Symbiotick Landscapes by Fawad Osman

Symbiotick Landscapes

SYMBIOTICK LANDSCAPES Section One Global Formal Development of Linear Aggregate Based Furnicular Shells with regard to Structural and Force Flow Optimization.

Written by: Fawad Osman Obuchi Laboratory The University of Tokyo Graduate School of Engineering Department of Architecture

SYMBIOTICK LANDSCAPES

TABLE OF CONTENTS

Figure Citations Chapter 1: Introduction

1.1 - Research Objectives 1.2 – Program Brief 1.3 - Design Considerations

07 09 10 14

Chapter 2: Material System Development 2.1 - Introduction 2.2 - Emergent Systems in Architecture 2.3 - Precedent Studies - Frei Otto’s Angle of Repose 2.3.1 - History 2.3.2 - Material Experiments

18 26 32 34

2.4 - Designed Granule Study 2.4.1 - Precedent Study - Achim Menges 2.4.1 - Material Experiments 2.4.2 - Digital Computation

36 38 40 42

2.5 - Stick Based Aggregate 2.5.1 - Geometric Properties 2.5.2 - Material Experiments

44 46 48

2.6 - Precedent – T_ADS Pavilion 2014 2.6.1 - Material Studies 2.6.2 - Complications/Further Explorations

58 60 64

Chapter 3: Development of Tools for Formal Development and Structural Analysis 3.1 - Anisotropic Materiality and Structural Considerations 3.1.1 - Structural Characteristics of Material System 3.1.2 - Generating Furnicular Shell Structures under Compression (FDM) 3.1.3 - Finite Element Analysis using Karamba with Material Properties

68 72 74 90

3.2 - Force Flow Optimization in Shell Structures 3.2.1 - Testing Force Flow Lines in Primitive Geometries 3.2.2 - Integrating Force lines Optimization in Design Process 3.2.3 - Identifying Discrepancies between Fabrication and Force Flow Generation

92 94 96 102

Chapter 4: Design Development and Implementation 4.1 - Site and Programmatic Context 4.1.1 - Site Analysis

118

4.2 - Formal Exploration 4.2.1 - Design Shape Adapting to Site Constraints. 4.2.2 - Employing Formal Tools for Shape Optimization. 4.2.3 - Reconciling F.F Lines and S.V.D. Lines into Design Scheme

122 136 142

4.3 - Architectural Realization.

152

Conclusion References

146

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chapter 1:

INTRODUCTION

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chapter 1 - INTRODUCTION

chapter 1

INTRODUCTION

This research forms the first half of the collaborative research conducted under the umbrella of “Symbiotick Landscapes”. This research focuses primarily on the development of a particular set of computational tools to generate a series of topologies for the “Temporary Event Structures”. The first chapter sets up the framework for the research methodology and also looks comprehensively into design considerations acquired from the project brief. Chapter two focuses mainly on the development of the Material System of the Linear Aggregates taking precedence from previous year’s T_ADS STIK Pavilion’s findings and shortcomings and projecting research trajectories further for developing. Chapter three forms the crux of the research whereby after re-evaluating structural properties of the material system from chapter two; systems and loops are devised to formulate a broad form finding strategy that takes into consideration the impacts of different force densities and load distribution paths occurring within a single geometrical framework. Chapter four takes the findings of the research and conclusions from the previous chapters and attempts to implement the tools of observation and production within realistic site constraints. The outcome of the results is documented in terms of form-finding tools, structural analysis and pattern development.

Figure 1.1 - 1:200 Scale Model of 1 out of 4 Clusters showing

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chapter 1 - INTRODUCTION

1.1

RESEARCH OBJECTIVES

The objective of this research is to improve and enhance a novel construction system that employs the use of individual linear aggregates starting from its whole macrostructure and down to its finest local texture. In stark contrast, the linear aggregates exclude themselves to strict hierarchies established by conventional construction in terms of parts and assemblies. The individual component, despite its lack of scale and weak internal structure, ends up achieving far more complex and structurally driven shapes when the material organization logic is in consideration to the applied forces flows and appropriate binding strength. The formal development tools employed in this research focus on identifying structural systems that comply with the intrinsic nature of the material and its ability to effectively neutralize internal/external forces by complexity in its local organization. Due to the anisotropic nature of the linear aggregates, the orientation of the linear elements becomes a dominant factor in determining an effective structural layout. The computational tools employed in the form finding research explore different potential of given topologies by modifying the force densities and external loads. By introducing different set of loads the research iterates within multiple formal varieties in order to achieve an efficient structural layout for the shell structures. The outcome of this research is then further investigated in terms of its fabrication in Section Two and also these tools are adopted to generate the design proposal and implementation for the Event Structures on the proposed site.

