fluid material framework that is seen as the origin of pneus.

“The ‘pneu’ is the essential basis for the world of forms of living nature.” It must be noted that the term “pneu” represents only a working title: cells and entire Frei Otto’s soap film aggregate experimentations[Figure 01.12], Shape study for an air hall with internal drainage[Figure 01.13] project study, 1971[Figure 01.14] Exhibition pavilion at the 1964 World Fair, New York[Figure 01.15].

objects in living nature, apart from a few exceptions in hydrostatic structures, follow the principles of pneumatic structures. .13

“Pneu (greek : Pneuma = air) as an all-embracing term for a structural system which can be clearly distinguished from many other systems and which has particular characteristics”

Living organisms grow. Cells divide and increase in size.

The process of increasing dimensions generally takes place by division or by enlargement of the internal volume, the medium. All these processes can only take place in a soft, non-hardened state. They need elastic, tensile stress, closed membranes—enclosures which are viable at each stage of growth and change. In addition to the key sentence stated in 1973, it can be stated that growth is only possible in soft conditions.

Pneumatic structures were one of the key areas of Otto’s research into the creation of forms drawn from nature. His experiments are primarily documented in photographs that appeared in IL 12 Convertible Pneus, published in 1975, depicting entire landscapes made up of plaster models that form contours and cast shadows; wire cables, cutting into elastic surfaces and tubes, rising up and collapsing down. _BURKHARDT, BERTHOLD, Natural structures - the research of Frei Otto in natural sciences, Article in International Journal of Space Structures 2016, Vol. 31(1) 9–15 .14

Frei Otto. Pneu and Bone, from the series IL[Figures 01.16 & 17 & 18 & 19]

Pneu : One of the most efficient technical structural systems is the pneu. A pneu is a structural system consisting of a ductile envelope which is capable of supporting tensile stress, is internally pressurised and surrounded by a medium. The pneu allows forces to transferred over considerable distances with a minimum use of materials , and extremely wide span structures to be erected.

Pneu is the structural system of the living nature.

Pneu as a structure used to transfer forces and also as an agent for form generation.

Whenever parts of such objects solidify and become hard like the carapaces of a single cell organisms(eg: radiolaria) like the wood of plants and the shells and bones of animals (shells of insects, internal skeletons of vertebrates). These components are rigid and take compressive loads.(they are no longer pneus) but retain the shape of the pneus from, the structural pneu system is always preserved in principle. It represents the active and living part, whilst the hardened parts maybe regarded as non living or at least less alive substance which can also have load bearing functions. They evolve as pneus , harden in that shape and become other structures such as structural members, skeletons, or shells or in brief: they become non- pneus in the form of structural members, Extract from IL35: PNEU AND BONE

beams and shells. Maybe its through selection from an infinite number of mutations and environmental factors. .15

01.03 WHY PNEULASTICS?

Pneulastics is an effort to produce complex geometries of double curvatures, both convex and concave in one single

Define Inflated Geometry

membrane, out of the pneumatic activation of initially flat elastic membranes.

Two

major

shortcomings

for

pneumatic

structures

in

architecture,(according to Rolf H. Luchsinger, Mauro Pedretti and Andreas Reinhard) are the strong form

Discretize to Developable pattern

restrictions for airhouses and strong load limitations for airbeams, with any inflated elastic membrane tending to be spherical, and elongated forms forced by the appropriate cutting pattern of inelastic fabrics .

The feature that permits this differentiation in the behaviour

of

pneulastics,

is

the

complex

tension-

Fabricate_Numerically Controlled Cut

compression system that is formed by areas of different elasticity by means of thickness upon the same surface.

Thus, under the same differential of pressure, each of these zones with different elasticity modulus distends to a non-linearly different extent. Thicker zones act as compression borders for their neighbouring thinner

Assembly: Sewing & Sealing

and more elastic ones, and on that very condition form emerges.

In fact, these reinforced zones play the role of external tensor elements, seen often as cables, in large span pneumatic structures, that in those cases were used for structural optimization purposes, by reducing curvature radii on the surface by discretizing it, and thus proportionally reducing the stresses developed on those non-elastic membranes. The cable tensors absorb the .16

Resulting Membrane: Area: = inflated configuration Tensor elements to assemble[cables, seams..]

Regular design routine for pattern-based pneumatic structures of complex geometry, as seen in Inflated Restraint(CITA,2016)[Figure 20].

surface stresses, now transformed into linear ones, and

Cable Tensors

redirect them to the anchoring perimeter of the entire structure, converting fundamentally the system into a hybrid cable-tensor one.

Similarly, in pneulastics, surface stresses are accumulated on the reinforced thicker zones, which by definition have

Discretized Membrane

Seamless cast membrane

higher tolerance to tension.

The initial intention of this research has been to propose an integrated design framework that simplifies the procedure of design, fabrication and assembly of complex geometries in pneumatic structures, in the most efficient way.

Define Inflated Geometry

One of the greatest advances proposed in comparison to traditional pneumatic structures fabrication, is avoiding the membrane pattern discretization of the target/designed

on

a ti

n t o flat c

ig on f

ur

a nfl Invert i

ti o

surface. Such processes often demand a wasteful use of sheet material, as well as a series of tolerances in terms of geometry accuracy that mostly accumulate during assembly process. Another important aspect in this topic is the aesthetics of seams position on such membrane structures, that can be easily debatable. The assembly process also embodies logistic needs of organization in order to facilitate identification of membrane pieces, that can not always be guaranteed.

Fabricate Resulting Membrane:Planar Area: << inflated configuration Differentiated cross section.

Common pneumatic membrane with complex geometry buildup Vs Pneumatic membrane buildup, Design routine for pneulastic structures of complex geometry [Figure 21].

Furthermore, in natural systems, performance variation and multifunctionality are often achieved with one single material. The success of these mechanisms lies in the organization of the material across multiple scales. .17

These natural systems have inherent the active properties of materials, as opposed to man'made ones with their distinct parts and multiple materials.

[a1]Loops Dome Membrane Pattern, flat layout

For the above reasons, we decide that discretization is to be avoided, and are therefore driven to the choice of an expandable membrane. Elastic surface materials have the capacity to increase their surface up to several times their initial measure,when bi-directionally distended under tension forces, in our case due to pneumatic activation.

This can be translated into a great advantage in terms of fabrication, because the surface produced, and therefore needed in the workspace, is much smaller that the surface that the inflatable structure will eventually measure, and therefore the structure is equal to its footprint, when loose. Also, the initial configuration when talking about domes, is thought to be flat(as opposed to a closed shape), thus minimizing fabrication maneuvers.

[a2]Triangular gridshell Dome Membrane Pattern, flat layout

Another undesirable feature of pneumatic structures with external tensor elements implies certain node complexity in the attachment of the third, linear member on the surface membrane element, without threatening the surface continuity. Pneulastics incorporate the tensor elements into one skin, leaving behind the problems of node-design and iterative assembly stages of each superposed element. [b]Pneulastic Membrane footprint Finally, in terms of structural behaviour, given that they behave as pre-stressed surfaces, pneulastic membranes demonstrate better performance against external loads, like wind, having developed very larger surface stresses .18

Fabrication plan for a dome [a] standard pneumatic structure pattern cutouts,[source: MPDA 2018, triangular gridshell and Loops membrane design] [b] pneulastic membrane. Fabrication error, node complexity, material use and aesthetic debates are minimized when discretization is avoided.

