Deployable Reciprocal Shells through auxetic behavior by Surendar Jayachandran

DOUBLE CURVED SHELL STRUCTURES

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.1.1 WHAT ARE CURVED SHELL STRUCTURES??

It is a well-known fact that a curved shell can resist loading acting perpendicularly to the middle surface by the agency of membrane forces. In those cases where the membrane reactions can be resisted and the corresponding deformations of the shell can freely take place, a force distribution pattern constituted solely by membrane forces is a good approximation of the transmission of forces that actually occurs - for a statically possible stress distribution in which bending and torsion are avoided will come close to producing the minimum strain energy in the structure. The usual procedure, therefore, is to begin by calculating the distribution of forces in the shell according to the membrane theory. Then a set of correcting forces will have to be applied so as to take the best possible account of the boundaries (edge beams or supports) of the shell, where the deformations due to the said state of membrane stress are prevented from freely developing. Let us suppose the edge member to be detached from the shell, thus enabling these deformations to develop freely: the edge of the shell and the edge member would then no longer fit at their junction.

Fig.1.1.1.1 Differenziazione tecnologica dei sistemi di tensione ad arco. Image Courtesy: Internet

(Chapter 1)

Fig.1.1.1.1 Differenziazione tecnologica dei sistemi di tensione ad arco. Image Courtesy: Internet

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.1.2 Structural Characteristics The behavior of any shell surface under the action of a load is analogous to a membrane, a surface element so thin that only tension forces can be developed (e.g. a soap bubble). Of primary importance is the existence of two sets of internal forces in the surface of a membrane that act in perpendicular directions. Also in existence is a type of tangential shearing stress which is developed within the membrane surface which helps carry the applied load. The shell tends to act in a fashion similar to a two-way plate structure.

Fig.1.1.1.2 Image Courtesy: Internet

1.1.3 Support Conditions Support conditions in both shells of revolution (spherical) and shells of translation (cylindrical) are a major design consideration. Some device must be employed to gather forces at the lower edges of the shell. In domes, common methods include circular buttressing systems or a tension ring. Cylindrical shells are usually supported by edge beams.

Fig.1.1.1.2 Image Courtesy: Internet

(Chapter 1)

Fig.1.1.1.3 Differenziazione tecnologica dei sistemi di tensione ad arco. Image Courtesy: Internet

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.1.4 Structural Morphology Any design process has to deal with multi-parametric problems. It could be then useful to identify the main parameters and to classify them so as to understand simultaneously the degrees of freedom, the variables for the designer, which can be alone, or associated. As far as engineering problems are concerned, five classes of parameters may be considered. • Form This can be the form of every component or of the whole system. Geometric information of size and position are generally sufficient, but many others can be useful for the description of double-curved surfaces (curvature radii for instance). • Force “Force” is the generic word for description of the mechanical characteristics of actions, stresses, prestress, strains, deflections. • Structure understood in its systemic meaning, this describes the component’s assembly and the boundary conditions selected by the designer. It could also be called the relational structure of the system.

Fig.1.1.1.4 Image Courtesy: Internet

(Chapter 1)

Fig.1.1.1.4 Image Courtesy: Internet

Fig.1.1.1.4 Geometric information of size and position. Image Courtesy: Internet

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.1.5 WORKING PRINCIPLE OF A DOUBLE CURVED STRUCTURE Imagine four people holding out a large thin square rubber or cotton sheet, one at each corner, pulling fairly hard. The sheet is flat and tight around the edges, and yet the sheet has very little resistance to movement in the central area. For example, even a light wind will cause it to bulge up or down, and a ball thrown onto the surface will deflect it significantly.

paper, it wouldn’t really take up the changed shape at all well. Although the rubber could easily adopt a double curvature, in reality it wouldn’t work for a tensile structure as the following will hopefully make clear. Why do we need to tension it in the first place? Well if the fabric was literally cut to fit exactly its final position, it would move around very easily in even light winds, and after a buffeting from very high winds or a heavy snowfall, the fabric would have stretched enough to not even return to its original installed size.

Now imagine that two diagonally opposing people peg their corners to the ground, and the other two maintain their position. The middle of the sheet is now halfway between the low points and high points. From this middle point, fabric is curving both downwards toward the corners on the ground, and upwards toward the people holding out the other two corners. This is a much more stable shape which will inherently resist movement from download or uplift. The fabric is in double curvature, the form in this instance is a “hypar”.

The other factor not to forget is that although the fabrics we use have a certain amount of stretchiness, it’s generally nowhere near stretchy enough to create a large doubly curved surface in a single piece. We have to cut the fabric into narrow strips, and join them up to create the appropriate 3d form to fit to the structure. As mentioned before, you couldn’t create a hypar form with a single sheet of paper, but you could recreate the shape with lots of thin strips

However what is also important here is the nature of the material itself. You could perform this trick with rubber because it’s very stretchy, so when you distorted it from being a flat square, it can accommodate the distortion quite comfortably. If you tried it with say a very large piece of

(Chapter 1)

Fig.1.1.1.5 Fractals Image Courtesy: Internet

Fig.1.1.1.5 Flow of Forces Image Courtesy: Internet vv

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.1.6 Construction Characteristics A consequence of carrying loads by in-plane forces (primarily tension and compression) is that shell structures can be very thin in comparison to their spans. Span to thickness ratios of 400 or 500 are not uncommon. (e.g. A 3 in. thickness is possible for domes spanning 100-125 ft.) Reinforced concrete has become the ideal material used for these types of three dimensional surfaces, however, they may also be made of assemblies of short, rigid bars. In concrete structures, the careful laying and specification of reinforcement is key to the success of the structure.

Fig.1.1.1.6 Shell Form Image Courtesy: Internet

1.1.7 Typical Materials Shells can be made of almost any material -- cold formed steel, wood, reinforced concrete, plastics. Structures made of short, rigid bars of wood or steel are technically not shell structures since they are not surface elements, however, their structural behavior can still be conceptualized in this fashion.

Fig.1.1.1.6 Shell Form Image Courtesy: Internet

(Chapter 1)

Fig.1.1.1.7 Shell unfoldedv Image Courtesy: Internet

Fig.1.1.1.7 Shell forms variations Image Courtesy: Internet

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.1.8 EXAMPLES OF DOUBLE CURVED STRUCTURES There are several ways in which double curve geometries can be achieved with building materials as single products, which can either create precision components. Below are some of the materials and methods available, and it’s not surprising that many of them have come from the automotive, aerospace and rail sectors of industry. As the manufacturers and suppliers will note, the extent to which double curves can be made often depends on the selection of the material, its thickness and the required size of the component:

ter finish. As a built-up system it is a good example of the site based craft of skilled workers being as important as the overall building technology which supports it.

Glass For double curved geometries in glass, companies to contact are Octatube, AGC(formerly Glaverbel) and Cricursa. Sizes of panels are constrained by the standard sizes of glass sheets, their logistical restrictions, and the size of the furnace they are molded in.

Timber For geometrically challenging structures in timber, Cowley Timber Works has lots of experience of fabricating double curves. Panel sizes are prefabricated and limited by logistical constraints. Geometric restraints are dictated by material selection and thickness.

Concrete Perhaps the best example of double curved geometries in concrete is the Darwin Centre’s Cocoon at the Natural History Museum in London. It was created through a combination Shotcrete spray applied concrete to a reinforcement mesh, insulation bonded to the exterior with a Dryvit Genesis high performance adhesive resin and Armourcoat top coats and polished plas-

Articulated sheets Articulating sheets with triangular sub divisions offers the ability to fold and form the sheet in to 3D forms. The individual segments remain flat, but the overall effect is curved. This option is possibly an economical solution to many building challenges.

(Chapter 1)

Fig.1.1.1.8 Glaverbel’s Bubble at the Nardini Distilleries Image Courtesy: Internet

Fig.1.1.1.8 The Cocoon at the Darwin Centre, Natural History Museum, London. Image Courtesy: Internet

(Chapter 1)

Fig.1.1.1.8 Top left: Suit at the Scin GalleryTop right: Ligne Roset, Clouds. Bottom left: Articulating paper. Bottom right: Theatre, Delft University. Image Courtesy: Internet

Fig.1.1.1.8 Timber pod at Strawberry Fields School, Leeds. Fabricated by Cowley Timber Works. Architect Adeas. Image Courtesy: Internet

(Chapter 1)

1. DOUBLE CURVED SHELL STRUCTURES

1.2 INFERENCES TO BE TAKEN (PROS OF THE TECHNIQUES)

UNDERSTANDING AND USING THE PANELING TECHNIQUE

FABRICATION TECHNIQUES OF SHELL STRUCTURES

LOAD DISTRIBUTION (SELF SUPPORTING) IN SHELLS

1. DOUBLE CURVED SHELL STRUCTURES

1.3 SHORTCOMINGS TO BE INCOMINGS (CONS OF THE TECHNIQUES)

+ The fabrication method involves Carefully selecting the forms breaking down into Parts that are unique in that double curves + This is later sent to fabricate in modules that require fabrication one by one with precision which makes it time consuming and expensive

+ Cant be reused into other forms – only predefined forms are possible + A prefabricated shape cannot be modified or not dynamic when it comes to structure

+ Has to be CONSTRUCTED IN PHASE

1.4 BIBLIOGRAPHY & REFERENCES

• (PDF) Structural Morphology Issues in.... Available from: https://www.researchgate. net/publication/245526176_Structural_Morphology_Issues_in_Conceptual_Design_ of_Double_Curved_Systems • https://www.coroflot.com/dmprijatna/college • https://www.researchgate.net/publication/315809235_Form-finding_of_shell_ structures_generated_from_physical_models • https://www.colorado.edu/engineering/CAS/ courses.d/AFEM.d/AFEM.Ch31.d/AFEM. Ch35.pdf • http://shells.princeton.edu/Grotz.html • https://www.slideshare.net/SusmitaPaul12/ shell-structure •

RECIPROCAL STRUCTURES

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.1 What are reciprocal structures ?? The “reciprocal frame” is a roof structure whereby each beam reaches from the top of a wall towards the centre of a room at an indirect angle, with the further end resting on the top of the beam next to it. When a full circle of these beams is completed, the roof is self-supporting without any central supports and creates an spiralling pattern of beams on the underside of the ceiling. The reciprocal frame, which is not a widely used term, essentially requires a circular - or polygonal - shaped room to be usable. The reciprocal frames are fascinating. Starting with only very simple material in the form of rods, one can build a complex grillage structure made of one or a few similar RF-units (see Figure 1), by iteratively putting RF-units around one another [Bertin 2001]. No central supports are required in the resulting RF-structures, and one can also disassemble and re-assemble these structures, facilitating their transportation from place to place. This makes RF a highly cost-effective deployable system, particularly suitable for rapid constructions of temporary structures.

Fig.2.1.1.1 Simple reciprocal structure Image Courtesy: Internet

Fig 2.1.1.1 Complex reciprocal structure Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

Apart from the technical aspects, the reciprocal frames also have their intrinsic beauty. Similar to bird nests in the nature, which are built from discrete simple elements, the reciprocal frames share a common characteristic of being a modular structure composed with simple rods. These rods nicely form self-similar and highly symmetric patterns, capable of creating a vast architectural space as a narrative and aesthetic expression of the building. Fig.2.1.1.1 Assembling and disassembling

2.1.2 How they work ?? A three-dimensional grillage structure mainly used as a roof structure,consisting of mutually supporting sloping beams placed in a closed circuit. The inner end of each beam rests on and is supported by the adjacent beam. At the outer end the beams are supported by an external wall, ring beam or by columns. The mutually supporting radiating beams placed tangentially around a central point of symmetry form an inner polygon. The outer ends of the beams form an outer polygon or a circle. If the reciprocal frame (RF) is used as a roof structure, the inner polygon gives an opportunity of creating a roof light.