Figure 1.2 - Creating a nexus between analogue simulation and digital computaitons

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1.2

PROGRAM BRIEF

Symbiotick Landscapes provides a platform for temporal city interventions that manifest the connecting of disjointed material systems from the forests and the city. These manufactured landscapes consist of Time-based Seasonal Event Structures that are highly sensitive to spatial qualities, constructability constraints and consumer appeal. The program envisages creating a new persona of the city which is highly inclusive but equally cognizant of the surrounding material systems and its subsequent economies around it. These structures form a new interpretation of urban marketplaces in dense mixeduse built environments. The ambition of this program exists to propagate a continuous duality; to sustain the eternal health of forests by creating new demands for non-standard wooden products such as recycled chopsticks. The Event Structure forms part of an initiative from the OMY (Otemachi | Marunouchi | Yurakucho) Urban Revitalization Authority as a prototype that reflects the values of the urban council in terms of environmental awareness, Community Interaction w.r.t to use of public spaces, and management of local waste resources.

chapter 1 - INTRODUCTION

Figure 1.2. Symbiotick Landscapes -

OMY - Otemachi | Maronouchi | Yurakucho

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District Redevelopment Project Council Roadmap for OMY Council

CS R A c t i o n M a p Statue of Masashige Kusunoki

Hibiya Park

Imperial Palace Outer Garden

Harum i-dori

Nijubashi Bridge

Avenu e

Kokyo Gaien Office

Chiyoda Line Hibiya Station

Hibiya Moat

Babasaki Moat

Meiji Life Insurance Building

Mita Line Hibiya Station DN Tower 21

Tokyo Chamber of Commerce and Industry

Babasaki-dori Avenue

The Peninsula Tokyo

Kokusai Building

Shin-Kokusai Building

Hibiya Line Hibiya Station

Chiyoda Line Nijubashimae Station

Marunouchi Brick Square

Marunouchi Cafe

Marunouchi Saezurikan

Mitsubishi Building

Shin-Tokyo Building Tokyo International Forum

Daimyo-koji Street

Mitsubishi Ichigokan Museum

Yurakucho Line Yurakucho Station Yurakucho Mullion Building

Bank of Tokyo-Mitsubishi UFJ Head Office Yur a

kuc

Sta

Yurakucho ITOCiA

Marunouchi South E (Tokyo Station)

tio

Tokyo Building TOKIA Statue of Dokan Ota

Tokyo Kotsu Kaikan

Ginza

JR Keiyo Line (Tokyo Station) Marunouchi Kajibashi Parking Four Seasons Hotel Tokyo at Marunouchi

Cutting edge eco-information at Ecozzeria

Sotob

ori-do

ri Avenu

Environment monitoring data can be viewed on the ‘Clock Map’ and ‘virtual earth’ touch screen displays or conduct experiments with intelligent lighting and air-conditioning systems, etc. Weekday tours OK!

The OMY district is home to two crowd-pulling markets. Marunouchi Marche, held periodically in the landmark Time travel ‘Clock Map’ Marunouchi Building in front of Tokyo station, which famously attracts neighbourhoodA chefs which touch-screen map that ensure allows you tousing travel fromquality inthe past to the future or take virtual ecotours of the gredients from across Japan. These two initiatives held weekly environment. Showing at Ecozzeria. on a smaller scale in the Gyoko-dori Street underground pasShin-Marunouchi sage has been acting as a bridge between people who work Building uses only in the city and the crop producers from across Japan. It hapFresh Green Electricity pens to benefit both ends of the spectrum as it gives the OMY All the electricity used by the Shin-Marunouchi Building (in frontin of Tokyo Station) renewable district much needed diversity terms ofis from consumer goods sources (wind or hydro power, etc.) and it provides a platform for crop-producers to highlight their produce to a more far reaching audience. Solar power generation

increasing rapidly.