Catenary Shape formwork and form shaping forces

that resist negative deformation due to compression stresses.

We see pneulastics as a more efficient solution in terms of production(design, fabrication, assembly) and structural capacity, for applications where pneumatic structures are Pneumatic Shape formwork and form shaping forces

used as sealed volumes and the external surface is used.

We focus on the choice of inflatable structures as formwork for compression shells, and in that of gridshells that need a gradual means upon assembly/bending to erect.

In the former, complex geometries for compression shells could emerge by inflation,with the only constraint of keeping a steady pressure in order not to alter the target geometry. This method is not new, having its first shotcrete on nylon bag patent in the 1940â&#x20AC;&#x2122;s with Wallace Neffâ&#x20AC;&#x2122;s Bubble houses, and Bini shells later on.

In the challenge of compression shells, two methods have been historically employed: catenaries and pneumatics as formwork and formfinding means. Out of the two, the most populary proved to be tha catenary, due to the quick and efficient method of the hanging membrane model. This technique ensures thatthe shell would only be subject to

compressive

forces

rather

that

tensile,

formed

by the self-weight of the cast material, supported at its ends. However, bending and torsion moments are not accounted for, leading to the need for reinforcements and a considerable rise in complexity of assembly.[Wesley, Pauletti, Meneghetti, 2017] BiniShell construction sequence: inflation and concrete cast [Figure 01.22].

[Wesley, Pauletti, Meneghetti, The Impact of pneumatic and catenary forms on the design of thin concrete shells,CILAMSE 2017]

.19

On the other hand, the pneumatic form is, as we've already mentioned, the result of an outward pressure with forces that act upon the normal of the surface. These vectors change direction during inflation and achieve equilibrium combating wind forces.

Lift up

Push up

Ease Down

Inflate

When it comes to pneulastics as falsework, where actively bent gridshell structures reach their form by gradually deforming

initially

planar

and

straight

elements,

pneumatic structures have already been proposed as an uplifting mechanism that guarantees smooth adaptation with no unnecessary local overstresses, but equally distributed stresses (Quinn, Gengnagel). In this case,

Schematic representation of three established (1-3) and one novel (4) methods of erecting strained grid shells [Quinn, Gengnagel].

pneulastics can, again, adapt to the shell outline of the gridshell structures, and participate in their erection.

Quin and Gengnagel's ongoing research with experimental measurements and FEM analysis both show that,within the context of a geometrically simple strained grid shell, the ‘lift up’ and ‘push up’ erection methods are likely to cause overstressing of the laths during erection and that ‘ease down’ is the most geometrically precise and the least structurally demanding method. However, an alternative method of using pneumatic falsework offers comparable precision but at a fraction of the speed and cost necessary in the ‘ease down’ method resulting from high scaffolding demands. The method of pneumatically erecting a strained grid shell is feasible and practical QUINΝ, ,GENGNAGEL:Pneumatic Falsework for the erection of strained grid Shells: A parameter Study Simulation Methods for the Erection of strained Grid Shells via Pneumatic Falsework .20

Gregory Quinn, Erection of post-formed gridshells by means of inflatable membrane technology [Figure 01.23].

Absolute Barometric Pressure(psi)

1 atm = 14,69psi

100

Nitrogen Narcosis

Oxygen Toxicity

High pressure

14.7

SEA LEVEL

10 4.7

Breathable Atmospheres

for simple shell shapes and curvatures

Low pressure

We can also envision pneulastics functionally working as

Hypoxia 1

0

20

40

80

100

60 40 20 Volume, percent of nitrogen

0

21

100

80

60

Volume, percent of oxygen

fluidsâ&#x20AC;&#x2122; containers, with a variation of the algorithmic calculation that substitutes air pressure for hydraulic.

The tank would change shape according to its contents levels, without exceeding geometrical constraints(here appearing as target geometry) depending on the site context(storage units, etc).

Finally, we must acknowledge that the levels of pressure required to activate the elastic membranes with the varying and at times unusually high thicknesses may reach rates of 200psi. As seen in the scheme [] the viable levels are much lower, hence making pneulastics uninhabitable spaces (Human beings can withstand 3 to 4 atmospheres of pressure, or 43.5 to 58 psi.). However, we should also remember that inflation is based on the search of equilibrium between exterior and enclosed pressure,which allows us to assume that the boundaries for possible applications lie further that the earth's atmosphere, where the interior/exterior pressure ratio changes and threrefore, in space, where much lower and almost zero pressures on the exterior could easily permit inflation by Mars Science City, BIG,2017 [Figure 01.24].

enclosing a normally pressurized space. .21

.22

02.00 STATE OF THE ART

02.01 CURRENT RELATED WORK

Over the past years, there has been an increased interest in the analysis and acquisition of geometry control in pneumatic structures. The challenge lies in defying the natural tendency of inflatables towards synclastic curvatures, as well as in the approximation of target geometries that are predetermined rather than form-found.Equally popular seems to be the field of soft robotics, where the adjustment of pressure activates elastic elbows.

Typical methods used to achieve the goals mentioned, frequently include the use of third external elements as tensors. These are met either as seams of the cut pattern, internal fabric connections, or most commonly, as external cables that restrain the growth of the membrane in specific â&#x20AC;&#x153;lowâ&#x20AC;? points.

In the case of elastic skins, the stiffening strategies have included additive manufacturing processes where material becomes rigid on the paths dictated by the toolpath, or dressing of the skin with varying density and elasticity textiles.

Our role in this evolutive thought is to integrate active material strategies and digital fabrication methods in order to embody this differentiated activation into one single multi-capable skin. Thus we not only maintain the forementioned advantages of elastic inflatable structures in lightness, transportability, load bearing capacities and economic value, but also shorten the fabrication and Lars Englund, Volym 1964-67 Warszawa Exhibition at Galeria Foksal, Warsaw [Figure 02.01].

assembly procedures. .23

Inflated Restraint CITA, 2016.

Pre-defined Non-elastic target geometry membrane

Seam and cable tensors

The project focuses on the generation of cutting patterns and stiffening net topologies in a pneumatic hybrid membrane structure. Starting with a target designed shape/geometry, that may include contradictory anticlastic zones that are not very commonly achieved in pneumatic structures, the workflow goes from a topology analysis, to a rationalized and optimized pattern cutting for the membrane, to the identification of net loops that sustain low points. The algorithm is closed into an evaluation loop by developing physical models and digital simulation, within whom calibration is possible and provides with satisfactory data for the optimization of the design decisions.

Even though the structures that are the object of this research are not elastic, but rather deal with efficiency in pattern cutting, we are deeply interested in the curvature analysis levels that determine the paths of the stiffening nets, as well as the levels of positive curvature. .24

Investigating cutting patterns and net topologies in a pneumatic hybrid: Global design shape, curvature analysis of the global shape, structure inflated and sustained by the wire network[Figure 02.02].