Image Courtesy: Internet

Fig.2.1.1.2 Tesellations and patterns Image Courtesy: Internet

(Chapter 2)

Fig 2.1.1.2 RF breakdown element Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.3 A Brief History Structures such as the Neolithic pit dwelling , the Eskimo tent, Indian tepee or the Hogan dwellings have some similarities to the RF concept. Perhaps the latter two examples have greater similarities to the RF than the neolithic pit dwelling and the Eskimo tent. Similarly to the RF the Indian tepee and the Hogan dwellings use the principle of mutually supporting beams. The differences between them and the RF are that the rafters forming the structure of the Indian tepee come together into a point where they are tied together and the integrity of the structure is secured in that way. Stretched animal skins provide additional stiffness to the conical form of the tepee. The animal skins have the role of the cladding roof panels used in RF structures, which in a similar way provide a ‘stretched skin effect’ and give additional stiffness to the structure. The reciprocal frame, also known as a Mandala roof has been used since the twelfth century in Chinese and Japanese architecture although little or no trace of these ancient methods remain. More recently they were used by architects Kazuhiro Ishii (the Spinning House) and Yasufumi Kijima, and engineer Yoishi Kan (Kijima Stonemason Museum).

Fig 2.1.1.3 Mandala roof; The Spinning House. Image Courtesy: Internet

Fig 2.1.1.3 Neolithic pit dwelling; Eskimo tent; Indian tepee. Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

be identical. However, the members will also be subjected to bending moments and shear forces, and will have to resist these forces in addition to the axial force.

2.1.4 Structure and Construction Details A reciprocal roof is assembled by first installing a temporary central support that holds the first rafter at the correct height. The first rafter is fitted between the wall and the temporary central support and then further rafters are added, each resting on the last. The final rafter fits on top of the previous rafter and under the very first one. The rafters are then tied with wire before the temporary support is removed. The failure of a single element may lead to the failure of the whole structure.

2.1.4.1 Two-dimensional, In-plane, RF Structures There are early examples of plane RF structures used in grids of floor beams. The flat grillages presented in the history part of the book designed by Sebastiano Serlio, Leonardo da Vinci and Villard de Honnecourt, are examples of this type of structure. These planar frames have members arranged very similarly to the frames with sloping beams described above.The unique interlocking arrangement of the members ensures that the structure is stable and acts in a similar manner to that of a moment frame – that is, a frame with stiff, fixed connections that can transfer bending moments.

An RF structure with inclined main members forming a pitched roof will typically have the inner end of the beams, or the central sections, at a higher level than the outer end sections that are at the perimeter of the structure. Arranged in this way, the members will be able to transmit the vertical forces (their own weight and any imposed loads) to the supports at the perimeter of the structure through compression in each member. For a symmetrical load (for example, selfweight) the forces in each member will

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.5 INITIAL RESEARCH

As with many inventions, the RF principles have emerged from a need. The flat configurations by Leonardo da Vinci of both simple and complex RFs from the fifteenth century (1998), the RFs by the architect Sebastiano Serlio from the sixteenth century, fourbeam assemblies or the stairwell configurations were all structures finding a solution for spanning a longer distance than the length of the available timber elements. A further development were inclined RF structures, such as the complex forms found in Leonardo da Vinci’s Codex Atlanticus, for creating RF grid roofs as well as his designs for temporary bridges (2008). Chinese bridges were also constructed using similar principles; furthermore John Wallis studied the complex RF configurations using three-, four- and six-member RF complex assemblies (1695).

¨ 2011] employed a Rhino-script to aid students to design RF-structures and arranged the RF-units over the cells obtained as the Delaunay triangulation of points on the input surface. However, since the point set can have arbitrary distribution, the resulting RF-structures can be rather irregular. Further, the users have little control on the RF patterns, and have no support to interactively preview and refine the designs. For many centuries, reciprocal frames have been used in design and construction, e.g., the classical bridge sketches by Leonardo da Vinci, the roof of Nagasaki Castle in Japan, as well as Eskimo tents. However, the term “reciprocal frame” was coined only in late 1980s by designer Graham Brown, and developed for constructing roundhouses with RF roofs. There exists little computational support to design and construct RF-unit based structures. Hence, most such realizations are restricted to small structures involving only a few RF-units. Such an approach does not generalize to larger structures due to various challenges involving where to place the RF-units, how to interconnect them, and how to realize a meaningful aesthetic design.

Although there have been recent attempts to support RF design, they are preliminary and offer only limited user controls. Brocato and Mondardini [2010] proposed a geometric method to design stone domes with extended number of RF-units, but their method supports only one class of RF patterns and offers a few parameters for user control. Thonnissen and Werenfels [

(Chapter 2)

Fig 2.1.1.4.1.Two dimensional RF Image Courtesy: Internet

Fig 2.1.1.5 Simple to Complex Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.6 DEFINING AND CONNECTING RECIPROCAL FRAME UNITS

Large RF-structures consist of a grillage of rods; however, they are designed as a two-level hierarchy. First, small RF-units are defined, and then aggregated into a large grid. The fundamental elements can be rods, beams, bars, or sticks. Hereafter, we will refer to them as rods. A reciprocal arrangement of at least three rods forms an RF-unit, which defines the building blocks of an RF-structure. There are four common approaches to physically construct an RFunit from rods, or in general to connect two intersecting rods in an RF-structure: notching, nailing, tying, and friction. In our work, we follow the common approach taken by architects [Larsen 2008] for constructing large-scale RF-units, and assume that they are nailed or tied.

RF structures can, in theory, be constructed of all the main construction materials (steel, timber and concrete). However, the complex geometry of three-dimensional RF structures,and the need to keep the self-weight low for practical reasons,means that (precast) concrete is not normally a preferred material. For smaller structures, from 2 to 3m up to approximately 12m overall span, timber will normally be the preferred material. If the designer has a clear understanding of the RF geometry, timber members can easily be pre-cut and brought ready for construction to site. For steel, the connections between the main members will be potentially complicated to design and fabricate. Most RF buildings built to date are in the 3–12m range of span. It is not surprising, therefore, that most of them are constructed from ordinary or glued laminated timber. The only built example in steel known to the author to date is Ishii’s Spinning House in Tokyo. As far as the author is aware, the only RF design in concrete is the Mill Creek housing project by Louis Kahn, described in the history section, which unfortunately was never built.

Rods, in general, have thickness, and thus the RF-units are nonplanar. To form an RF-unit, the rods are placed over one another in a closed circuit, forming a dome-like 3D geometry. However, it has been known that for creating free-form shapes, one may need some non-circular arrangements of the type.

(Chapter 2)

Fig 2.1.1.6 Intersection of rods; Force and load applied in different rod intersections Image Courtesy: Internet

Fig 2.1.1.6 RF patterns in various forms Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.7 Examples of Reciprocal Strcuture The German engineer Friedrich Zollinger (1880–1945), developed a system of lamella domes constructed from short timber elements using RF joints. The system was developed to achieve ease and speed of construction. The short timber members do not meet in a single point— instead they form a RF joint with beams that are offset. The system was developed after the first world war to serve a need for housing and allow for fast, inexpensive construction. At the time, there was a serous lack of housing and deficit of funding and the Zollinger system helped fulfill this very important need. Lamella domes were later used by Pier Luigi Nervi for the aircraft hangers in Orvieto, destroyed in World War II. Also, a beautiful steel lamella dome is the early-twentieth-century Copenhagen School of Architecture, canteen roof structure initially constructed for and used by the Navy (2009).

Fig.2.1.1.7 Zollinger-type lamella structure with offset joints; The Orvieto hangar structure by Pier Luigi Nervi, physical model Image Courtesy: Internet

Fig.2.1.1.7 Steel lamella dome canteen roof structure, Copenhagen School of Architecture Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.8 Rokko Shidare Observatory- Japan Mount Rokko-Shidare Observatory, designed by architect Hiroshi Sambuichi and Ove Arup and Partners1 in Japan, was completed in 2010. Built on the top of the Rokko Mountain at 900 m altitude, the observatory is directly above the Kobe bay, and on a clear day offers an amazing view over the sea and coastline. The RF structure forms an open canopy with a complex geometry. It is a meshed irregular dome-like laced RF structure 16 m in diameter. The irregular shape of the complex RF is built from a regular single-unit. The main structure is made of 50 mm welded steel tubes 1–2 m long arranged in an RF pattern in-filled with 15–20 mm thick wooden (Japanese cypress) RFs of varying density. The overall shape was based on the requirement to passively induce air movement facilitating natural ventilation, to be relatively easy to construct and to be built within the constraints of the budget. The choice of the pattern and its density, on the other hand, was based on the necessity for the structure to provide shading (the south) and enable air movement.

Fig.2.1.1.8 The RF pattern is interrupted with the bamboo tubes which channel the wind and create a tune; The RF pattern is denser where it needs to provide shading Image Courtesy: Internet

Fig.2.1.1.8 Structural breakdown of the structure Image Courtesy: Internet

(Chapter 2)

Fig 2.1.1.6 The RF pattern and a detail of the welded connection and tied wooden timber battens Image Courtesy: Internet

Fig 2.1.1.8 Reciprocal Frames Image Courtesy: Internet

(Chapter 2)

Fig 2.1.1.8 Structure in different color pigments Image Courtesy: Internet

Fig 2.1.1.8 Structural detail of the observatory Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.1.9 KREOD PAVILLION- LONDON

In winter the lace-like RF structure creates a delicate icy roof just like those we see in Nature. The architect’s idea of the lace forms were inspired by tree patterns, which the engineers developed into a RF pattern following ideas from traditional Japanese RF structures. The geometry is based on chop-stick model of single RFs supporting each other that have been associated/overlaid onto a surface of a multi-faceted cylinder that could be manipulated parametrically. The problem becomes quite complex geometrically with the introduction of the depth of the members because the depth has an influence on the overall geometry. A shift frame geometry (SFG) solver was developed by Arup, which had the capacity to incrementally shift all elements simultaneously and find, through an iterative process, the converging geometrical solution for the actual member sizes. Using this approach, the pattern was optimized by the Arup software based on Bentley’s Generative Components. The aim of the optimiza-

tion was to produce a visually pleasing form that complied with the architectural vision, one that is structurally efficient and that could be constructed easily. The contractor developed a method of checking the complex geometry during construction. This was extremely important because had the precision not been high enough—it would not have been possible to construct the RF and to connect the RF members . KREOD consists of three compartments and has a footprint of 60 square meters (3 x 20 square meters). It is 3 meters high. The structural design aims to show a sustainable and forward thinking building method in the digital age, challenging the new way of thinking, designing, engineering, fabricating and installing. The design will have the practical considerations for transportation, store, dis-assembly and reassembly i.e. stackable components, modularity.

(Chapter 2)

Fig 2.1.1.9 Skeleton of the RF structure Image Courtesy: Internet

Fig 2.1.1.9

KREOD pavilion

Image Courtesy: Internet

(Chapter 2)

Fig 2.1.1.9 KREOD

pavilion

Image Courtesy: Internet

Fig 2.1.1.9

KREOD pavilion

Image Courtesy: Internet

(Chapter 2)

Fig 2.1.1.9 KREOD

pavilion

Image Courtesy: Internet

Fig 2.1.1.9

KREOD pavilion

Image Courtesy: Internet

(Chapter 2)

2. RECIPROCAL STRUCTURES

2.2.1 POST ANALYSIS

There are many factors that will influence the design of a building: a synthesis of considerations related to the site, the historical context, the function of the building, the aesthetic appearance, building physics and other issues. The structural system will be only one of them. We judge the quality of a design on how harmoniously the synthesis of the multitude of influential factors has been achieved. One can argue that for different projects and for different people the level of importance of the influential factors will vary. Regardless of the fact that there always will be a level of subjectivity in judging design, in most cases the masterpieces and the failures are easy to spot and agree upon.

it forms and is part of the harmonious composition that we class as architecture, it is an influential factor that, to a lesser or greater degree, determines the level of success of a building design. And although the structure as such cannot determine the quality of a building design, if integrated appropriately it can influence it greatly. Reciprocal frames are presented here as simply one more option that is available for building design. It is a system that offers great opportunities but also has its limitations. I hope that by introducing readers to the world of reciprocal frame architecture, it may inspire talented and skilled design teams to create new and imaginative buildings using reciprocal frames.