Electricity generation from solar panels is increasing

The area cooling Uchimizu Project Lowering temperatures by water sprinkling the entire area mitigates the heat island effect. As well as Gyoko-dori Avenue, Naka-dori Street stores participated in Uchimizu in July and August.

Electric Vehicles ZeRO Taxis Two i-MiEV taxis are running in OMY. Fares are the same as an ordinary taxi. The electric vehicle experience is included in the fare!

Electrically powered Marunouchi Shuttle The Marunouchi Shuttle is a free bus service

Map showing the various CSR activities undertaken by OMY

Uchibori-dori Avenue

Eidai-dori Avenue

Yusen Building

Nikkei Building

Karugamo Pond

Wadakura Fountain Park

Wadakura Moat

Gyoko-dori Avenue

Exit

chapter 1 - INTRODUCTION

Shomonzuka Memorial

Mitsui Bussan Bldg. Keidanren Kaikan

Chiyoda Line Otemachi Station

Mita Line Otemachi Station

Hibiya-dori Avenue

Otemachi Building

Shin-Marunouchi Building

Hanzomon Line Otemachi Station Tokyo Sankei Building

Ecozzeria Industry Club of Japan Mitsubishi UFJ Trust and Banking HQ Building Marunouchi Building

Marunouchi Line Otemachi Station Ecozzeria

Marunouchi Line Tokyo Station Marunouchi Central Exit (Tokyo Station)

Marunouchi North Exit (Tokyo Station)

Tozai Line Otemachi Station

Marunouchi Oazo Building

Fresh Green Electricity Communications Museum

Marunouchi Hotel

Shin-Otemachi Building

Marunouchi Shuttle bus stop (as of June 2011) Marunouchi Shuttle route Electric Vehicle charging points Drymist

JR Tokyo Station

Digital meteorological instrument shelter Uchimizu Project implementation area Uchimizu Week implementation area Metropolitan Hotel Marunouchi

Nippon Building

Tokiwabashi Park

Roof Greening Water-retentive pavement Solar panels Ginkgo

Yaesu

Sycamore Shangri-La Hotel Tokyo

Marunouchi Trust Tower

JX Building

Zelkova / Japanese Lime, etc Zelkova / American Maple, etc Zelkova / Katsura, etc

See the data! Digital instrument shelters

‘Drymist’ makes it feel cooler in midsummer

To monitor area conditions, digital instruments have been set up to measure and report in real time on

Drymist, a very fine mist, evaporates quick doesn’t feel wet and operates automatically (wh

temperature, precipitation, humidity, wind direction

temperature/humidity exceed pre-set levels). A

and speed. The data can be seen at Ecozzeria.

water evaporates it cools the air.

Animals and plants of OMY

Roof greening/ wall greening

Being close to the Imperial Palace, even betwe Roof and wall greening measures, which improve thermal insulation and absorb atmospheric pollution,

and around the buildings of OMY, 49 species plants, 29 insect species, 12 kinds of wild birds c

have been taken by many buildings in OMY

be found.

Figure 1.4 - OMY Road-Map

Cooling effect of water-retentive paving Roads and sidewalks have been surfaced with

Various kinds of 13 trees flourish

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1.3

DESIGN CONSIDERATIONS The design considerations are a key component of the research framework as they identify the scope and limitations of how the research is structured around the entire project. The event structures were expected to have certain performative features that could enhance and augment the serviceability of the markets that operate underneath them. The OMY Council also had core sustainability values in terms of material utilization and energy regeneration and they were considered as part of the design considerations. The following points highlight some of the key design considerations that were taken to formulate the bedrock of the research framework for form-finding as well as fabrication methods.