Designing Inflatable Structures ETH Zurich, Disney Research Zurich, Columbia University.

Pre-defined target geometry

Non-elastic membrane

Seam tensors

Research project where an interactive, optimizationin-the-loop tool for designing inflatable structures is proposed. Given a target shape, the user draws a network of seams defining desired segment boundaries in 3D. According to the method, optimally-shaped flat panels for the segments are computed, such that the inflated structure is as close as possible to the target while seam positions are determined by both aesthetic criteria and fabrication optimization.

In order to achieve optimal shapes with minor differences from the target user-determined geometries, the algorithm may propose internal connections as well, therefore increasing complexity in assembly, as well as material use. The interactive loop element, however, offers a very wide range of results/solutions, allowing the user to Target shape, Seam interractive sketching, flat panel calculation, physical prototype fabricated [Figure 02.03].

counterweight the perks and shortcomings of the available solutions. .25

Adaptive Pneumatic Shell Structures: Feedback-driven robotic stiffening of inflated extensible membranes and further rigidification for architectural applications ITECH Master Thesis, University of Stuttgart Emergent geometry

Elastic membrane

Second body tensors

Research project attempting to reduce complexity in freeform pneumatic structures, by introducing external tensor elements. An elastic, pneumatically distended membrane is restrained by additive stiffening in the form of carbon fibers, and is later on rigidified to its entirety by the superposition of glass fibers in order to perform as a thin shell in compression.

Detecting the same complications we have mentioned in the design of non-expandable pneumatic structures, mostly in matters of material waste in pattern making, the project proposes a form-finding-based design method, where tensor elements are applied externally by additive fabrication methods locally, following with respect a design philosophy that supports optimal-form subject to external forces.

Iteratively, tensor elements are laid locally, robotically aided, and the rest form is subsequently scanned in a cyber-physical setup, allowing

calibration

between digital and physical model. The inverted, under compression, shell is then evaluated.

Eventually, the project investigates the limits of the user-involvement in a machine-driven process, introducing the possibility to intervene between each iteration according to his subjective evaluation of the resulting balanced form. .26

Physical setup for small scale experiments, robotic aplication of fiber tensors, 3d scanning and calibration/ comparison of digital with physical model [Figure 02.04].

Knitflatable Architecture: Pneumatically activated preprogrammed knitted textile space ITECH Master Thesis, University of Stuttgart

Pre-defined target geometry

Elastic membrane

Knitted skin tensors

The aim of the project is to investigate the potential of textile o architecture through a multi-layered study of the knitting technique and to show how the pre-programmed surface pattern affects the global geometry while being inflated.

In this case, a generic rubber pneumatic membrane is constrained by differentiated knitted textile skin that is stretched under air pressure.

A pre-programmed pattern defines structure, geometry and formation, that are all activated under pneumatic pressure.

The researcher experiments with inflatable-knitting, and how the differentiated textile skin acts as a surface tensor, in order to systematically comprehend and apply the Bottom up approach: patter design and consequent inflation, Top down approach: target geometry analysis and pattern derivation, inflation of multiple balloons in differentiated tension-cushions [Figure 02.05].

hybrid body behaviour, to find application as a controlled spatial expression. .27

Furl: Soft Pneumatic Pavilion Interactive Architecture Lab, UCL, 2014.

Emergent geometry

Elastic membrane

Borrowing principles from the domain of soft robotics, this project attempts to integrate pneumatically activated elastic muscles in interactive architecture applications.

The wide palette of deformation due to inflation, thanks to the combination of soft and thick membrane members, enables FURL to act as a kinetic responsive architectural platform, adapting to environmental and user needs.

In this case, a single cast skin of varying thickness in cross section and therefore varying elasticity, is inflated under also varying pressure differential, adapting to its balance form according to external stimuli. As air pressure changes, so does the form of the object. This form will be ever adapting to the ever changing environmental conditions and does not necessarily respond to a concrete, predetermined geometry. .28

[Figure 02.06]

Single skin tensors

Computational Design of rubber balloons ETH Zurich, Disney Research Zurich

Pre-defined target geometry

Elastic membrane

Rest Shape computation

This research deals with the design of uninflated rubber balloons with a given target shape they need to approximate upon inflation.

Bearing in mind non linear material deformation properties, and with a fabrication orientation, the researchers invert the inflation process by experimentally tracking the pressure-deformation relation, in order to come up with the geometry that when inflated best approximates the target, user-defined shape. The procedure is evaluated by carrying out physical and digital models and both are calibrated compared to the initial geometry.

The resulting geometry of this inverted process is going to serve as a mold for the conventional dip-in-rubber fabrication of balloons.

This

is

made

possible

by

a

physics-driven

shape

optimization method, which combines physical simulation of inflatable elastic membranes with a dedicated constrained optimization algorithm.

There is a conscious choice of constant-thickness membrane with an optimized, yet complex(even though less than the one of the target shape) geometry, given the ambition of the project to achieve a very wide shape variation.

Even though considered, the differentiated cross section thickness option is rejected for the sake of fabrication Target geometry definition, experimental acquisition of material properties,computation and fabrication of an optimal balloon shape, approximation of target shape by inflation, poor approximation by non computed mold [Figure 02.07].

means that are to be followed, as well as the purposes/ applications that are intended and are limited to small product scale (rubber balloons). .29

Tough Puff GLD Architecture & MIT School of Architecture, 2014

Pre-defined Non-elastic target geometry membrane

Second body tensors

In a hybrid fabrication system that recognizes the potential of both inflatable structures, in affordability, scalability and easy-tailoring, and fiber matrix composites, in longevity, rigidity and structural capacity, this research uses inflatable vinyl bladders as molds for composite production. The expenses and inflexibilities of the fabrication process are thus radically reduced, with the promise of viably introducing composites to architectural design and building construction.

These so-called â&#x20AC;&#x153;cured-surface inflatablesâ&#x20AC;? address in the process a broad material palette, always entail cutting and seaming flat sheets of anelastic material.

Sartorial

techniques (including pleating, darting, folding and layering) will obviate the need for the expensive molds or

frames

production.

needed The

in

conventional

research

composite

leverages

surface

innovations

in

material technologies, tooling, computational simulation, and

sheet

formal

geometries,

opportunities

to in

tease

out

cured-surface

structural inflatables

and at

an architectural scale. The results exhibit a radical consolidation of thin cladding and structure, suggesting an expanded set of constructive and formal possibilities available to architecture. .30

Unrolled pattern of flat sheet fiber composite material, form-finding iterations and constraints on onflatable mold, Cured shell [Figure 02.08].

Rapid Deployment of Curved Surfaces via Programmable Auxetics EPFL, Carnegie Mellon University

Pre-defined target geometry

Elastic membrane

Second Body Tensors

The aim of this paper is to investigate on the employment of deployable structures as a means of implicit encoding of complex double curvature surface shapes. The novel network that is designed consists of two-dimensional rigid mechanical linkages via a user-programmable pattern that permits locally isotropic scaling under load, imposed by inflation or gravitational load.