Although structure is only one of the multitude of, at times opposing, factors that influence building design, there are instances when the structure becomes part of the overall narrative, form and architectural expression. More importantly, when

Fig 2.1.2 Reciprocal Distribution on Shells - Hemisphere Image Courtesy: Internet vv

Fig 2.1.2.2 Reciprocal Distribution on Shells - Different shapes of Shapes Image Courtesy: Internet vv

Fig 2.1.2 Reciprocal Distribution on Shells - Breakdown Image Courtesy: Internet vv

2. RECPROCAL STRUCTURES

2.3 INFERENCES TO BE TAKEN (PROS OF THE TECHNIQUES)

+ STRUCTURAL BREAK DOWN AND LOAD TRANSFER PRINCIPLE

+ CONSTRUCTION AND JOINERIES

Fig 2.1.1.9 Analysis of Reciprocal Structure Image Courtesy: Generated

2. RECIPROCAL STRUCTURES

2.4 SHORTCOMINGS TO BE INCOMINGS (CONS OF THE TECHNIQUES)

+ The fabrication method involves Carefully selecting the forms breaking down into Parts that are unique in that double curves

+ Cant be reused into other forms – only predefined forms are possible + A prefabricated shape cannot be modified or not dynamic when it comes to structure

+ Has to be CONSTRUCTED IN PHASE

2.5 BIBLIOGRAPHY & CITATION

• Cavanagh, Ted. (2012). Innovative structures and the design/build model of teaching. presented design/ build conference Berlin 2012. https://www.academia. edu/2144320/Innovative_Structures_and_the_Design_Build_Model_of_Teachng • • Parigi, Dario and Pugnale, Alberto. (2012). Three-dimensional reciprocal structures: morphology, concepts, generative rules. In Proceedings of the “IASS Symposium 2012: From spatial structures to space structures”. Seoul. • • Popovic Olga. (1998). Reciprocal Frame Architecture. Ph.D. Thesis, School of Architecture, University of Nottingham. • • Popovic Larsen, Olga. (2009). Reciprocal Architecture in Japan. In Proceedings of the IASS Symposium: Shell and Spatial Structures, IASS International Symposium. Valencia, Spain, (Key note paper).

DEPLOYABLE STRUCTURES

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.1 WHAT ARE DEPLOYABLE STRUCTURES ??

Deployable structures are structures that can be easily reduced in size for transportation or storage. A number of everyday structures could be classed as deployable; tents and umbrellas are two simple examples. Current interest in deployable structures arises mainly from their potential in space. Many space applications, both current and proposed, require large structures in space. Typical examples include satellites for communications, earth observation, astronomy, and space exploration. However, launch vehicles, such as NASA’s space shuttle, are, and for the foreseeable future will continue to be, limited in size. The generic name deployable structures is used for a broad category of structures that can be transformed from a closed compact configuration to a predetermined expanded form, in which they are stable and can carry loads. The use of deployable structures is very old, as most of nomadic populations have developed such kind of, sometimes sophisticated, shelters. Talking about tents, it may be for example funny to compare nomadic shelters to contemporary hiking tents.

In modern terms, due to their inherent transformability, deployable structures can be considered a special case within the broader class of adaptive and morphing structures, which are characterized by their ability to change the shape, the mechanical and physical properties, according to the external excitations and the requirements emanating from their use at any given time. In the context of the present paper, the behavior and purpose of deployable structures are however considered to be quite specific, focusing on the change of shape, which is usually obtained by a single degree of freedom (SDOF) transformation and between only two configurations (start/compact and final/deployed). Moreover, the compact and deployed configurations are defined a priori and thus the structure is not conceived to respond or adapt to real-time changing scenarios, nor is designed to be used with different conditions in a same context. On the contrary, the conception of a deployable structure looks towards two different uses in two different contexts, the first being the transportation or erection of the structure and the latter its static and functional behavior when deployed.

(Chapter 3)

Fig 3.1.1.1 Deployable mechanism Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.2 Few Uses Of Deployable

Structures

The generic name deployable structures is used for a broad category of structures that can be transformed from a closed compact configuration to a predetermined expanded form, in which they are stable and can carry loads. The use of deployable structures is very old, as most of nomadic populations have developed such kind of, sometimes sophisticated, shelters. Talking about tents, it may be for example funny to compare nomadic shelters to contemporary hiking tents. Deployable structures can provide a change in the geometric morphology of the envelope by contributing to making it adaptable to changing external climate factors, in order to improve the indoor climate performance of the building. They have the ability to transform themselves from a small, closed or stowed configuration to a much larger, open or deployed configuration being also known as erectable, expandable, extendible, developable or unfurlable

structures. According to their structural system, deployable structures can be divided in four main groups: spatial bar structures consisting of hinged bars, foldable plate structures consisting of hinged plates, strut-cable (tensegrity) structures and membrane structures. In this paper a short review only on two of these groups of deployable structures for architectural applications will be presented. 3.1.3 Working Of Deployable Structures The dissertation is split into three parts. Each part introduces a concept, and gives some general analysis concerning the shape and unfolding characteristics of that concept. The three concepts are: a method for folding a cylinder; a method for folding a membrane; a method for folding an antenna with a rigid surface. Of these concepts, the first and the third are completely new. The second concept, the method of folding a membrane, has been suggested a number of times before, but this dissertation gives the first correct analysis of the fold pattern, which also suggests a number of ways that the folding concept can be extended.

(Chapter 3)

Fig 3.1.1.2 Deployable mechanism Image Courtesy: Internet

(Chapter 3)

Fig 3.1.1.3 Deployable mechanism Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.4 Initial Research

be more readily understood by knowing the change in the relative height coordinates of two successive nodes between the open and closed configuration. The difference in height between two nodes on the a-helix is 9mm, and on the b-helix 64mm. It can be seen that the basic periodicity of the plot has a wavelength corresponding to successive nodes on the b-helix folding. One important effect shown in the photographs is the formation of a second transition zone close to the base of the cylinder. This occurred when the cylinder had been compressed by 125 mm. For the rest ofthe test it was this transition zone which moved up through the cylinder. A possible reason for the formation of this second transition zone is the weight of the cylinder, which led to a compressive force approximately 55N greater in the second transition zone than in the top transition zone.

A cylinder was manufactured using a copper beryllium alloy (Cu-De) as a hinge material. Cu-Be ~as used because it has a large elastic strain range when it has been correctly heat-treated. This means that a thin strip of Cu-Be can be elastically bent around a small radius. This feature is desirable so that the cylinder remains elastic during folding, and also has a compact folded shape. A Cu-Be cylinder such as this would be suitable for an application such as the collapsible hydrazine fuel tank. Four compression tests were performed on the Cu-Be and steel model described in Section 5.1.1. A plot of the force required to fold the cylinder during the first compression test shows four photographs taken during this test. As can be seen from the cylinder had to be initially slightly folded to fit in the testing machine. The plot of force during folding can

(Chapter 3)

Fig 3.1.1.4 Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.5 Existing Applications At first glance, deployability might seem to be a very unfamiliar term but examples are more common than one might think. The umbrella is a typical example of a simple deployable device of every-day use;it is portable, easy and quick to erect, and reusable. These same characteristics will persist in more complex and large deployable devices. We are surrounded by every-day objects that are deployable: foldable furniture, old telephone stands, elevator doors, shop gratings, collapsible boats, automobile tires, water containers, antenna masts, etc, to mention only some. Activities like camping are replete with ingenious forms of collapsible shelters, furniture, and accessories. The reason for making collapsible products is clear: mobility. Deployable gadgets can be found in some military applications : masts, parabolic antennas, shelters, bridges.

Fig.3.1.1.5

Image Courtesy: Internet

Fig.3.1.1.5 Movable hangar Image Courtesy: Internet

(Chapter 3)

Fig 3.1.1.5 Working of an umbrella Image Courtesy: Internet

Fig 3.1.1.5 Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.6 EXAMPLES Deployable structures are suitable in response to the following needs:

can not be transported in full open size and needs to be erected in a very quick way. Examples: - Portable radars and antennas -Portable hangars -Portable bridges -Protection and camouflage of military equipment The US Army has developed two new bridges. One uses foldable aluminum graphite-epoxy honeycomb panels that fold over a trailer for transportation and can be unfolded in few a minutes by means of hydraulic jacks, the second one, using scissor-hinges and triangular frames, is deployed by pulling it with a cable.

A) A situation in which there is a need to create enclosed or protected space for a short period of time and then move that space to another location for erection or storage. Examples: -Traveling expositions 1 -Fairs -Provisional shelters -Movable Hospitals B) Difficult access places, and/or lack of labor. Examples: -Remote retransmissions units -Antenna masts -Meteorological or research stations -Military installations - Emergencies in distant localities, requiring Shelters, Bridges, Hospitals, etc.

D) Need to enclose space due to variable weather conditions. Examples: - Stadium covers, Cover-plazas.

C) Special applications equipment and shelters for special equipment which

(Chapter 3)

Fig 3.1.1.6 Movable hospitals; Military installations Image Courtesy: Internet

Fig 3.1.1.6 Portable hangars; Stadium covers Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.7 METHODS OF DEPLOYABILITY

There are many mechanisms which fall into the category of deployable structures, but we can group them into two general categories: A) Struts Structures : scissor-hinged, tensile, and sliding mechanisms, etc. B) Surface Structures: folded ,inflatable ,telescopic ,etc. The general characteristic of group A is that these structures are made out of struts which commonly work as compression, tension or bending components connected by joints or hinges. This first category includes the scissor-hinged, or lazy tong mechanism, and the sliding, or umbrella mechanism. This work will emphasize these mechanisms.

the deployed state, which is a three-dimensional body. 3.1.7.2 Sliding Or Umbrella Mechanism This method consists of deploying the structure around a rectilinear support or guide, by sliding a cylindric or hollow joint over it, the more common example is the umbrella. 3.1.7.3 Hinged-Collapsible-Strut Mechanism This is another method of 3 deployability which consists of a set of struts hinged at the ends, that allows the structure to be folded. After reaching the final open configuration the hinged joints are locked and the structure behaves as a single continuous piece. In Group B stresses are carried by surfaces. In some, cases a continuous surface carries only tension forces like, in pressurized or inflatable construction; other structures are made out of small surfaces or planes joined together by some usually flexible means of forming a continuous structure.

3.1.7.1 The Scissor-Hinged Mechanism The basic element of this system is the deformable truss shown in which is a set of struts ( one dimensional rectilinear members) connected by nodes ( universal joints) , and scissor-hinges ( a rotational degree of freedom about the normal plane defined by two connecting struts ). This assembly has the characteristic that by rotation of the struts with respect to one another, the assembly encompasses two forms; the first form is the compact state having theoretically one dimension, and the second form is

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.8 COMPONENTS AND REQUIREMENTS OF DEPLOYABLE STRUCTURES

3.1.8.1 Joints

the material.

The successful behaviour, duration, and reliability of a deployable structure will depend on a great way in its joints. The joints are points at which forces converge, and their ability to resist and transmit those forces will determine to an important degree the soundness ovf the structure the joint should meet the following criteria:

5. Friction between the moving pieces should be minimized to avoid excessive wearing and to facilitate the erection and dismantling processes. 6. As we are dealing with moving connections (usually pin connections), it is important to take into account, when designing and choosing the material, that the transference of forces between bodies which are not bonded together can occur only by the pressure exerted by one body against another; the values of compressive or tensile stresses increase at the joint. The flow of compressive forces are curving in the vicinity of the joint resulting in the need for an internal pulling action towards the center of the element; such an action always causes traversal tension to develop within the material. As a result, the element may crack and split longitudinally, if measurements are not taken. Thus, it is very important to have tension resisting materials around the connection.

1. Should transmit the forces evenly throughout the components which arrive at that point. 2. It should firmly hold all the struts which meet at that point. 3. It should give every strut enough freedom to go from the closed stage to the open one, but avoid holding the struts too loosely. 4. In the cases were re usability is required, the joint has to be designed to stand the stresses created during the erection process, minimizing fatigue in

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.8.2 Opening And Closing Mechanisms

ment process running horizontally over the erecting surface, for those structures to be erected over surfaces or terrains it is convenient to mount them over wheels in order to reduce friction with the surface, thus reducing the force needed for the erection.