Design C

- Ease of A - Ability to be - Multi-fun - Highly A - Transpare

Criteria

Assembly e Recycled nctional Adaptive ent / Open

chapter 1 - INTRODUCTION

1 – Ease of Assembly – The event structures should be relatively quick and easy to assemble as a prototypical system so that it can be replicated in multiple places in a short period of time. 2 – Ability to be Recycled – The city itself should be seen as a repository for construction material. The material that is used by the event structures should be freely available from the confines of the urban environment and must be cheap to process and recycle. 3 – Multi-functional – The event structure should facilitate a variety of different events and should have the capacity to accommodate the function’s specific requirements accordingly under one roof. 4 – Highly-Adaptive – The prototype must be able to adapt to the complex urban conditions of Tokyo in terms of topologies, circulations etc. 5 – Transparent – Due to the nature of the program the event structures must be accessible physically as well as visually and must have highest degree of transparency to allure all kinds of customers

Figure 1.5 - OMY Road-Map

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chapter 2:

Material System Development

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2.1

INTRODUCTION With the proliferation of digital technologies, information in our cities is becoming highly pervasive, while material resources are in a constant state of decline. In the Japanese context, cities such as Tokyo are increasingly monopolizing the demographics leaving peripheries vulnerable to overwhelming problems with economy, industry and livelihood. 66% of Japanâ&#x20AC;&#x2122;s land mass happens to be utilized for forestry and the depopulation of these rural areas has had a tremendous impact on the health of the forests adversely affecting the industrial output. Projected to lose a third of its population in the next 35 years, Japan is only going to see an addition to the problems to its ailing economy, including a huge reduction in skilled labor for the construction industry. The aim of this research is project future trajectories in terms of new construction technologies which are responsive to the socio-economic problems Japan faces along with several other developed countries around the world.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.1 - Man Vs. Machine

0 Production

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Figure 2.2 - Forest and the City

Consumption

With the increasing use of digital and computational technologies in the design environment the limitations on what could be built and what cannot be built have become blurred. However, not long ago, there was a time when material was not considered a finite entity while geometry in architecture was considered to be an expensive commodity. Architects today now are looking towards their habitats i.e. cities as a repository for material resources that have the possibility to be employed in their energy intensive systems. They seek to utilize the advantage they have gained from the decentralized, fragmented properties of network culture and devise comprehensive and open systems that break down linear streams of architectural production to non-linear self-correcting and conscious â&#x20AC;&#x153;smartâ&#x20AC;? systems.

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Figure 2.3 - Robots 3-d printing a bridge

Figure 2.4 - Contour Crafting

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The space created by the lack of skilled labor is being expected to be replaced by automated construction technologies. There have been rapid developments in additive manufacturing techniques at the product scale and a variety of different methods have been explored to achieve high precision and accuracy in terms of products. However, when the same techniques are applied to the architectural scale they face a lot of complications primarily which can be summarized in: 1 – The entire setup (e.g. contour crafting) which involves the gantry system is too heavy and complicated to move around 2 – The existing 3-D printing methods are restricted by the scale, cost and logistical constraints of the material 3 – Economic unattractiveness of expensive automated equipment.

Figure 2.5 - FabClay - Barcalona

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The use of linear aggregates is an attempt to address the issues that are related to present additive manufacturing techniques. Aggregates due to the contingencies in their inherent geometries and spatio-behavioral patterns have the unique ability to act as rigid bodies but still retain fluidity in their organization. (Karola) The linearity in the aggregates employed for this research is an attempt to address issues of scale and material optimization with the addition dimension of linearity in the aggregates. There have been precedents in the past that employed the used of custom designed aggregates (Karola 2012) which addressed issues that were not resolved by design of the individual granule. This thesis moves away from those objectives and instead focuses on how having controlled complexity within the material organization can lead to significant formal and fabrication systems.

SYMBIOTICK LANDSCAPES

2.2

EMERGENCE IN NATURAL SYSTEMS Emergent patterns are apparent in complex natural systems where seemingly simple objects end up making structures with far greater complexity, information capacity and assembly instructions compared to even the most advanced structures possible with our current technologies (Tibbits 2014). Looking into these natural systems, there is a recurring theme to question where do these organizations initiate from? Seeing how ant colonies manage to make such elaborate systems for foraging food, defending their colonies without any central control command seems confounding at best, but upon closer inspection, the behavior of pheromones in ants at the local level can explain the phenomenon at the scale of the colony (Johnson 2011). These key trajectories give insight over how architects can mirror such phenomena in order to re-define the contours surrounding architectural systems. The method of aggregation in the linear aggregates is observed in the existing emergent systems in nature.

Figure 2.6 - Ant Bridge

However there are precedents available in nature that demonstrate its ability to maximize the use of resources for its standard operating procedures in daily life. There are various instances where emergent phenomena in complex natural systems (ant colonies, formation of sand dunes, human neighborhoods) provides insight on how we as human beings can effectively mirror these natural processes to address the.