The system described is a hybrid layer-based configuration that combines

pneumatic activation with deployable

mechanisms and their transition from a flat to a curved surface target configuration. Placed and fixed one above the other, the membrane is subjected to internal pressure and expands under the constraint of the network of triangles, that have been designed spatially varying the triangle sizes,to

effectively

control

the

maximum

possible

expansion.

However, the geometrical information still lies embedded in a second layer and its mechanical interpretation as an auxetic surface. Digital fabrication is necessary for the large number of triangular panels that are manually assembled in a flat-by piece- linkage, while the underlaying membrane can remain plain.The

linkage has

regular connectivity, but spatially varying scale, which consequently results in an irregular spread of triangle sizes to fabricate. Complexity in fabrication and joint assembly is a big part of the equation in this system, that seems to otherwise achieve the aims set in terms of Input design, Deployed State, Rest State, Mounted Structure, Deployed Structure [Figure 02.09].

precision in the approximation of target geometry. .31

.32

03.00 RESEARCH HYPOTHESIS

-2 mm

-4 mm +-0 mm

Experimental process: [from top, left and clockwise] Toolpath design, CNC engraved mold, cured cast latex, Progressive inflation [Figure 03.01].

match for the entire deformation range of the experiment.

03.01 MATERIAL SYSTEM Pneumatic Activation

4.2. Evaluation As can be seen from Fig. 3, the measurements reveal an unusual deformation behavior. The average extension ratio first increases almost linear with respect to the pressure. At a certain point, however, there is a clear inflection in the curve indicating a second deformation regime of the material. In a third regime, the material stiffness increases again.

Inflated balloons will in general exhibit inhomogeneous deformations, most likely covering all three regimes. If good approximations are to be obtained, then this particular behavior must be reproduced by the material model. We will discuss some candidates Pneumatic in the following and, in order to facilitate comparison, weActivation provide stress-strain curves for all models considered in Fig. 3. The interested reader is referred to the textbook by Bonet and Wood [BW97] for details.

Pressure [kPa]

Figure 3: Experimental for the pressure-extension beExperimental data for data the pressure-extension behavior havior silicone membrane of of a arubber-like membrane and and approximations approximations with with difdifferent material models [Figure 03.02]. ferent material models.

The membrane formulation described in Sec. 3 guarantees volume preservation through geometric assumptions (thickness stretch compensates change in area) and thus avoids the numerical problems typically associated with incompressRubber membranes can be inflated to several times their ible elasticity. In this setting, the simplest nonlinear material model is the Neo-Hookean solid, which describes the strain initial volume and still return to their original rest energy as a linear function of the first invariant I1 . However, as can be seen in Fig. 3, this model fails dramatically to apshape upon deflation. proximate the deformation behavior of real rubber. The reaFor the purpose of describing the form finding processes son for this is that the Neo-Hookean material has a pressure we shall refer to the bi-directional isotropic expansion

c 2012 The Author(s)

c 2012 The Eurographics Association and Blackwell Publishing Ltd.

of the membrane upon inflation as pneumatic activation.

It is the expression of the inherent elastic properties of the material under tension forces that are developed by the vertical on its surface pressure loads. This expression is accompanied by changes in the geometry of the membrane, that will obtain double curvature abandoning its planar initial configuration, will raise its area by thickness stretch as a compensation, and consequently reduce its opacity. .34

ge er m Sm sc de

w fo m ne co re ex Average Extension Ratio

that take place on our elastic membranes upon inflation,

re se al se th in de st tio pl

Pneumatically activated elastic membrane Geometric Assumptions: tension forces allow the expression of elastic properties and rise of enclosed volume, that are accompanied by a reduction in opacity and and thickness.

[Figure 03.03]

pu

T ha B th to cu

5.

T re st

Differentiated Pneumatic Activation: Tension-compression system The variation of elasticity rates by means of thickness in cross section in selected locations of a surface membrane shall affect accordingly the form finding process that takes place upon inflation.

As we have already mentioned, in pneumatic structures the uniform distribution of pressure stresses vertically upon the membrane surface provokes uniformly stressed shapes that approximate spherical/ellipsoidal geometries. In pneulastic membranes, when certain surface elements tend to resist more than others to expansion upon inflation, non-uniform curvatures are observed, and depending on the difference in resistance, the stresses developed Latex balloon exhibits near conformal deformation, as indicated by the preservation of right angles.

[Figure 03.04]

might even result in negative curvatures on the distended membrane surface.

This strategy of conscious manipulation of the surface properties that will result in a non-uniform deformation upon inflation finds it counterpart in the digital world in the concept of “steering of form”(Kilian 2014). The term “steering” emphasizes a more active role of the designer

Stress

Rubber (B) Rubber (A)

in the form finding process by allowing varying degrees of sub-optimal solutions. The goal is to use the power of computational methods to extend the canon of forms established through conventional analytical techniques.

At the same time this methods should allow the designers to selectively deviate from optimal solutions to achieve more integrative design solutions.

Similarly, we are negotiating the uniform distribution of tension stresses on the surface of our elastic membrane Strain

for the sake of geometrical complexity and a pursuit of richer forms .

Stress-Strain curve for rubber materials A,B upon inflation, where elasticity rates nA>nB [Figure 03.05]

_KILIAN, AXEL ,The Steering of Form , Article in Journal of the International Association for Shell and Spatial Structures · November 2007

.35

Possible Configurations

In

our

initial

attempts

to

prove

the

capacity

of

differentiated elasticity membranes to form find complex geometries, we set up a digital model to simulate the pneumatic activation of an elastic membrane.

Transversal Section of Distended Membrane

Pneumatic Activation

.36

Flat membrane _ Remeshed _ Equal Elasticity rates

1.00

Activated membrane _ Deformation rates gradient

1.25

In this same attempt, we tried to raise complexity by adding internal connectivities, in points or linear layouts. By varying the length of the linear connector we are adding another border-condition that will act as another attractor for a thickness gradient, affecting the expansion upon inflation.

Plain membrane trace

Transversal Section of Distended Membrane B

B

A

A

1.00

Flat membrane _ Remeshed _ Anchored points A,B

Activated membrane _ Deformation rates gradient

1.58

.37

Plain membrane trace

Pneumatic Activation Seam

Transversal Section of Distended Membrane

Seam

Pneumatic Activation Anchor Points

1.00

Elastic membrane .38

Flat membrane _ Remeshed _ Anchored points A,B

Activated membrane _ Deformation rates gradient

1.33

Then,

to

introduce

the

idea

of

differentiation

in

activation and the emergence of varying curvature, we

Transversal Section of Distended Membrane

started experimenting with closed shapes, consisting of two seamed membranes of constant, but different thickness from each other. Digital and analogue models confirmed this hypothesis.

Elastic membrane

Activated cushion _Elastic membrane _ Deformation rates gradient

Stiff Membrane 0.28

2.66

Stiff membrane

Elastic membrane Flat cushion _ Remeshed _ 2 Elasticity rates

Activated cushion _ Stiff Membrane _ Deformation rates gradient

.39

In a third phase, we developed a configuration of single, planar membranes with locally differentiated thicknesses.