Another fundamental aspect to consider when designing a deployable structure is the open-closing mechanism. As size and weight increase opening and closing a deployable structure become a more and more problematic factor in the effective good functioning of the concept. The structures have to be provided with a mechanism to accomplish the 5 erection-dismantling process,these mechanisms can go from manually driven ones to fully automatic and even remote-controlled ones. But every system will depend on each structure, and in particular, on its size and weight, frequency and conditions of deployment, environmental factors, possibility of energy sources, etc. Opening and closing mechanisms can be hydraulic systems, motor or manually-driven screws, cables and pulley mechanisms, spring-driven mechanisms, etc. But any mechanism use should provided a even movement of all the parts at a controlled rate. Since the structures usually start the deploy-

3.1.8.3 Covers There are some situations which require a protected or enclosed space, and the deployable structure has to be designed with an enclosure or cover system. There are many different solutions: The enclosure system can be attached to the structure or free-standing; the enclosure can be added after the structure is erected, or it can be permanent part of the structure. It can also operate as a structural member, stabilizing member and/or locking member of the open configuration. Enclosures can be made out of light and flexible materials, which can act as tension carries, Such as teflon coated nylon or fiberglass fabrics, etc. Or they can be made out of rigid materials like metals or plastics.

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.1.9 Structural Requirements Clearly an essential structural requirement for all the forms with which we shall be concerned is that they shall stand and not collapse. They should carry their own weight and the live loads to which they will be subjected (wind, snow, other components attached to the structure, etc.), and under normal circumstances they should have adequate margins and stiffness in all structural elements and in their interconnections. The basic element of the scissor-hinged mechanism, as we saw before, is the deformable truss shown in. Due to its one degree of freedom this truss is unstable, and has no structural properties. Although if height “h” is fixed ,the truss will be able to carry loads acting on its plan. As it is not triangulated, its struts are working in flexion . By adding compression and tension members to the system, bending stresses can be reduced and the truss will become a triangulated one, where stresses are mainly transmitted by tension or compression. By using more suitable geometrical forms, and by locking the joints, the structural characteristic of the system can be improved.

Fig.3.1.1.9 Deformable truss

Image Courtesy: Internet

Fig.3.1.1.9 Deformable truss Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

3.2.0 Umbrellas At Madina Mosque- Saudi Arabia To such an exceptional situation, there had to be an exceptional solution and German designers, SL-Rasch, in collaboration with SEFAR Architecture came up with an ingenious way that improved the mosque’s natural micro-climate without destroying its architectural character. In November 2010, they completed the plantation of a forest of giant foldable sunshades, each being almost 20 meters tall. They were the largest umbrellas built up to that time and are really something unseen. The members of the Medina Haram Piazza project, as it was named, include general contractor Saudi Binladin Group (SBG), customer Saudi Arabian Ministry of Finance, architect SL-Rasch, German umbrella manufacturer Liebherr and Japanese manufacturer Taiyo Kogyo.

Fig 3.1.2.0 Umbrellas closed at Al Madina mosque

Image Courtesy: Internet

Fig 3.1.2.0 Opened umbrellas Image Courtesy: Internet

(Chapter 3)

3. DEPLOYABLE STRUCTURES

The first retractable dome structure is said to be the circularly sliding retractable roof of the Pittsburgh Civic Arena opened in 1961 and closed in 2010. The 127 m-span roof consists of eight 300 ton sections, six of which are able to rotate by five motors per panel. All panels are fixed on the top to a gigantic, 80 m tall steel truss cantilever. The roof could be opened in about two minutes. The structural form of the civic arena is initially optimal as bending moments are minimal due to geometry. Unfortunately for retractability this optimal shape had to be sliced in parts, thus the cost was the huge cantilever that supports the panels, and the bigger structural height. A similar geometry was achieved by a more recent construction that did not apply an external structure to hold the panels.

The Fukuoka stadium in Japan opened in 1993 spans 222 m. The three parts of the roof ― two of which are rotatable ― are independent. Highly Flexible Deployable Structures Architectural Background 18 frameworks, with remarkable bending moments. Though careful shape correction was performed for the geometry of individual parts to avoid singularities in reaction forces at the inclination lines, the structural height is still gigantic. Each panel is four meters thick, and the total roof weighs 12 000 tons. The sliding rotation of the two panels is enabled by 24 bogie wheel assemblies . It takes approximately 20 minutes to open the roof.

(Chapter 3)

Fig 3.1.2.1 After completion Image Courtesy: Internet

Fig 3.1.2.1 Sectional elevation Image Courtesy: Internet

(Chapter 3)

Fig 3.1.2.1 Top View Image Courtesy: Internet

Fig 3.1.2.1 Construction Model Image Courtesy: Internet

3. DEPLOYABLE STRUCTURES

3.2 INFERENCES TO BE TAKEN (PROS OF THE TECHNIQUES)

+ HOW THE DEPLOYABLE PRINCIPLE WORKS STABLE GEOMETRIES

+ JOINERIES THAT ENABLE DEPLOYABLITY

3. DEPLOYABLE STRUCTURES

3.3 SHORTCOMINGS TO BE INCOMINGS (CONS OF THE TECHNIQUES)

+ Deployablity takes place from the depth axis (z axis) which offers lesser opportunity for Deployablity

+ Cant be reused into other forms – only predefined forms are possible + A prefabricated shape cannot be modified or not dynamic when it comes to structure

+ REDUCES THE STRUCTURAL STABILITY IN BIGGER STRUCTURES

3.4 BIBLIOGRAPHY & CITATION

• Hoberman C. (1990): Reversibly expandable doubly-curved truss structure • • Hoberman C. (1991): Radial expansion/retraction truss structures • • Hoberman C. (2004): Retractable structures comprised of interlinked panels, • • Hoberman C, Davis M. (2009): Panel assemblies for variable shading and ventilation • • Fuller B. R. (1962): Tensile integrity structures • • https://www.researchgate.net/publication/235329328_ Deployable_Structures • • http://daveaton.com/Deployable-Structures • • https://www.google.com/search?q=deployable+structures&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiQ6uHUwfPcAhWIvI8KHWdPBDoQ_AUICigB&biw=1366&bih=662#imgrc=xyFUXQVNQMbX9M:

AUXETIC MATERIALS

(Chapter 4)

4. AUXETIC MATERIALS

4.1.1 WHAT ARE AUXETIC MATERIALS??

a body submitted to a tensile load [1]. It provides a universal way to compare the structural performance of real homogeneous and non-homogeneous materials. This elastic constant was implicitly assumed to be positive [3], as common sense dictated that no isotropic material in nature had a value of Poisson’s ratio less than zero [4]. However, there are materials that present an inverse behavior. These materials expand their transverse dimensionwhen submitted to an axial tensile strength and decrease it when compressed [5]. This way, they have a negative Poisson’s ratio. The materials that reveal this behavior have been called anti-rubber [and dilational materials.

4.1.1 What Are Auxetic Materials?? An auxetic material becomes thicker in one or more width-wise directions when it is stretched along its length. Conversely, it becomes thinner when compressed lengthwise. This contrasts with ‘normal’ materials which tend to thin when stretched – think of stretching an elastic band, for example – or thicken when compressed. The defining property of an auxetic material is, then, that it possesses one or more negative Poisson’s ratios. The Poisson’s ratio of a material is a dimensionless constant that depends on the direction of an applied load, and describes the ratio of negative transverse strain to the longitudinal strain of

(Chapter 4)

Fig 4.1.1.1 Tension At Ends Image Courtesy: Internet

(Chapter 4)

Fig 4.1.1.1 Image Courtesy: Internet

Fig 4.1.1.1 Sports Shoe Image Courtesy: Internet

(Chapter 4)

4. AUXETIC MATERIALS

4.1.2 Poisson’s Ratio Poisson’s Ratio Poisson’s Ratio, defined by Siméon Denis Poisson a French Mathematician in 1829, describes the behaviour of materials when they are deformed. When a tensile load is applied to a cube of material it will tend to extend in the direction parallel to the load (axial direction) and contract in the two directions transverse or perpendicular to the load (see below). When a compressive load is applied to a cube of material it will tend to contract in the direction parallel to the load (axial direction) and expand in the two directions transverse or perpendicular to the load (see below). The ratio of the shape change in the transverse and axial directions is known as Poisson’s Ratio and for most materials this value is between 0.0 and 0.5. The Poisson Effect is caused by the stretching of bonds in the material lattice in order to accommodate the applied stress. When the bonds elongate along the stress direction they shorten in the other directions.

Fig.4.1.1.2

Image Courtesy: Internet

Fig.4.1.1.2 Image Courtesy: Internet

(Chapter 4)

4. AUXETIC MATERIALS

4.1.3 Strcuture And The Materials

The range of materials includes natural and man-made. It covers from large-scale structures right down to the nanoscale, and it spans the classic categories of polymers, composites, metals and ceramics. So in terms of natural materials, we can look at naturally-occurring crystalline silicates; α-cristobalite is known to be auxetic. There are also related materials such as zeolites and a number of those are known now to be auxetic. On the bio-materials side, a number of skin tissues and soft tissues have reported to be auxetic, and there are hints that some forms of bone are auxetic. In addition, early stage embryonic tissue has been reported to be auxetic. It looks as though in nature we’re starting to scratch the surface and discover more materials that are auxetic.

Fig.4.1.1.3

Image Courtesy: Internet

Fig.4.1.1.3 Image Courtesy: Internet

(Chapter 4)

4. AUXETIC MATERIALS

4.1.4 How They Work?

The approach to the manufacturing of auxetic materials, considering not only the base material, but the internal structure and deformation mechanism allowed the expansion of the scale in which this behavior occurs. The control of the material structure made possible to tailor the material properties . This way, it became possible to elaborate auxetic macrostructures. Using these structural models, many theories have been developed to explain the behavior of these materials.

Fig.4.1.1.4 Deformation

Image Courtesy: Internet

Fig.4.1.1.4 Deformation Image Courtesy: Internet

(Chapter 4)

Fig 4.1.1.4 Different auxetic materials Image Courtesy: Internet

Fig 4.1.1.4 Application Image Courtesy: Internet

(Chapter 4)

4. AUXETIC MATERIALS

4.1.5 WHAT ARE THEY MADE OF?

Auxetic materials can essentially be made in two different ways. In the topdown approach everyday polymers are manipulated to give the desired structure and properties. In the bottom-up approach the material is built up from scratch, molecule by molecule, allowing them to be engineered on a very small scale. In both cases the objective is to create a repeating pattern of building blocks or cells which contain the necessary hinge-like features. The first synthesised polymer-based auxetic material was created in 1987 using the top-down approach. Rod Lakes of the University of Iowa started out with an ordinary polyurethane foam which consisted of a honeycomb of hexagonal cells. When he applied heat and pressure to this cell structure it caused the side walls of the cells to buckle resulting in the auxetic hexagon shown earlier. The first synthesised polymer-based auxetic material was created in 1987 using

the top-down approach. Rod Lakes of the University of Iowa started out with an ordinary polyurethane foam which consisted of a honeycomb of hexagonal cells. When he applied heat and pressure to this cell structure it caused the side walls of the cells to buckle resulting in the auxetic hexagon shown earlier. The following year Ken Evans from the University of Exeter created another auxetic structure in PTFE. This structure consisted of oval nodules connected at their tips by long strands or fibrils. Under normal circumstances the nodules overlap with the fibrils wound round them. When the material is stretched in the direction of the fibrils they pull taut and this causes the nodules to rotate and snap into a rigid grid-like arrangement. Liquid crystal materials can be engineering to have auxetic properties by building up a structure consisting of alternating rigid and flexible units molecule by molecule.