Figure 2.7 - Ants contacting through Pheromones

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.8 - Desert Formations

Figure 2.9 - Detail from Circus Sideshow

Figure 2.10 - Emergence in Pointilism

DIFFERENT BRICK SYMBIOTICK LANDSCAPES

Mater Geom Sand Granules Frei Otto â&#x20AC;&#x2DC;s Angle of Repose

Interac

Conting

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rials metry

Custom Designed Granule

ctions

gencies

DIFFERENT BRICK SYMBIOTICK LANDSCAPES

Organi Contingent Interactions

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ization Emergent Behaviours

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2.3

PRECEDENT STUDY FREI OTTO

Figure 2.11- Frei Otto

“Any granular material falling from a fixed point f orms a cone on the surface below and a funnel within the granulate mass with the same angle of inclination, the natural angle of repose, 35 degree.” Frei Otto, 1972 32

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Wind Direction

Angle of Repose

Sloughing Sand

Granular Aggregate Structures in Nature - Movement of Sand Dunes Figure 2.12- Angle of Repose

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2.3.1

MATERIAL EXPERIMENTS To investigate the emergent patterns existing in nature, this research team did experiments inspired by Frei Otto’s research on aggregation occurring in natural elements in his Institute for Lightweight Structures in Stuttgart along with Ralph A. Bagnold on the science behind desert dunes (Bagnold 1971). This primary aspect of the research was to understand the inherent dynamics of sand particles as they underwent forces in gravity and wind pressures. The loose granular state of sand particles exhibited states ranging from completely solid grains to displaying liquid like behvaiour. This quality was observed to be amongst the most significant attributes of unbound aggregates in terms of its architectural potential. The research observed that “a sand pile, or dune, for instance, is a dynamically stable shape as it retains the inclination of its slope during the process of accumulation of granules.” (Menges 2008).

Figure 2.13- Dry Sand Box

Figure 2.14- Sandbox after the removal of the lid

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.14 - Sand Granules finding their Angle of Repose

Figure 2.15 - Detail - Dry Sand Box Experiment

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2.3.2

CONCLUSIONS

The “Dry Sand-box” experiment was an important step to understand the behavior of unbound aggregates and the inherent intelligence they possess to generate dynamic self-stable geometries. One of the major lessons learnt from this research was to try to understand the intrinsic nature of how any material with a characteristic geometry could be accumulated to generate complex but contingent geometries. The ability of these loose granules to self-organize and “support themselves and external loads, as well as resist shearing stresses” (Menges 2008) was in itself an interesting trajectory to follow in terms of development of an alternative design and construction approach for architecture. In the coming sections, the research was taken forward in terms of the understanding the linear aggregates system which included the element of directionality that came with the linear elements and coupled with spatial organization, specific load-bearing behavior become dependent on surfaces of contact the linear elements have within them.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

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2.4

DESIGN GRANULE STUDY

“The greatest potential of aggregates may lie in not assigning such a sub-ordinate role to granular substances, but, instead in utilizing the way in which granular substances shift between liquid and stable states.” Achim Menges 2008

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2.4.1

PRECEDENT STUDY ACHIM MENGES Achim Menges in his research for unbound designed granules noted that the application of bound aggregates was based â&#x20AC;&#x153;on the imposing shape on material constructs with a higher degree of controlâ&#x20AC;? (Menges 2008) but he argued that it stripped the aggregates intrinsic nature for pattern formation due to external factors such as gravity loads, wind pressures. So the context of this research was to explore the potential of loose custom-designed granules could possibly give future trajectories for architectural assembly systems.

Figure 2.16 - Aggregates Installation Rice University 2009

Figure 2.17 - Detail Aggregates Installation Rice University

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.18 - Designed Granule Aggregating against Primitive Formwork

Figure 2.19 - Designed Granule Aggregating against Pneumatic Formwork

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2.4.2

CONCLUSIONS

- One of the fundamental factors in determining structural strength were to have the proportional number of contact surfaces according to the number of granules. - To achieve significant output in terms of geometrical stability it was observed that the production of designed granules was needed to be exponentially increased to achieve maximum of contact surfaces between the components. - The production process of the designed granules employed was found to be too labour intensive and extremely specific to the design of the granule - It was found that the design of the granule itself was not a primary determining factor to control the contingency of the geometrical outcome. - To expedite the production process, it was realized to choose an existing material in the current urban environment that could exhibit the similar qualities of loosely bound aggregates - Within the current framework it is observed that without binding the limitations of the unbound aggregate system leave very little room for potential formal and structure exploration due to its dynamic shape changing dynamics, in the next chapter the addition of binding agent in the material system is further explored.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.20 - Designed Granule against primitive formwork.