In this category, we have tried the following variations of local thickened conditions:

Plain membrane trace

Gradient thickenning

Transversal Section of Distended Membrane

1*Length

1.25*Length

Flat membrane _ Elasticity Gradient .40

0.00

Activated membrane _ Comparison to constant elasticity membrane

0.33

Thickened zones.

By comparing the deformation rates and the curvature ranges

obtained

by

pneumatic

activation

between

a

membrane of constant elasticity and another with the same characteristics but the thickness and therefore stiffness rate in selected zones, we observe that the differentiation of elasticity along the surface of an elastic skin can result in the disruption of the generally constant curvature upon pneumatic activation, without necessarilly meaning the formation of anticlastic surfaces.

Plain membrane trace

Transversal Section of Distended Membrane

Flat Membrane

Activated membrane Comparison between constant elasticity and thickened zones membrane

Stiff membrane

Elastic membrane .41

Out of the above, and for the sake of simplicity in execution, we shall focus on the initially planar membrane configuration, sealed at its perimeter, that when inflated distends to doubly curved dome-like geometries.

.42

03.02 FABRICATION POTENTIAL

Screws

In order to study the potential of pneulastics, we have

Wooden frame

had to devote time on a material pursuit, and through

Rubber ribbon for sealing

multiple trial and error loops, we have narrowed down

Rubber tube ÎŚ5mm

us well for the purpose of our experiments. At all steps

to a material and a fabrication process, that has served

of this process, we have been bearing in mind the large scale production counterpart solution in case of an actual architectural implementation.

Pressure pump 2-5 bar Latex membrane Wooden base

In order to perform physical stiffening, different methods have been used, such as: Laying manually material(liquid latex, white glue, power glue, glueing extra layers of latex strips) on top of a latex membrane.

Opposite page: Set of tools used for the fabrication and air inflation of pneulastic membranes.

Top: Experimental layout for the testing of pneulastic membranes [Figure 03.06].

Casting from scratch the membrane in molds that included the reinforcements topography. .43

Cast material

CNC Milling

Our experimental process starts with the CNC milling of the mold where liquid latex will be cast. We have narrowed down to choosing plasterboard as a fast, and

Cellulose Derivative Material

Cast material

Experimental Fabrication Scheme

reliable solution for well defined geometrically surfaces and edges by milling. We waterproof the plaster surface to avoid material absorption and then cast the liquid latex, that will have to cure. When dry, the membrane with the engraved topography can be easily removed from the mold, which can be reused.

In a larger construction scale, several molds can be

a

a

a =max milling table dimension

fabricated similarly and joint on or off-site, in order to form the overall surface of the membrane. When cured, the membrane can be directly assembled or folded in order to have it easily transported on the site of construction.

The molds can be reused for several productions. .44

Large scale Counterpart Space limitations in milling tables lead to the discretization of the overall mold in segments that are joined for the casting process [Figure 03.07].

Additive Digital Manufacturing

Robotic\drone deposition However effective the production line described above, within the framework of the experiments conducted, we have also contemplated an alternative, that needs to be further investigated on behalf of material sciences, in terms of stretchable elastomers that could be 3d printed in a fused Cellulose Derivative Printing Material Proposed Fabrication Scheme

filament deposition fabrication process.

Trusting that digital fabrication methods guarantee the most efficient control over the fabrication of complex geometries, and due to some scepticism over the large space needs of the previous fabrication method (casting off site in cases that climate conditions are prohibitive for the safe curing of the membrane), we have conceived the following fabrication configuration, as seen in the scheme:.

The alternative we propose employs a smart folding strategy of the elastic membrane, so that its boundary volume can fit into a reasonable space that 3d printing with robotic aid is possible. After removing the auxiliary soluble printed material that acts as a support of the

Left:MIT Self Assembly Lab: Liquid Printed Pneumatics(2018) Right: Innochain ESR15 â&#x20AC;&#x201C; Small scale robotic manufacturing for the large scale buildings [Figure 03.08].

folded membrane, and refrains the membrane form glueing to itself, we can manually unfold it. .45

03.03 FORM FINDING WORKFLOW A.Bottom up

This approach includes the experimental calibration findings of physical with

Mapping theirProperties corresponding digital models of membranes with

digital model

Curvature Analysis

Properties Assignation

Fabrication

Digital Simulation

Inflation

pneumatic activation.

Calibration Loop

differentiated elasticity rates on their surface, under

This series of experiments was led by pure curiosity and

Measurements_Scanning

the very initial hypothesis that on the border of the transition between two thicknesses, form and therefore Digital Simulation negative curvature would emerge.

Furthermore, on this stage of the research, the parametric definition of the Resulting thickened form zonesevaluation: location did not have to Target geometry Vs do with formalistic pursuits, rather the reinforcement Inflated but geometry

Resulting form evaluation: Digital Model Vs Inflated geometry

of the plain elastic membrane on the zones that accumulated the highest stress rates. .46

Bottom-Up approach process scheme

physical model

Reinforced Zones Pattern

Target Geometry Mesh

CN C

Intuitive determination of Pattern l Mi

g li n

t

Ca s

ma

ial te r

Ma te

ria l

Discretizing by remeshing of surface and split into zones

ng Curi

Assigning Elasticity Rates and Perform Digital Inflation

of

va Remo

l

Me m

o

f

bra ne .47

Inflated Membrane Section

Flat Mesh

.48

Mesh Post-inflation

Plain elastic membrane sets the norm for following experimentations.

Plain membrane trace

Inflated Membrane Section

Flat Mesh

Inflation process reveals imperfections in curing due to non levelled casting(one triangle is weaker and absorbs all the deformation).

Stiff membrane

Elastic membrane Mesh Post-inflation

.49

Plain membrane trace

Inflated Membrane Section

Inflated Membrane Section

Flat Mesh

Stiff membrane

Elastic membrane

.50

Mesh Post-inflation

Iflation process.

Plain membrane trace

Inflated Membrane Section

Flat Mesh

Stiff membrane

Elastic membrane Iflation process.

Mesh Post-inflation

.51

Plain membrane trace

Inflated Membrane Section

Flat Mesh

Stiff membrane

Medium Stiffness membrane Elastic membrane .52

Mesh Post-inflation

Top: Gradual thickness cast membrane.

Bottom: Inflation process and common imperfections in curing.

Plain membrane trace

Inflated Membrane Section

Flat Mesh

Tom and Middle: Cast membrane and engraved plaster mold.

Bottom:Inflation process and imperfections due to nonlevelled casting made obvious.

Stiff membrane

Elastic membrane Mesh Post-inflation

.53

Plain membrane trace

Inflated Membrane Section

Flat Mesh

Stiff membrane

Elastic membrane .54

Mesh Post-inflation

Top: Cast Membrane.

Top & Bottom: Inflation process

.55

Systematic Study of geometrical properties in relation to behaviour: Hypothesis and tests

nd

stage

of

material

experimentations,

and

having

developed some intuitive perception of how reinforced zones function in the form-finding process, we proceed to a more systematic control/confirmation of this functional stiffness gradient in relation to the curvature range we can achieve by pneumatic activation.