(Chapter 4)

Fig 4.1.1.5 Synthesized polymer pattern Image Courtesy: Internet

Fig 4.1.1.4 Auxetic hexagon Image Courtesy: Internet

(Chapter 4)

4. AUXETIC MATERIALS

4.1.6 USES

There have been many suggested uses for auxetic materials, but most of these have yet to come to fruition commercially. These materials can be difficult to process on a large scale, making industrial manufacture difficult. Some potential areas for use are described below.

gery. A piece of auxetic foam, possibly made from PTFE would be inserted into the blood vessel and then tension applied to this to cause lateral expansion and open out the vessel. Auxetics could also be used in surgical implants and prosthesis and for the anchors used to hold sutures, muscles and ligaments in place.

Biomedical applications Many of the materials that are currently used in medical applications can be processed to exhibit auxetic properties. Schematic diagram of nodule and fibril auxetic material (top) showing idealised structure (bottom). Schematic diagram showing how lateral expansion occurs under tension in a nodule and fibril auxetic material. It has been suggested that auxetic materials could be used to dilate blood vessels during heart sur-

Filters Traditional filters can be incredibly difficult to clean, leading to them being thrown away prematurely. A filter made from an auxetic foam could be cleaned much more easily by simply applying a tensile force to open up the pores. Once clean the force can be removed and the filter refitted.

(Chapter 4)

4. AUXETIC MATERIALS

4.1.6 USES

Auxetic fibres

Auxetic fibre reinforced composites

This is one area which does show real potential for exploitation. The key here is the development of a continuous process for developing auxetic materials in the form of fibres. The resulting fibres could be used in monofilament or multifilament form and could be knitted or woven together to make cloth. It has been suggested that these fabrics could be used in crash helmets, body armour and sports clothing where their dent and fracture resistance would be exploited. It may also be possible to spin an auxetic fibre with another functional fibre and / or a more traditional textile to produce yarn with a range of useful properties for technical applications.

There is no reason why woven fabric made from auxetic fibres cannot be used to reinforce a polymer in the same way that carbon or Kevlar cloth is used. However, the addition of an auxetic material could dramatically improve the fracture performance of the resulting composite. If the Poisson’s ratio of the reinforcing fibres and matrix material are carefully matched the possibility of delamination at the matrix-fibre interface is reduced, thus making it more difficult for a crack to propagate and failure to occur. As the matrix contracts laterally when placed in tension, the auxetic fibre expands, allowing the interface to be maintained. Auxetic materials could also be added to metallic materials such as steels to create composites with improved resistance to cracking under shear strain (twisting).

4.2 BIBLIOGRAPHY & CITATION

(PDF) Auxetic materials — A review. Available from: https:// www.researchgate.net/publication/259865336_Auxetic_materials_-_A_review http://en.wikipedia.org/wiki/Meta_materials http://en.wikipedia.org/wiki/Auxetics http://www.silver.neep.wisc.edu/~lakes/Poisson.html http://research.dh.umu.se/dynamic/artiklar/shape/stretch.html http://www.wisegeek.com/what-are-auxetic-materials.htm http://www.azom.com/details.asp?ArticleID=167 http://www.azom.com/details.asp?ArticleID=168 http://data.bolton.ac.uk/auxnet//background/index.html http://en.wikipedia.org/wiki/Poisson’s_ratio

#5 AUXETIC PATTERNS

(Chapter 5)

5. AUXETIC PATTERNS

5.1.1 WHAT ARE AUXETIC PATTERNS?? Typically, the materials to which we are accustomed have positive Poisson’s ratio, that is, the act of stretching is expected to cause shrinking and the act of compressing results in bulging. However, this common knowledge has been challenged by auxetics, a class of materials which exhibit the unusual property of becoming wider when stretched and narrower when compressed (Evans, 1991). This results from having a negative Poisson’s ratio (v) - the ratio of the lateral contractile strain to the longitudinal tensile strain for a material undergoing tension in the longitudinal direction (Evans, 2000). This class of materials has a relatively recent history, even if they have been known among scientists for about a century.

Design (Evans et al, 1991). It comes from the Greek (auxetikos), literally translated in “which tends to increase” and has its root in the word, or auxesis, signifying “an increase”. Auxetics can be essentially considered as metamaterials which are artificially engineered to gain emerging properties and functionalities otherwise unattainable in natural materials. They rely on specific spatial arrangements rather than material composition, and for this reason they are organized in patterns with precise shape, geometry, size, orientation and arrangements. Performance and behaviour are direct consequence of the design of their inherent architecture. Expanding this concept, the research investigates the architecture of auxetic materials towards their implementation in architectural structures, taking advantage of their unique properties.

One of the earliest known publications on this topic is titled Foam Structure with a Negative Poisson’s Ratio (R.S. Lakes, 1987), but the term auxetic first appeared in the scientific article Molecular Network

(Chapter 5)

Fig 5.1.1.1 Polygonal auxetic patterns Image Courtesy: Internet

Fig 5.1.1.1 Ceiling design with auxetic pattern; Auxetic patterns in honeycomb Image Courtesy: Internet

(Chapter 5)

5. AUXETIC PATTERNS

5.1.2 MECHANISM AND APPLICATION

The deformation mechanisms of auxetics depend on their hinge-like structure, which flex outwards when stretched. Their spatial organization in particularly-shaped lowdensity patterns allows the hinge-like areas of the auxetic microstructures to flex. The study and the computational development of these patterns offer an interesting perspective for their future applications Auxetic structures exist in many different scales: from the microstructural and molecular to the mesoscopic and macroscopic scales (Evans, 2000). A large number of auxetic structures have been developed, such as foams, fibers, or composite materials, and many other examples can be found in nature as well. In this research the design and fabrication of macro-scale auxetics is explored for architectural applications. Metamaterial computation and fabrication of auxetic patterns for architecture Abstract The paper investigates the potential of auxetics in architectural applications by means of computational design and additive manufacturing. This class of metamaterials expresses interesting behaviour related to the unusual characteristics of a negative Poisson’s ratio. Different patterns have been studied through a design workflow based on parametric software and the use of Particle Spring systems to support the form-finding process of bending-active auxetic structures.

An advanced understanding of their bending capacity is explored with the use of variable infill patterns informed by structural analysis. Furthermore, principles for the design and fabrication of auxetic gridshells are discussed, Nowadays auxetic structures have found several applications in the biomedical industry for the design of stents and prostheses in the creation of filters for chemical processes auxetic foams mostly in the generation of auxetic fibers for crash helmets/body armours as well as in the production of panels with high energy/vibration absorption coefficients Interestingly, transforming a wellknown material into its auxetic configuration often offers improved mechanical features. Nevertheless, due to their low density and complex structure, auxetics are inefficiently manufactured with traditional processes, which involve complex multistep procedures with heat-compression molding. For this reason, current applications are generally restrained to high-tech fields. In medical and chemical sectors auxetics are mainly used for their capacity to variegate their porosity, whereas in medical, chemical engineering and in sport applications they are mainly exploited for their specific mechanical properties.

(Chapter 5)

Fig 5.1.1.2 Hinge like structures Image Courtesy: Internet

Fig 5.1.1.1 Metamaterial computation Image Courtesy: Internet

(Chapter 5)

5. AUXETIC PATTERNS

5.1.3 Properties Of Auxetic Patterns

the form in this case might be directly driven and informed by the application of an out-ofplane bending moment and the physical behaviour of the auxetic material to which it responds. Synclastic surfaces in architecture are difficult to be achieved using traditional construction methods. Moreover, lightweight synclastic surfaces are currently limited to the use of air-supported structures. Considering the necessity to preview the dynamic behaviour of bending-active structures, the research implements a computational design methodology to simulate the form-finding of synclastic auxetic gridshells. Additive Manufacturing (AM) is used in different phases to prototype test models as well as to empirically investigate different material configurations, to tune and enhance the response of an auxetic pattern. Sub-goals of the research are: (i) implementing a convenient computational methodology to design and simulate auxetic bending behaviour in a controlled way; (ii) determining optimal auxetic patterns for their structural implementation in architecture; (iii) understanding the main parameters which affect the configuration of auxetic structures and their spatial articulation; (iiii) proposing custom infill patterns to modulate bending performance in auxetic components.

The interest in auxetic structures experienced a remarkable spike during the last decades . A set of five fundamental characteristics of auxetic structures, actively explored and applied in various fields of research, can be outlined . Synclastic curvature: the capacity of auxetics to form dome-like, synclastic surfaces when bent (characterized by a positive Gaussian curvature (K) at every point of the surface. Compressive strength and shear stiffness: the capacity of auxetic structures to resist forces both in compression and shear. Indentation resistance: the capacity of auxetic structures, mostly of foams, to shift more mass under the point of compression. Variable permeability: the capacity of auxetic structures to compress and expand, causing a variation in their porosity. Energy absorption and dissipation: the capacity of auxetic structures to absorb and dissipate the energy received from another body. 5.1.4 Objectives Of Auxetic Patterns The objective of this research is to understand how auxetics can perform in architecture as bending-active structures towards the generation of lightweight synclastic gridshells. The generation of

(Chapter 5)

5. AUXETIC PATTERNS

5.2.1 METHODOLOGICAL PROCEDURES 5.2.1 Parametric Design Of Auxetic Patterns

a standard PLA filament allowing for an intuitive understanding of the bending properties of the different patterns.

A variety of auxetic patterns exist and each of them is characterized by a set of parameters which influence their behavior. In literature, auxetic structures are classified into several macro groups: re-entrant structures, chiral structures, rotating rigid units, angle-ply laminates, molecular auxetic structures, polymer models, origami-like structures and others (Mir, 2014). Scientific literature already tackled the topic of 3D origami-like auxetics and their potential applications in lightweight architectural structures (Schenk, 2010). Our research, on the other hand, focuses on two dimensional auxetics whose architectural potentialities have not been yet fully explored. In contrast to origami-like auxetics, these types of auxetic patterns achieve synclastic curvature through the active-bending of structural elements rather than through the rotation of faces along edges. In the initial phase of research, different basic patterns have been explored and developed parametrically with the use of Grasshopper for Rhinoceros as lattice samples divided into a defined grid of 20 by 20 cells. After the digital models were designed, prototypes were materialized with a double extruder FDM printer using

The comparative tests highlighted the 2D re-entrant honeycombs as a compelling design option for further research and development given the enhanced synclastic curvature they are able to generate, their simple geometric configuration (Malgorzata, 2009) and ease of customization. This pattern is composed of indented elastic rods which are called Chevron Rods and inelastic rods which are called Parallel Rods. This bi-directional pattern reaches a different configuration according to the axial direction of bending forces (Fig. 6). Research and experiments on the creation of isotropic auxetic lattices can be found in literature (Lorato, 2010). In our research differential responses according to the bending direction is considered as an exploitable feature to generate less predictable architectural results. Empirical tests proved that forces applied on the indented sides produced synclastic curvatures in opposition with forces applied in the parallel direction.

(Chapter 5)

Fig 5.1.1.3 Synclastic structure Image Courtesy: Internet

Fig 5.1.1.4 Comparative analysis on 3d printer auxetic patterns. Horizontal rows show: A) relaxed state - top view, B) compressed state - top view, C) compressed state - lateral view. All the samples perform auxetic behaviour in the in-plane stretching, while only the Re-entrant honeycombs and mesostructured patterns show auxetic response also in the out-of-plane bending. Image Courtesy: Internet

(Chapter 5)

Fig 5.1.2.1 Schematization of rod typologies. The re-entranthoneycombs pattern is defined by two types of rods: the indented elastic rods called the Chevron rods and the inelastic rods which are known as the parallel rods. Image Courtesy: Internet

Fig 5.1.2.1 Bending analysis on a 3d printed model showing two different curvatures obtained by changing the axis of action.