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2.4.3

DIGITAL COMPUTATION To test the potential of this new architectural system there needs to be a thoroughly defined cycle that encompasses two domains of research the material aspect(analogue simulation, material properties) and the information aspect(digital tools, machine computation). There has to be a feedback loop in this process of experimentation where output from the analogue simulations will be fed to the machine computation which will further analyze and evaluate the content and then feed the information back into the loop. 3D simulation platforms which can simulate and animate rigid body dynamics. One of the most significant insight with machine computation is our ability to understand the relationship at the micro level where they intersect. Since simulation requires processing large amounts of information there are limitations to the amount of information that can be computed. These experiments further allow us to study the micro-molecular interactions between components which can help us ascertain the nature and controllability of the global geometry. These simulations are valuable for us to further assess and analyze properties such as collision stress/loads by Computational Fluid Dynamics software and Finite Element Method and Discrete Element Method - Mathematical models that allow us to find approximate solutions to boundary value problems for differential equations. Conclusions: To understand the effectiveness of the digital simulation, it would be important to note how by controlling factors such as distribution angle, speed of distribution, boundary conditions, mass of particle, size of particle, binding strength (if applicable) it is possible to ascertain changes in the frequency of contact areas between the designed granules. A script was developed in Rhinoceros 5.0 + Grasshopper + Gh-Python component to iteratively recognize where the granules would intersect and highlight the surfaces which are in contact. By manipulating the constraints mentioned above it would be interesting to explore what conditions could amplify the contact surfaces in order to achieve greater structural stability.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.21 - Physical Aggregation of Designed Granules

Figure 2.22 - Contact Surfaces extracted through Aggregation Logic

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2.5

DEVELOPMENT OF LINEAR AGGREGATE SYSTEM This research was a natural departure from the findings of the previous sections that explored in-depth about the accumulation of aggregates existing in nature such as sand grains, the potential of designed granules as alternate architectural assembly systems and potential of computation to extract and augment control over aggregate systems. In this section, the linear stick material is chosen as the local component and tested out at various scales to see its compatibility with the architectural, logistical, formal constraints.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.23 - Chopstick Aggregated Wall 1.0 Meter

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2.5.1

GEOMETRIC PROPERTIES

Additive manufacturing techniques of the past and present have been being explored to find ways to incorporate them to the architectural scale. However, numerous challeneges in the form of the scale of the depositing material, size of the gantry, issues of scaffold and formwork have proved to be great hurdles which still need to be overcome. This research in its bid to answer some of the concerns picks a granular material which could potentially be applicable to the architectural scale and also maintain its aggregation behaviour.

Contour Crafting | Additive Manufacturi Cement , Sand, Plasticizer, Water

The linear stick material with the combination of wood glue is used as an additive manufacturing material for the architectural scale. The structure is highly porous and due to the uncontrolled nature of the chopsticks, it acts as a fibrous material taking up greater volume compared to its method of aggregation. The material is readily available from the city, it does not need to be manufactured just as a primary construction material but can be recycled after its use. Disposable chopsticks or “Waribashii’ more commonly known in Japan are found in abundance and the dimension of the chopsticks can prove to be of immense value in terms of finding the suitable architectural scale. The characteristic scale of the chopsticks makes it an ambigious element that can not be categorized as a purely casting based material or a stacking based material. This property as we will see in the next sections makes it an ideal material for the aggregation logic in an emergent material system.