First, we define a target shape, and a quick curvature

Series 01

analysis combined with an intuitive knowledge of the pneumatic mechanism allow us to locate approximately the thickened zones on the membrane. We produce a series of models with parametrically varied thickness, width and area where form is expected to emerge, and with the help of photogrammetric measurements, we can develop an empirical method for the development of a more precise and convincing digital simulation.

The first model where only two rates of elasticity are

Series 02

assigned to our mesh elements, in a binary system that reads thin zones as elastic and thick as stiff, seems from an early stage to fail our criterion. .56

Gaussian Curvature Analysis on target shapes reveals the zones where thickness will be assigned.

R l

A stiffness gradient is then applied through all the mesh and is modulated with multiple attractor points, that in this case is the proximity to the thicker zones. The transition already seems to be smoother and more realistic when the higher tension zones, the ones neighbouring to the non-elastic zones deform less than the rest of the Thickness t1

Series 01

surface.

Thickness t2, t2 >t1 On a next level, we realize that not only the thicker l

zones, but also the support/anchoring perimetre will

d

behave similarly to the reinforced zones, as a tensor.

We therefore have to apply the elasticity pattern also depending on the relative distance of the surface elements from the perimetre of the membrane, in order to achieve a gradual rise in deformation as we move further from high tension zones.

Thickness t1

Series 02

Thickness t2, t2 >t1 Assignation of thickness on digital model according to proposed models.Variables.

The mesh is then subjected to air pressure, and when converged,

we

evaluate

whether

the

digital

balance

condition corresponds to the physical. .57

Systematic Study of Formation Rules: Hypothesis and tests

R

l

Result Result

t1

Result Result

Series 01

Result

Geometrical Features

Hypothesis to test

l = 30mm R = 15mm t1 = 3mm t2 = 1mm

_a thicker ring-zone results in non-spherical shapes upon inflation

l = 30mm R = 15mm t1 = 5mm t2 = 1mm

_a raise in cross section thickness difference can result in smaller curvature radii upon inflation

l = 50mm R = 25mm t1 = 3mm t2 = 1mm

_a raise in the width of the reinforced ring-zone provokes a smoother transition with bigger radius of curvature upon inflation

l = 30mm R = 25mm t1 = 5mm t2 = 1mm

_a raise in the area of the central zone provokes the emergence of a smaller radius of curvature upon inflation.

l = 50mm R = 52.5mm t1 = 5mm t2 = 1mm

_a raise in both the area of the central zone and the width of the reinforced ring prove to affect bigger curvature emergence upon inflation in ways similar to the above.

.58

t2

Experimental Procedure 0 psi

200 psi

.59

Series 02

2mm 2mm 2mm

t2

Series 02 Geometrical Features

tures tures

2mm 2mm tures

t1

Geometrical Features Hypothesis to test

Hypothesis to test Hypothesis to test

t1,2, =

t1 = 3mm t2 = 2mm

t1 = 6mm t2 = 2mm

2mm

3-2mm

_The introduction of a

The introduction reinforced of a reinforced zone in zone results The introduction of a reinforced zone results in an ondulated geometry upon an corrugated geometry results in an ondulated geometry upon upon inflation. inflation inflation.

Hypothesis to test

The introduction of a reinforced zone = geometry 6-2mm results in ant1,2, ondulated upon inflation. _a raise in the cross section A raise in cross thickness section difference canresult difference can A raise in cross section difference can result in smallerincurvature radii upon smaller curvature radii result in smaller curvature radii upon upon inflation inflation. inflation

A raise in cross section difference can result in smaller curvature radii upon inflation

t1 = 6mm t2 = 2mm

.60

_introducing thick patches on zones of high curvature rates will smoothen them down.

Hypot

The i resul infla

A rai resul infla

Experimental Procedure 0 psi

200 psi

.61

Material & Digital Models Calibration

This first series of physical experiments only involved material investigations which intended to confirm the binary hypothesis stated, the ability of the latex membrane to shape itself under pressure to different extents according to its elasticity rate.

Parallel digital simulations proved the potential of reproducing the behavior of inflated latex membranes under

Digital Assignation of Properties by area

predetermined conditions. With the help of Grasshopper plugin and Kangaroo by Daniel Piker, we have assigned differentiated stiffening conditions to the members of our interest.

For this purpose, we have employed a

plain discretized mesh with each of its elements having an assigned elasticity rate (which is translated into a freedom to deform) related to its local stiffening conditions.

the

assigned

stiffness

rates

have

been

defined. However, even on this first intuitive comparison, we can tell how this may produce inaccurate results.

i at ul Sim

differentiated by the enclosure in the different zones we

on

_

op

Initially,

Co

io mpa zat rison _ Op t i m i

Rubberlike materials have non-monotonic pressure-radius characteristic, and do not deform according to Hooke's law, according to what we have already seen for rubber spherical balloons.

The combination of different elasticity rates on one single surface subjected to inflation constitutes a very complex tension-compression model, which we do not hope to mathematically describe in this research. .62

Geometry Approximation

n

Lo

However, in order to describe in a more convincing way the pneumatic activation of pneulastics, we have proceeded to a series of digital models for calibration and comparison to photogrammetric measurements of a physical inflated model. The aim of this step is to aproximate the elastic deformation seen in the pneulastic membrane, and set a more accurate rule for our simulations.

Observing that a binary definition of stiffness (elasticnon elastic) is not realistic, we proceed to consider a functionally graded object depending on the distance of the boundary condition between two thicknesses. the closer to the borderline and therefore the stiffening condition, the less the discrete element deforms. The same principle may apply for the thick zone, if we consider it also stretches, even if it does to a much smaller extent, and also for the boundary conditions around the compression ring/perimetre.

A comparative study of the results, compared to annotated points on the physical surface and their correspondants on the digital mesh, will help us approximate the best simulation of the pneumatic deformation. .63

Calibration Taking into account physical non-linear properties of envelopes's material

Reproduced mesh by marked points and their measured coordinates.

The latest experimental configurations can now serve as calibration means for the definition of the computational tool we are attempting to compose. Analogue measurements that derive from the inflation of the model are compared to a series of digital simulations, where different coefficients and relations of elasticity are assigned to the different members, in order to fine-tune the representation of the differentiated inflation digitally.

.64

Values Measured in physical Model and reproduction of the material model according to measurements.

Method 01 Values of elasticity are assigned in a binary Spread of Deviation Rates.

Average deviation: 1.75 Scanned Model

0.07

way to the two thickness conditions: Stiff / Elastic.

Simulated Model

7.27

Cross sectional Comparison between simulation model and scanned mesh reveals deviations in the area of pronounced anticlastic curvature

0.00

9.87

Deviation from measurements

STIFF

ELASTIC

.65

Method 02 Elasticity seems affected by proximity to the thick edges, and therefore a gradient of elasticity is applied according to distance from neighbouring conditions:

Spread of Deviation Rates.