Image Courtesy: Internet

(Chapter 5)

5. AUXETIC PATTERNS

5.2.2 Auxetic Behaviour In 2 Dimensional Patterns The simulation of the bending behaviour of an auxetic pattern is fundamental in order to develop its architectural application and to preview configurations under certain loading conditions. Considering the advantage of working within a common modelling environment, simulations were performed with the Particle Springs Engine (PS) Kangaroo for Grasshopper. This workflow guarantees the easy and effective testing of different pattern solutions by defining anchor points and forces applied to the structure, without the need of exporting geometries, a factor of great importance in evaluating many different patterns. An initial test was performed on a default 2D reentrant honeycomb structure with no extrusion on the z axis in order to understand the auxetic expansion/ compression in relation to the variation of the parameter t, which defines the angles characterizing the hexagons Through the variation of this parameter within a range from 0 to 1, it is possible to generate different kinds of hexagons: values from 0 to 0.5 define convex hexagons , while values ranging from >0.5 to 1 produce re-entrant hexagons The simulation shows how the variation of this parameter influences the Poisson ra-

tio and consequently the auxetic properties of the structure shows the results of this test, with presenting the layout of the structure in a relaxed condition, showing the expanding behaviour of the structure in an auxetic configuration whereas reveals how the structure is stretched when turned into its non-auxetic version and the overall area decreases. 5.2.3 Pattern Comparison Through this computational approach, a set of 3D-printed samples have been designed and tested showing typical inplane auxetic behaviour. However, in contrast to what was expected, only a few have produced synclastic curvatures when an out-of-plane bending moment was applied. Among the tested typologies, only the re-entrant honeycombs and mesostructured materials demonstrated an actual synclastic curvature. A comparative test highlights the 2D re-entrant honeycombs as a compelling design option for further research and development given the enhanced synclastic curvature they are able to generate, their simple geometric configuration (Malgorzata, 2009) and ease of customization towards the design of form-active gridshells.

(Chapter 5)

Fig 5.1.2.3. From Top: Planar Structure, Halfway Bent Structure, Bent Structure.

Image Courtesy: Internet

5. AUXETIC MATERIALS

5.3 INFERENCES TO BE TAKEN (PROS OF THE TECHNIQUES) + HOW THE AUXETIC WORKS AND EXPANDS AND WORKS

+ AUXETIC PHYSICS

+ MATERIALS REFERENCES

SHORTCOMINGS TO BE INCOMINGS (CONS OF THE TECHNIQUES)

+ RESTRICTION AT PRODUCT DEIFGN LEVEL BASED ON MATERIAL PROPERTIES + HOW TO CONVERT MATERIALS REACTION IN AUXETIC MATERIALS TO CONSTRUCTION –IN LARGE SCALE STEEL

89°

(Chapter 5)

14° 133°

19°

121°

119°

97°

161

38°

128°

78°

152°

142°

68°

3°

173°

172°

0°

102°

78° 162°

0°

138° 90 °

120°

0°

Fig 5.1.2.3. Available pattern and their study .Image Courtesy: Internet

(Chapter 5)

8°

0°

2°

178°

2°

Fig 5.1.2.3. Available pattern and their study .Image Courtesy: Internet vv

100

108

120°

132°

109°

30°

10°

124°

210°

101

(Chapter 5)

100°

0°

75°

158°

120°

9°

173°

127°

0°

2°

117

170°

122° 64°

100°

0° 15

68°

165°

38°

2°

120°

0°

2°

122°

Fig 5.1.2.3. Available pattern and their study .Image Courtesy: Internet vv

102

0°

18 127°

8°

103

148°

Fig 5.1.2.5. Available pattern and their study .Image Courtesy: Internet vv

104

127°

105

84°

1 14

67°

7°

119°

2°

74°

175°

84°

Fig 5.1.2.6. Available pattern and their study .Image Courtesy: Internet vv

106

119°

175°

67°

0 12

166°

67°

2 14

174°

0° 12 0°

1°

157°

0° 12

73°

6°

36°

37°

7°

0°

12 168°

156°

68°

6°

173°

67°

19°

107

91°

56°

9°

213°

8°

121°

90 °

0°

9°

122°

92° 2°

18 0°

148°

92°

Fig 5.1.2.7. Available pattern and their study .Image Courtesy: Internet

108

9°

0°

12 °

152°

88°

80° 129°

12 0°

55°

179°

55°

109

5.4 BIBLIOGRAPHY & CITATION

Cremers, J. M. (2011). Energy Saving Design Of Membrane Building Envelopes. Structural Membranes 2011, 147-157. Evans, K.E., Nkansah, M. A., Hutchinson, I.J., Rogers, S.C. (1991). Molecular Network Design. Nature, 353, 124. Evans, K.E., Alderson, A. (2000). Auxetic Materials: Functional Materials and Structures from Lateral Thinking!. Advanced Materials, 12, No.9, 617-628. (PDF) Auxetic materials — A review. Available from: https://www.researchgate. net/publication/259865336_Auxetic_materials_-_A_review http://en.wikipedia.org/wiki/Meta_materials http://en.wikipedia.org/wiki/Auxetics http://www.silver.neep.wisc.edu/~lakes/Poisson.html http://research.dh.umu.se/dynamic/artiklar/shape/stretch.html http://www.wisegeek.com/what-are-auxetic-materials.htm http://www.azom.com/details.asp?ArticleID=167 http://www.azom.com/details.asp?ArticleID=168 http://data.bolton.ac.uk/auxnet//background/index.html http://en.wikipedia.org/wiki/Poisson’s_ratio

110

#6 AUXETIC +RECIPROCAL + DEPLOYABLE

DEPLOYABLE RECIPROCAL STRUCTURES THROUGH AUXETIC BEHAVIOR (AUXETICS IN CONSTRUCTION)

111

112

1. The Hypothesis discusses about the possibility of taking the characteristics of the Auxetic Behavior - mainly the Expansion and Bending option to Improve Volumetrically on a Shell structure . 2. The possibility to use this principles to make a deployable structure that has the self supportive Structural ability of a Reciprocal frame structure 3. The analysis has been broken down on various steps from analysis of the Auxetic physics to a mechanical joinery principal and studying and implementing the same for a new technique in constructing - with the Proof of concept by building a physical prototype that suggests the possibility in more than a hypothesis level .

113

6.1 AUXETIC PHYSICS

Fig 6.1.1. Auxetic physics

Image Courtesy: Generated vv

114

Fig 6.1.2. Auxetic physics

Image Courtesy: Generated vv

115

6.2 AUXETIC PHYSICS INTO CONSTRUCTION JOINERY

Fig 6.1.3. Auxetic physics into mechanical constrcution joineries Image Courtesy: Generated

116

Fig 6.1.4. Auxetic physics into mechanical constrcution joineries Image Courtesy: Generated

117

6.2 AUXETIC PHYSICS INTO CONSTRUCTION JOINERY

Fig 6.1.6. Joinery Exploded View Image Courtesy: Generated

118

6.2 AUXETIC PHYSICS INTO CONSTRUCTION JOINERY

Fig 6.1.7. Joinery Alternative Image Courtesy: Generated

119

6.2 AUXETIC PHYSICS INTO CONSTRUCTION JOINERY

Fig 6.1.7. Joinery Alternative Image Courtesy: Generated vv

120

Fig 6.1.8. Joinery Base rail

Image Courtesy: Generated vv

121

89°

6. 3. 1 AUXETIC PATTERNS IN CONSTRUCTION

14°

133°

19°

121°

119°

97°

161

38°

128°

78°

152°

142°

68°

14 3° 173°

172°

0° 12 102°

78° 162°

0°

138° 90

120°

Fig 6.3.1 Auxetics in Constrcution Image Courtesy: Generated

122

120°

0°

120°

123

6.3 .2 AUXETIC PATTERNS IN CONSTRUCTION

8°

0°

2°

178°

2°

Fig 6.3.2 Auxetics in Constrcution Image Courtesy: Generated

124

8°

120°

132°

109°

30°

10°

124°

210°

125

6.3.3 AUXETIC PATTERNS IN CONSTRUCTION

100°

0°

75°

158°

120°

9°

173°

127°

0°

2°

117

170°

122°

64°

100°

0° 15

68°

165°

38°

2°

120°

0°

2°

10 122°

Fig 6.3.3 Auxetics in Constrcution Image Courtesy: Generated

126

0°

127°

8°

127

127°

148°

Fig 6.3.4 Auxetics in Constrcution Image Courtesy: Generated

128

6.3.4 AUXETIC PATTERNS IN CONSTRUCTION

129

6.3.5 AUXETIC PATTERNS IN CONSTRUCTION

84°

0° 12

7°

175°

1°

119° 2°

74°

84°

Fig 6.3.5 Auxetics in Constrcution Image Courtesy: Generated

130

119° 175° 67°

0°

166°

67°

2 14

174°

68°

° 12 0

0°

6°

157°

1°

36°

37°

7°

73°

0°

168°

156°

67°

6°

173°

131

6.3.6 AUXETIC PATTERNS IN CONSTRUCTION

122° 12

0°

91°

0° 15 56°

9°

9° 11

213°

8°

121°

9°

92°

2°

18 0°

148° 92°

Fig 6.3.6 Auxetics in Constrcution Image Courtesy: Generated

132

9°

0°

152°

88°

80°

129°

179°

55° 14

55°

133

6.5 DEPLOYMENT TECHNIQUES

Fig 6.5. Deployment technique Image Courtesy: Generated

6.5.1 HYDRAULIC DEPLOYMENT- PUSH-UP The method under construction consists of a system of towers and jacks that push the structure from bottom to top, developed by engineers in order to reduce costs. These towers were raised vertically using forklifts until reaching the project quota desired. A key feature of the erection process is the introduction of a network of cables coupled with the lattice of the structure was introduced subjected to flexion, this to prevent the collapse of the grid during erection.

In the case of the gridshell Toledo the tower was one single tower, but in the case of the Multihalle Mannheim, the spacing between the towers it was described by a circumference of radius equal to 9 meters this to allow a bending of the elements, including between the “Spans” between tower and tower, for own lost, (just as it happens for the principle of the catenary arc studied in the preparatory models).

134

Fig 6.5. Deployment technique Image Courtesy: Generated

6.5.2 CRANE - PULL UP TECHNIQUE strength of membrane compression. To cope with the bending problem of the out of plane elements, the elements tend to have deformations closer to their maximum stress limit. The crane mounting method can apply a single force in the direction vertical and no horizontal direction is taken into account which comes into play once the elements flex. The lack of constraints in the horizontal direction, however, is advantageous as it allows the necessary distortion of the grid during the erection phase.The structures erected by crane, actually require much more time for avoid the formation of sudden peak loads that may goto damage the structure, for this reason it is only practical for training of small shells.

The first known example of gridshell, formed by bending a lattice elastic, is an experimental prototype of Frei Otto, built in Essen in 1962. This shell was erected by using a single mobile crane combined with wooden stilt houses used to support the pretimetro. We also see a similar situation for the erection of the pavilion German of the Montreal Expo, built by hoists and suspended cables hanging from an existing structure. This method of erection finds advantage in the speed of formation of the structure, however there are some disadvantages to report. The dislocation of cables that are anchored to the structure introduces at static level an equivalence of large point loads and concentration. The groups of cables that join the elements of the grid induce

135

Fig 6.5. Deployment technique Image Courtesy: Generated

6.5.3 LAYDOWN FROM TOP For the formation of the latest elastic Gridshell (Downland gridshell,Savil Garden Gridshell, Pavilion of Japan), built by the Buro Happold, they were erected by means of scaffolding supports under the entire coverage area coupled with a displacement strips from top to bottom incremental and controlled. During the construction of these three projects, a scaffolding system was used through innocent pipes. The particular aspects of this method lies precisely in the fundamental steps for the

elevation of the grid.v The structure is still flat, raised to a predetermined level and then flexed by moving the free elements downwards. In this case the scale physical models played a fundamental role in planning, forecasting and controlling the erection process.

136

Fig 6.5. Deployment technique Image Courtesy: Generated

6.5.4 INFLATION In some respects similar to the push-up methodology, it is the case of the inflate. This constructive principle consists in the homogenization of the forces that go to act on the erection structure, going to eliminate the specific concentrations discussed above. The pneumatic cushion that you go to place under the still flat grid works like a real formwork that supports the structure in all phases

of elevation until complete formation 19. This involves a transition fundamental for the construction of the grid shell, the structure and the supporting elements that bring it to the final shape develop in unison, without introducing additional stresses that go beyond the study structural development occurred during the design phase.