Average deviation: 2.005 Scanned Model

Simulated Model

0.02

Cross sectional Comparison between simulation model and scanned mesh reveals deviations in the area of pronounced anticlastic curvature

Functional Stiffness gradient attractors

STIFF

.66

8,61

Elasticity map

ELASTIC

0.00

Deviation from measurements

11.7

Method 03 We examine the case where the stiff membrane Spread of Deviation Rates.

Average deviation: 2.86 Scanned Model

0.07

also expands in a gradient pattern according to proximity to its own edges:

Simulated Model

16,59

Cross sectional Comparison between simulation model and scanned mesh reveals deviations in the area of pronounced anticlastic curvature

0.00

24.00

Deviation from measurements

Functional Stiffness gradient attractors

STIFF

ELASTIC

Elasticity map

.67

Method 04 The anchored perimeter also seems to act as a tensor element, and thus we must consider both distances of elements from thickness and naked perimeter, in a linear relation:

Spread of Deviation Rates.

Average deviation: 2.36 Scanned Model

Simulated Model

0.04

9,6

0.00

14.7

Functional Stiffness gradient attractors

STIFF

.68

Elasticity map

ELASTIC

Comparison to measured values

Method 05 Perimeter and thickness edges affect their Spread of Deviation Rates.

Average deviation: 2.32 Scanned Model

0.04

neigbouring mesh members, in an exponential relation.

Simulated Model

7,41

Cross sectional Comparison between simulation model and scanned mesh reveals deviations in the area of pronounced anticlastic curvature

0.00

13.00

Comparison to measured values

Functional Stiffness gradient attractors

STIFF

ELASTIC

Elasticity map

.69

B. Top down

Target Geometry Mesh

Curvature Analysis

This

approach

aims

to

algorithmically

automate

the

translation of an inflated geometry into a pattern for the fabrication of a differentiated cross-section, expandable membrane. It is a final step in the trajectory of our

experimental findings Properties Mapping

findings that were presented.

A first approach will include the flat mapping of the target shape on a flat configuration. A curvature analysis combined with the experimental quantitative findings of the previous

Digital Simulation

Calibration Loop

investigation, that fully depends on the experimental

step will help us redistribute the zones of elasticity on the plane.

On a second hypothesis, we proceed to a curvature adaptive remeshing of the target geometry, so that the zones of

Resulting form evaluation: Target geometry Vs Inflated geometry

bigger stiffness are more densely populated, and therefore when the flat mesh is relaxed, the thicker areas occupy a larger percentage of the membrane area. .70

Top-down approach process scheme.

Ta

r

metry Defin it Geo io n

g

et

Topology/ Cu rv

Curvature

a

-A da p

gy to pol o

to pol o

gy

nalysis e A

hi Remes ng ve ti

r tu

a Flat f s me s h o

me

a Flat f s me s h o

me

Re-distrib on are as/relaxati

h

s

n io

Me

ut of

re la

xation .71

Series 01 Method A

Curvature Analysis

Flat Map _ Relaxation of mesh

The strategy that shall be followed begins with a curvature analysis of the mesh that is taken as an input, followed by a mapping of the distended form to a flat configuration, according to an inverted expansion mockup, that takes into account the differentiated properties of the zones marked by curvature. Here we can reverse the quantitative

Redistribution of Lengths & Naked edge Relaxation of Patch Elements

relations we found on the previous step.

The loop is closed with the evaluation of the digital simulation results, that may either be approximating satisfactorily the given target geometry, or not, in which case we shall return to the mapping phase and manipulate according to the error we detected the properties thickness and width of reinforced zone. .72

Inflation and comparison to initial Geometry

Series 02

Curvature Analysis

Flat Map _ Relaxation of mesh

Redistribution of Lengths & Naked edge Relaxation of Patch Elements

Inflation and deviation comparison to initial Geometry .73

Other Shapes:

Target Shape

.74

Curvature Analysis

Flat map _ Relaxation of mesh, Redistribution of Lengths & Naked edge Relaxation of Patch Elements

Inflation and comparison to initial Geometry

.75

Method B Even though we find a lot of potential in a curvature adaptive remeshing of the target surface, the current tool provided y Daniel Piker's Kangaroo, apart from being a component under development, cannot embody on no account the complexity of the gradient of growth that we have been trying to describe in previous chapters. The remeshing process includes all areas of tighter curvature, including the positive ones, and is therefore not satisfying the goals we pursue.

Series 01

Series 02

.76

Other Shapes:

Target Shape

Curvature Adaptive Remeshing .77

.78

04.00 RESULTS _ EVALUATION

In the previous chapters we experimented with the variable expansion rates of pneulastics, differentiated elasticity membranes subjected to pneumatic activation, with the aim of comprehending their mechanism in order to eventually develop an algorithm that would invert this procedure and help as a design tool of

flat configurations of such

undistended membranes.

We have proposed two methods, one of which has managed to provide us with satisfactory results-approximations of pneulastics'behaviour.

The other, which is based on a hypothesis

on curvature

adaptive remeshing, did not prove effectivewith the composition of the given digital tools we have available at the moment. However, we consider it worth investigating and do not discard its further development in the future. .79

.80

05.00 CONCLUSIONS _ FURTHER RESEARCH

CONCLUSIONS With pneulastics we have managed to confirm our initial hypothesis and demonstrated the capacity of elastic membranes of differentiated thickness in adapting to complex geometries upon inflation. Our various steps have allowed us to observe and quantify behaviours, until we reach a control over the differentiated inflation conditions and invert the inflation process, in order to come up with the flat configuration of the undistended surface that would lead to a given target shape approximation.

This research has focused on the potential of combined elasticity/stiffness properties on a single expandable membrane, from an experimental design point of view. The growth of the membrane surface upon inflation is non-linear and given the tools and the scope of our research, it has only been approximated, rather than calculated.

Given the orientation of architectural purposes we have in mind for pneulastics,we have not included the case of closed shapes in the sample geometries we have studied, given the extra complexity that would require some sort of sealing during fabrication.

Another issue that was acknowledged early on, is the pressure levels required for the pneumatic activation of pneulastics that are prohibitive for habitable spaces on earth conditions. However, the growing interest for space exploration and speculation on viability on other planets constitute pneulastics extremely relevant for pressurized spaces in conditions where external conditions of lower pressure and internal pressure donâ&#x20AC;&#x2122;t cancel each other. .81

FURTHER DEVELOPMENT

For the sake of presenting a concise research method that leads to the development of a tool that eventually will aid in the design of complex inflatable structures, we have limited our scope of interest to the approximation rather that the mathematical calculation of pneulasticsâ&#x20AC;&#x2122; behaviour. A more thorough exploration of the potential of the structural system we described would require answers to the following questions: -What is the design space for pneulastics? Which curvature functions can be encoded in thickness patterns? We would have to define the range of feasibility for shapes that can be satisfactorily approximated by pneulastics. Similarly, in the future we could define which are the non-compatible shapes for pneulastics, by branching out, investigating other geometries and fully understanding the constraints. With a wider range of geometries, a more detailed catalogue could be developed and then the full control over pneulastics could be made possible.

Another issue can be spotted upon scaling up to architectural applications. We have detected that the potential of pneulastics lies in the differential of elasticity as acquired by thickness. However, in membrane structures such thickness ranges are not usual. We would therefore need consultation on material and fabrication alternatives, that maintain the principle of embedding stiffness in one single body, via density or other. Together with this concern we would have to combat the issue of fragility that we have encountered in various occasions during our experiments. .82

Although throughout the process we have been concerned with the feasibility of the prototypes and have provided suggestions for their fabrication, we only proceeded to a simple casting and curing process, for the sake of proving our hypothesis. In this sense, we have left unexplored the opportunities for a more efficient, digitally controlled and space-saving fabrication method, that would be an additive production of the elastic membrane. In order for this to be possible, a material exploration is needed in the direction of converting the elastic material(latex, silicone etc) into a filament-friendly condition, that combines and reacts friendly to removable and printable materials.

Finally, we are leaving open the case of adaptive activation, and a detailed control/ prevision/design of the progressive/iterative states of pneulastics during their growth when subjected to different levels of pressure. the field of soft robotics and

This would be rather interesting for

air muscles in engineering. .83

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Pneumatic Falsework for the erection of strained grid Shells: A parameter Study

Simulation Methods for the Erection of strained Grid Shells via Pneumatic Falsework INGO MULLER, HENNING STRUCHTRUP

Inflating a Rubber Balloon, Technical University of Berlin & University of Victoria (Received 2 April 2002; accepted 31 May 2002) J.G. HELMCKE AND BERTHOLD BURKHARDT

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Variation of Reference Strategy- A novel Approach for Generating Optimized cutting patterns of Membrane Structures KEVIN C. GALLOWAY, PANAGIOTIS POLYGERINOS, CONOR J. WALSH, AND ROBERT J. WOOD

Mechanically Programmable Bend Radius for Fiber-Reinforced Soft Actuators.

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A Reasearch Document on Frei Otto's and Buckminster Fuller's Architecture, 2012.

MINA KONAKOVIĆ-LUKOVIĆ, JULIAN PANETTAKEENAN CRANE, MARK PAULY

Rapid Deployment of Curved Surfaces via Programmable Auxetics, EPFL, Carnegie Mellon University MELINA SKOURAS, BERNHARD THOMASZEWSKI, BERND BICKEL, MARKUS GROSS

Computational Design of Rubber Balloons,ETH Zurich, Disney Research Zurich,Columbia University MELINA SKOURAS, BERNHARD THOMASZEWSKI, PETER KAUFMANN, AKASH GARG, EITAN GRINSPUN, BERND BICKEL, MARKUS GROSS

Designing Inflatable Structures, ETH Zurich, Disney Research Zurich,Columbia University NIELS WOUTERS

Pneumatic Structures: A revival of formal experiments, 0930132 PAUL POINET, EHSAN BAHARLOU, TOBIAS SCHWINN, ACHIM MENGES

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Inflated Restraint, CITA, 2016.

PHILIP DREW,

Frei Otto, Form and Structure, Crosby Lockwood Staples, London,1976 PIERRE ALLIEZ, ÉRIC COLIN DE VERDIÈRE, OLIVIER DEVILLERS, MARTIN ISENBURG

Isotropic Surface Remeshing. RR-4594, INRIA. 2002.

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Pressure Induced Stability: From Pneumatic Structures to Tensairity ® ,VII International Conference on Textile Composites and Inflatable Structures STRUCTURAL MEMBRANES 2015 19 - 21 October 2015, Barcelona, Spain E. Oñate, K.-U. Bletzinger and B. Kröplin (Eds.) RUSLAN GUSEINOV, EDER MIGUEL, AND BERND BICKEL

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Symposium on 3D Data Processing, Visualization, and Transmission, September 2004.

UNCUBE

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Knitflatable Architecture: Pneumatically activated pre-programmed knitted textile spaces, ITECH MSc Thesis, 2015.

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LIST OF FIGURES

Figure 01.01 http://journals.sagepub.com/doi/abs/10.1177/0266351116642060?journalCode=spsa Figure 01.02 http://www.america-scoop.com/index.php?option=com_content&view=article&id=1027: beken-of-cowes-gb&catid=230&Itemid=423&lang=en Figure 01.03 http://www.pneumocell.com/pneumocell.nature.english.html Figure 01.04 http://javastraat.co/harnessing-atmospheric-electricity.html Figure 01.05 http://thegolfclub.info/707566666572/puffer-fish-before-and-after.html Figure 01.06 https://selfassemblylab.mit.edu/liquid-printed-pneumatics/ Figure 01.07 https://issuu.com/ninajotanovic/docs/soft_skin_pneumatics_booklet Figure 01.08 http://acadia.org/projects/JFHW9X Figure 01.09 Frei Otto, Form and Structure, Crosby Lockwood Staples, London,1976 Figure 01.10 https://www.moma.org/documents/moma_catalogue_2662_300299029.pdf Figure 01.12 & 01.13 & 01.14 & 01.15 Frei Otto, Form and Structure, Crosby Lockwood Staples, London,1976 Figure 01.16 https://www.e-periodica.ch/digbib/view?pid=buw-001:1978:32::949#232 Figure 01.17 http://journals.sagepub.com/doi/abs/10.1177/0266351116642060?journalCode=spsa Figure 01.18 http://hybios.blogspot.com/2011/06/frei-ottos-il-25-pneu-and-bone.html Figure 01.19 http://www.uncubemagazine.com/sixcms/detail.php?id=15508949&articleid=art1429001789303-71c8ac75-dcca-4664-8331-3fb42d523bb0#!/page1 Figure 01.20 http://www.complexmodelling.dk/?p=1379 Figure 01.22 https://www.architectural-review.com/essays/viewpoints/skill-inflatableconcrete-domes/8641827.article Figure 01.23 https://www.researchgate.net/publication/283070999_Pneumatic_Falsework_for_the_ Erection_of_Strained_Grid_Shells_A_Parameter_Study Figure 01.24 http://m.big.dk/getslideshow/230/2

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Figure 02.01 http://www.larsenglund.se/page9/files/page9-1039-full.html Figure 02.02 http://www.complexmodelling.dk/?p=1379 Figure 02.03 https://www.disneyresearch.com/publication/designing-inflatable-structures/ Figure 02.04 http://papers.cumincad.org/data/works/att/ecaade2016_113.pdf Figure 02.05 https://issuu.com/yuliya_baranovskaya/docs/knitflatables_ybaranovskaya_2310201 Figure 02.06 http://www.interactivearchitecture.org/lab-projects/furl-soft-pneumatic-pavilion Figure 02.07 https://graphics.ethz.ch/publications/papers/paperSko12.php Figure 02.08 http://www.gldarch.com/projects/show?utf8=%E2%9C%93&tag=18&project=20 Figure 02.09 https://lgg.epfl.ch/publications/2018/ProgrammableAuxetics/index.php

Figure 03.02 https://graphics.ethz.ch/publications/papers/paperSko12.php Figure 03.04 https://lgg.epfl.ch/publications/2018/ProgrammableAuxetics/index.php .87