137

6.4 FABRICATION PROCESS

ON DESK

DESIGNING THE SHAPE

UNWRAP THE FORM

CONFORMAL MAPPING (POPULATE WITH GH DEFINITION)

MAPPING AND DISTRIBUTION WHILE EXPANDED AND THUS (WITH GH DEFINITION)

WHILE SHRUNKEN

SEND TO FABRICATION ON FACTORY

138

ON FACTORY SHEET FABRICATION AS PER THE CONFORMAL MAPPING

RETRACED FABRICATION LOGISTICS TO SITE

ON SITE FIND OUT MOVING POINTS IN THE STRUCTURE

ANCHORING IT TO THE STRUCTURE

LAYING OF INFLATION DEPLOYED LAYING OF SHEET (COMPRESSED) INFLATION DEPLOYMENT STABILITY ANCHORING ON POINTS

DEFLATION OF DEPLOYER

139

6.4 FABRICATION PROCESS

6.4.1 ON DESK PROCESS 6.4.1.3 KINETIC PROGRAMMING OF AUXETIC

Step 1 : Choosing the most efficient Auxetic pattern based on the patterning Principles : Patterns are choosed based on : • Non expansive by material itself – meaning that the material auxetic behavior should not be exhibited through expansion or contraction of the materials property • • The Auxetic behavior has to be exhibited by realignment of pattern itself • • The pattern has to realign through rotation majorly • • The patterns have to be reciprocal in nature – Self supportive and load distribution – in normal and realigned state

140

Stable Lattice Geomtry Equilateral traingle

Auxetic Expansion- how it works

Fig 6.4.Auxetic behavior in Construction Image Courtesy: Generated

141

Auxetic Expansion boundary - the pattern has an expansion ration as mentioned

Auxetic Expansion- how it works

Fig 6.4.Auxetic behavior in Construction Image Courtesy: Generated

142

6.4.1.3 KINETIC PROGRAMMING OF AUXETIC

Step 2 . The Auxetic material geometry is studied and Grasshopper program to define the expansion and movement of the Auxetic pattern in flat surface

Fig 6.4.Grashopper Programming Image Courtesy: Generated

143

Fig 6.4.Grashopper Programming Image Courtesy: Generated

144

6.4.1.3 KINETIC PROGRAMMING OF AUXETIC

Step 3 The pattern is created as array based on the principles to expand and contract on a single controller that controls the movement of the entire array

Fig 6.4.Grashopper Programming Image Courtesy: Generated

145

Step 4. Since the Patterning and Deformation of Auxetic is based on the displacement from the XY plane the contour study is directed to define the Auxetic pattern at that particular contour-

Important note: But in our examples and study we have considered tat to be fully Unanimous expansion since the programming was too complex to intergarte dynamic patterning based on the XY displacement

Fig 6.4.Grashopper Programming Image Courtesy: Generated

146

Fig 6.4.Grashopper Programming Image Courtesy: Generated

147

6.4.1.4 DESIGNING THE SHELL PROFILE

Design the shape of the Shell in isocurves

6.4.1.5 UNWRAP THE SURFACE

Unwrapping the Surface Fig 6.4.Surface Designing

Image Courtesy: Generated

148

Contour Analysis

Curvature Analysis Fig 6.4.Surface Analysis

Image Courtesy: Generated

149

6.4.1.6 CONFORMAL MAPPING (on curved planes)

(on Flat planes unwrapped)

Conformal mapping EXPANDED GEOMETRY on Curved developing surface Fig 6.4.Surface mapping

Image Courtesy: Generated

150

Conformal mapping of same EXPANDED GEOMETRY on Flat unrolled version of Surface

Conformal mapping of same CONTRACTED GEOMETRY on Flat unrolled version of Surface Fig 6.4.Surface mapping

Image Courtesy: Generated

151

6.4.1.7 PNEUMATIC SCAFOLDING

Using the Shape Simulations from the Curved shell structure the BASE SCAFOLDING PNEUMATIC structure is designed in various stages of deployment

Fig 6.4.Surface mapping

Image Courtesy: Generated

152

6.4.1.8 RAILING DESIGN

Fig 6.4 . Rialing Design

Image Courtesy: Generated

Using the Shape Simulations from the Curved shell structure-the Rail design on

site(based on The movement of the base anchor from the simulation)

After the development simulation of the shape and the number of tessellation joineries in contracted form . The details are sent to the factory to make the custom tailored tessellation that fits into this particular pattern. Informations primarily include: • • • • • •

Number of unit lattice Number of Connecting ratchet joineries Profile of the tessellation Number of base rail joinery The Rail design on site (based on The movement of the base anchor from the simulation)

153

6.4.2 IN FACTORY PROCESS After the development simulation of the shape and the number of tessellation joineries in contracted form . The details are sent to the factory to make the custom tailored tessellation that fits into this particular pattern.

• THE PREFABRICATION OF MODULES : The unit modulars are already prefabricated in modules that are based to take any shape and size in various thickness for different structural stability

• THE UNIT LATTICE JOINTS : The unit lattice and joineries which are already manufactured to be joined , are taken in specified numbers and joined as per te shape and numbers of the tessellation based for this specific design

• THE PNEUMATIC SCAFFOLDING : The Pneumatic developmental scaffolding is manufactured based on the simulation data required from the previous steps

• THE RAIL SYSTEM : based on the simulations the moving anchor points are deiced and rail system with base anchor is formulated.

154

6.4.3 DEPLOYMENT TECHNIQUE - INFLATION

Stage #1 - Inflation scaffolding below and auxetic sheet on Top

Fig 6.4 . Deployment Construction process Image Courtesy: Generated

155

Fig 6.4 . Deployment Construction process Image Courtesy: Generated

Stage #2 - Inflation deploying Starting

156

Fig 6.4 . Deployment Construction process Image Courtesy: Generated

Stage #3 - Inflation deploying Process

157

Fig 6.4 . Deployment Construction process Image Courtesy: Generated

Stage #4 -Completely Deployed and the rotational joineries are fixed

158

Fig 6.4 . Deployment Construction process Image Courtesy: Generated

Stage #5 -After Fixing joineries the Scaffolding is deflated

159

160

#7 the_PROTOTYPE PROOF OF CONCEPT (WORKING MODEL OF HYPOTHESIS)

161

7 .1 PROOF OF CONCEPT

7.1.1 Single unit lattice The Unit lattices are Laser cut on cardboard as a single Triangular lattice with holes on the edges - the Holes will be housing the Screws that allows rotation and the Edges will be scored to allow bending for the double curves Rotational Joinery (Holes for screw)

Cut Scoring done on Edges to allow rotational bending Stem of Unit lattice (common strength)

Fig 7.1 . Prototype Model

Image Courtesy: Generated

162

7.1.2 Multiple Joinery schedulepossibility #1

Fig 7.1 . Prototype Model

Image Courtesy: Generated

Rotational Joinery - Loose Screws That allows Rotational movements between two lattices

Fig 7.1 . Prototype Model

Image Courtesy: Generated

Multiple Joinery schedulepossiblity #2 vv

163

7. 1 .3 Multiple Joinery scheduleSingle Hexagonal Joinery

Fully Contracted

Expansion 1

Fully Expanded

Fig 7.1 . Prototype Model

Image Courtesy: Generated

164

7 .1 .4 Multiple Joinery schedulePossible Extension to Sheet

Fully Contracted

Fully Expanded Fig 7.1 . Prototype Model

Image Courtesy: Generated

165

7 . 1. 5 Multiple Joinery schedulePossible Extension to Sheet

Fig 7.1 . Prototype Model

Image Courtesy: Generated

Fully Contracted

166

7 . 1. 5 Multiple Joinery schedulePossible Extension to Sheet

Fig 7.1 . Prototype Model

Image Courtesy: Generated

167

7 . 1. 6 AUXETIC SHEETCURVE FLEXIBILITY

Fig 7.1 . Prototype Model - shell Flexibility Image Courtesy: Generated vv

168

7 . 1. 6 AUXETIC SHEETCURVE FLEXIBILITY

Fig 7.1 . Prototype Model - shell Flexibility Image Courtesy: Generated vv

169

7 . 1. 6 AUXETIC SHEETCURVE FLEXIBILITY

Fig 7.1 . Prototype Model - shell Flexibility Image Courtesy: Generated

170

7 . 1. 6 AUXETIC SHEETCURVE FLEXIBILITY

Fig 7.1 . Prototype Model - shell Flexibility Image Courtesy: Generated

171

7 . 1. 6 AUXETIC SHEETCURVE FLEXIBILITY

Fig 7.1 . Prototype Model - shell Flexibility Image Courtesy: Generated

172

7 . 1. 6 AUXETIC SHEETCURVE FLEXIBILITY

Fig 7.1 . Prototype Model - shell Flexibility Image Courtesy: Generated

173

7 .2.1 Mechanical Joinery- Junctions

The mechanical joinery at every junction has a Ratchet joinery that allows unidirectional Movement. This is to lock the fixed geometry when fully deployed so it acts as a reciprocal structure

Fig 7.2 . Prototype Model Mechanical Joinery The ball rotational joinery allows bendImage Courtesy: Generated ing at planar level so that the bending movement on the lattice frames does not apply completely - This promotes flexibility at joint level and avoids breaks and fragmentation becomes easier

174

Fig 7.2 . Prototype Model Mechanical Joinery Image Courtesy: Generated

175

7. 2. 2 - Mechanical Joinery- Base Junctions The ball rotational joinery on base plate allows bending at base level to enable flexibility at base level The base is placed on a movable rail track

Fig 7.2 . Prototype Model Mechanical Joinery Image Courtesy: Generated

176

Roational base

7. 2 .3 - Mechanical JoineryBase Junctions The base rotational rail is a movable rail system that also rotates in this base . Once fully deployed the moved and rotated the rails will be screwed permanently to the ground to make it fixed in the pavilion

Movable rail base

Rotational base

Fixed base - Screw holes to fix to ground

Fig 7.2 . Prototype Model Mechanical Joinery Image Courtesy: Generated

177

178

#8 the_PROJECT Auxetic Pavilion - Single prototype Pavilion

(AUXETICS IN CONSTRUCTION)

179

(Chapter 8)

8. THE PROJECT

8. 1. 1 FORM JUSTIFICATION The Motto is to create a Prototype that can exhibit the ability of this auxetic construction to be deployed into any double curved shape Taking into example a very basic yet complex double curve surface that will put the auxetic to test A PARABOLIC HYPERBOLA Justification for the shape is that a parabolic hyperbola is the most basic shape that can have varied contours in a single fragment .

180

Fig 8.1. Pavilion Design form Image Courtesy: Generated

181

8.1 THE BASE CURVE

Fig 8.1. Pavilion Design form - base Curve Image Courtesy: Generated

182

Fig 8.1. Pavilion Design form - base Curve Image Courtesy: Generated

183

8. 2. 1 DEPLOYMENT ON SITE Stage #1

Fig 8.2. Deployment On site

Image Courtesy: Generated

As per the Methods The Rails base are planted Then the Rails are placed on top of the base The pneumatic scaffolding (the balloon ) is laid on the base surface The Sheet fabricated from the factory is laid on the site The Base rail is attached to the base on site AUXETIC sheet

184

Stage #2

Fig 8.2. Deployment On site

Image Courtesy: Generated

The Scaffolding is slowly inflated The movable base rail Rotates and the Slider moves along the expanding base as per the Digital Projections This is closely monitored and assisted manually if needed with cranes and mechanical joints

185

Stage #3

Fig 8.2. Deployment On site

Image Courtesy: Generated

The inflation process keeps going on The Movements in base are still monitored

186

Stage #4

Fig 8.2. Deployment On site

Image Courtesy: Generated

The Inflation continues till the Auxetic Framework fully deploys Once the Full inflation is done the fixing joineries are fixed up . The base rail joinery is Riveted to the Ground so they dont move anymore

187

Stage #5

Fig 8.2. Deployment On site

Image Courtesy: Generated

After all the fixing in positions takes place, the pneumatic scaffolding is slowly deflated with caution Any deviations or collapsing at this stage shall be re inflated and taken care of to be held in position Th ratchet can be reprogrammed accordingly

188

Stage #6 -Covering up the Triangular lattice with Covering Plates

Fig 8.2. Deployment On site

Image Courtesy: Generated

Once the Framework Auxetic are ensured to be stable and self supporting fully , the Top cover plates are fixed . Alternatively the can be fixed before the deployment too which is much easier way of deployment but to reduce the load while deployment via Pneumatic scaffolding we do this attachment later. Also the plates might get in the way of fixing the ratchet position and repairs during deployment so its advisable to fix it in the End

189

Stage #7-Completed pavilion Design

Fig 8.2. Deployment On site

Image Courtesy: Generated

190

Once the Full attachments are done the base is nailed to the ground to avoid any further movement and the Rail system is Slid under and removed completely

Fig 8.2. Deployment On site

Image Courtesy: Generated

191

8. 3 .1 PLAN , ELEVATION

Rotational joinery for unit lattice

5.48

0.3

0.33

0.3

3 0.47

Auxetic frames

0.4

0.23

0.33

0.1

0.33

0.2 4

1.9

Base rail system Support dial

9.16

PLAN OF THE PAVILION Frame Work

Fig 8.3. Technical Drawings

Image Courtesy: Generated

9.13 Auxetic frames

Rotational joinery for unit lattice

2.7798

Covering Plate

192

Base rail system

5.48

0.3

3 0.33

0.33

0.3

Auxetic frames

Base rail system Support dial

9.16

PLAN OF THE PAVILION Covering Plate

9.13 Auxetic frames

Rotational joinery for unit lattice

2.78 0.22

Covering Plate

0.33

0.3

0.21

0.19

0.23

0.15

0.3

0.27

0.26

0.28

0.34

0.19

0.20

0.09

0.24

0.26

0.23

0.3

0.23

0.25

Base rail system

0.27 1.60

0.32 4.81

ELEVATION OF THE PAVILION Fig 8.3. Technical Drawings

Frame Work

Image Courtesy: Generated

193

Rotational joinery for unit lattice

5.48

0.3

0.33

0.33 0.3

Auxetic frames

Base rail system Support dial

9.16

PLAN OF THE PAVILION Covering Plate

Fig 8.3. Technical Drawings

Image Courtesy: Generated

9.13 Auxetic frames

Rotational joinery for unit lattice

2.78

vv 5

0.3

0.21

0.15

194

0.33 6

0.2

0.19

0.28 0.2

0.26

0.09

0.24

0.22

0.3

0.27

0.26

Covering Plate

5.48

0.3

3 0.33

0.33

0.3

3 0.47

Auxetic frames

0.4

0.23

0.33

0 0.1

0.33

0.2 8 4 1.9

Base rail system Support dial

9.16

PLAN OF THE PAVILION Frame Work

9.13 Auxetic frames

Rotational joinery for unit lattice

2.7798

Covering Plate

Base rail system

ELEVATION OF THE PAVILION With Covering Plate

Fig 8.3. Technical Drawings

Image Courtesy: Generated

195

Movable track system on a Base Rail Anchoring joints on movable joints once the shape is deployed fully Base Rail system that moves the frame according to the Auxetic pattern development

8. 3.2 TEHNICAL DRAWING

0.33

0.3

33 0.

0.30

Axis lines

Base rail system

0. Rotational joineries

0.33

TRIANGULAR UNIT LATTICES Demonstration of how 6 traiangular unit lattices work with joineries

Fig 8.3. Technical Drawings

Image Courtesy: Generated

196

X plane axis

Clamps that grip the frames to the rail

Joinery that allows rotation in the Y plane axis

ISOMETRIC JOINERIES OF THE PAVILION Rachet joinery for unit - lattice

Frame Unit Lattices

Joinery that allows rotation in the X plane axis

( for Unidirectional rotaion while development )

Base frame on which the skin fits on top

Skin / Plate cover Frame supporting base rail and cover plate

Axis lines

0.33

Rotational joineries Base rail for tessalation

Frame supporting base rail and cover plate Skin / Plate cover

Fig 8.3. Technical Drawings

Image Courtesy: Generated

197

ps that he frames rail

Ratchet Joinery

Joinery that allows rotation in the X plane axis Frame Unit Lattices

Joinery that allows rotation in the Y plane axis

Rachet joinery for unit - lattice ( for Unidirectional rotaion while development )

Joinery that allows rotation in the X plane axis

Top cover Plate details

Clamps that grip the frames to the rail

Skin / Plate cover

Joinery that allows rotation in the Y plane axis

Frame supporting base rail and cover plate

Rach ( for U while

Axis lines

Base frame on which the skin fits on top

Rotational joineries Fig 8.3. Technical Drawings

Base rail for tessalation

Image Courtesy: Generated

198

Triangular Unit Lattices

Base joinery to rails and frames

Movable track system on a Base Rail Anchoring joints on movable joints once the shape is deployed fully Base Rail system that moves the frame according to the Auxetic pattern development

BASE RAIL SYSTEM

Fig 8.3. Technical Drawings

Image Courtesy: Generated

0.33

0.3

199

8. 4 Fully Deployed Pavilion DeisgnConceptual Views

Fig 8.4. Pavilion Design

Image Courtesy: Generated

200

8. 4 Fully Deployed Pavilion DeisgnConceptual Views

Fig 8.4. Pavilion Design

Image Courtesy: Generated

201

8. 5 OTHER POSSIBLE ARCHITECTURAL IMPLICATIONS

Apart from the shell pavilions the same construction technique can be used to other Architectural Purposes also as follows

Fig 8.5 . Alternative Implications Image Courtesy: Generated

Domes on top of New / Existing Buildings The Same technique can be used as Dome roof tops with help of cranes and not inflation Paneling filling can be done after full deployment

202

Fig 8.5 . Alternative Implications Image Courtesy: Generated

Very effective technique as a Additional Architectural feature in Existing Buildings In places with space constraints to build scaffoldings and other heavy equipments , this technique can be bought in Folded and then deployed

203

Fig 8.5 . Alternative Implications Image Courtesy: Generated

Also can be used to develop flat roofing systems frame work On spreadable flat roofs this frame work without bending capacity can be used effectively because of its ability to self support up to certain spans

204

Fig 8.5 . Alternative Implications Image Courtesy: Generated

Double curved facade systems Frame system for Double curve Facades can be deployed using this construction technique but with different parameters as it is Horizontal deployment - Techniques and calculations will vary but the same hypothesis can be use

205

Fig 8.5 . Alternative Implications Image Courtesy: Generated

Double curved Interior walls : With the help of Bi-Metallic thermal reactive sheets that has laser cut auxetic pattern we can make double curve walls by giving the right heat reactions while deployment into desired shapes

206

Fig 8.5 . Alternative Implications Image Courtesy: Generated

Unmanned Construction System This deployment technique is a Very easy and effective Method for Unmanned Robotic Construction as it requires lesser space for transportation , can be robotically coordinated and deployed .

207

Fig 8.5 . Alternative Implications Image Courtesy: Generated

The Proposal was for an international competition to design a station in Mars . It uses this deployable unmanned shells structures in most of the places as it is easy to transport from earth (occupying lesser size in payload) and can be attached and deployed by robotic construction without human interference.

208

CONCLUSION So through out the Hypothesis we saw all the possibilities for using Auxetic materials in construction field. Trying to use a mixture of reciprocal and Auxetics we have made the deployablity of a shell structure apart from the customary deployment or reciprocal structure. With this new Hypothesis we can make any predesignated double curved shell structure without having to custom make like in the traditional methods. This gives the ability to develop a new system that is cost efficient , doesn’t spend much time on custom designing parts but to use common prototypes . The Prototypes or the physical models brings it closer to proof of concept for this hypothesis . With further development on this same contemplation this hypothesis has the potential to be made as a new construction technique and makes fabrication of double curve structures much easier and extensive usage too

209

BIBLIOGRAPHY & REFERENCES

DOUBLE CURVE STRUCTURES

(PDF) Structural Morphology Issues in.... Available from: https:// www.researchgate.net/publication/245526176_Structural_Morphology_Issues_in_Conceptual_Design_of_Double_Curved_Systems https://www.coroflot.com/dmprijatna/college https://www.researchgate.net/publication/315809235_Form-finding_of_shell_structures_generated_from_physical_models https://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/ AFEM.Ch31.d/AFEM.Ch35.pdf http://shells.princeton.edu/Grotz.html https://www.slideshare.net/SusmitaPaul12/shell-structure

210

RECIPROCAL STRUCTURES

Cavanagh, Ted. (2012). Innovative structures and the design/build model of teaching. presented design/build conference Berlin 2012. https:// www.academia.edu/2144320/Innovative_Structures_and_the_Design_ Build_Model_of_Teachng Parigi, Dario and Pugnale, Alberto. (2012). Three-dimensional reciprocal structures: morphology, concepts, generative rules. In Proceedings of the “IASS Symposium 2012: From spatial structures to space structures”. Seoul. Popovic Olga. (1998). Reciprocal Frame Architecture. Ph.D. Thesis, School of Architecture, University of Nottingham. Popovic Larsen, Olga. (2009). Reciprocal Architecture in Japan. In Proceedings of the IASS Symposium: Shell and Spatial Structures, IASS International Symposium. Valencia, Spain, (Key note paper).

211

DEPLOYABLE STRUCTURES

Hoberman C. (1990): Reversibly expandable doubly-curved truss structure Hoberman C. (1991): Radial expansion/retraction truss structures Hoberman C. (2004): Retractable structures comprised of interlinked panels, Hoberman C, Davis M. (2009): Panel assemblies for variable shading and ventilation Fuller B. R. (1962): Tensile integrity structures https://www.researchgate.net/publication/235329328_Deployable_Structures http://daveaton.com/Deployable-Structures https://www.google.com/search?q=deployable+structures&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiQ6uHUwfPcAhWIvI8KHWdPBDoQ_AUICigB&biw=1366&bih=662#imgrc=xyFUXQVNQMbX9M:

212

AUXETIC MATERIALS

(PDF) Auxetic materials — A review. Available from: https://www. researchgate.net/publication/259865336_Auxetic_materials_-_A_ review http://en.wikipedia.org/wiki/Meta_materials http://en.wikipedia.org/wiki/Auxetics http://www.silver.neep.wisc.edu/~lakes/Poisson.html http://research.dh.umu.se/dynamic/artiklar/shape/stretch.html http://www.wisegeek.com/what-are-auxetic-materials.htm http://www.azom.com/details.asp?ArticleID=167 http://www.azom.com/details.asp?ArticleID=168 http://data.bolton.ac.uk/auxnet//background/index.html http://en.wikipedia.org/wiki/Poisson’s_ratio

213

AUXETIC MATERIALS

Cremers, J. M. (2011). Energy Saving Design Of Membrane Building Envelopes. Structural Membranes 2011, 147-157. Evans, K.E., Nkansah, M. A., Hutchinson, I.J., Rogers, S.C. (1991). Molecular Network Design. Nature, 353, 124. Evans, K.E., Alderson, A. (2000). Auxetic Materials: Functional Materials and Structures from Lateral Thinking!. Advanced Materials, 12, No.9, 617-628. (PDF) Auxetic materials — A review. Available from: https://www. researchgate.net/publication/259865336_Auxetic_materials_-_A_review http://en.wikipedia.org/wiki/Meta_materials http://en.wikipedia.org/wiki/Auxetics http://www.silver.neep.wisc.edu/~lakes/Poisson.html http://research.dh.umu.se/dynamic/artiklar/shape/stretch.html http://www.wisegeek.com/what-are-auxetic-materials.htm http://www.azom.com/details.asp?ArticleID=167 http://www.azom.com/details.asp?ArticleID=168 http://data.bolton.ac.uk/auxnet//background/index.html http://en.wikipedia.org/wiki/Poisson’s_ratio

214