Resin Granule Typical layer thickness is around 100 µm for 3D printing

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Stick Based Aggregate

ing

Prefab Building Components e.g Nakagin Capsule Tower 2.3m x 3.8m x 2.1m Casting Based

Stacking Based

Component Size Cast-in Place Concrete > 5mm Water , Aggregate, Cement

Compression Based Masonry System Brick - 222mm x 106mm x 73mm

Figure 2.24 - Scale Changes in Construction Material

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2.5.2

MATERIAL EXPERIMENTS Due to the contingent and unpredictable nature of the material, this research devises a system that can create maximum control over how material distributes. The material possesses an inherent of intelligence that leads it aggregate a specifica A number test samples werefor developed to in ascertain way. architectural perspective,construction. the way the The material properFrom size an of the sticks for architectural size distributes creates makes a tactileit nature which behaves dynamically of the chopsticks possible to print quickly in an arwith changing light conditions to create unique spatial qualichitectural scale. ties. Structurally, this interlocking behavior can create more structural whileability simultaneously utilizing poThe sticksintegrity due to their to interlock efficiently and with their linearity rosity createoutwards a lightweight structure. could to project fromporous their base making it possible for sticks to make doubly curved surface. In order to create greater control over material behavior, a variety of digital fabrication techniques are on employed, The Material system is developed to perform two fronts;rangone ing physical computation (usingproperties Arduino Controlled Disis tofrom analyze and evaluate the intrnsic of the material pensers) 3D scanning technology (Kinect and 3D) optimize and physics itself, the to second is to apply those findings the simulations (Processing-bRigid Theproperties.The fundamental process of form finding to best fitLibraries). the material objective is tothat study and effectively mimic material behavior target surface is generated is dissected into multiple secwithin real world conditions respect tocontrolled gravity ordispenser adhesive tions which are then taken towith an arduiono friction within components and to physically which latches on to the CNC Router.The maintranslate objectivedigital is to processes. Withdigital the addition of the by 3-Ddigitally scanning process, reproduce the target surface simulate the this research attempted to create a live material on how it distributes and then usefeedback the same process findings which could distribute control material and respond to any to physically it on anybehavior given surface. contingencies that arrived within the process of fabrication. Fig 2.25 shows material process that starts from generating The third partthe is to evaluate the physically distributed material a geometry the digital realm and then physically translating realtime by ain depth sensing 3-d camera which captures the that geometry through a smart tool is operated an distributed mass and analyses andthat compares it tothrough the digital Arduino microprocessor. model. Any discrepancies are identified and pointed out which can later be rectified or the guidance system adapts itself to In following nextgeometry pages, some experiments are explained thethe modified digital . and demonstrated which utilize the principles and the design flow from this live feedback loop.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.25 - Creating a Live Feedback Process

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The initial experiments were conducted at various scales in order to test out several aspects of the material behvaiour and the material system. This experiment was carried out using 10 mm segments of toothpick made out of wood and were bound together by wood glue. The First few experiments dealt with the digital to physical translation of the material by the target surface to the physical output produced by the arduino controlled dispenser. These experiments were significant in determining a smooth flow from the digital to the physical aspect of the project. They consolidated the branches that linked the digital target surface to the physical output. The Kinect camera installed took live feedback of the digital models to assess if there were any discrepancies within the model.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.26 - 1:20 Model for chopstick made by Arduino Controlled dispenser

Figure 2.27 - Arduino Controlled Dispenser Translates the target surface into G-Code for the CNC

Figure 2.28 - Vaccumming Unglued components off from the glued surface

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After having worked at smaller scales, the ideas that were tested were re-envisaged for scales that came closer to the architectural scale. Toothpicks (1.5 mm x 60mm) were then tested within the similar framework previously tested at the CNC scale. The setup that can be seen in the fabrication photographs as seen in Fig. 2.30 demonstrate a central dispensing unit that distributes and aggregates the material to a certain height while the ropes are connected to the three corners of the fabrication space. What was interesting in these experiments was that the same setup was then further developed for the Smart tool that was used in the fabrication of the STIK Pavilion 2014 where the ropes holding the conical dispenser were further developed in to Position Tracking system that sent the real world XYZ coodrinates back to the system so we could position in the digital space where the smart tool was located in the real world. So these intial studies however primitive were significant in opening up various trajectories where digital fabrication improved and augmented these processes to better understand the material system.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.29 - 1:3 Model made by Toothpicks and Wood Glue.

Figure 2.30 - Fabrication Process

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The major objective during these different material studies was to experiment with the various scale of linear aggregates and to substantiate an appropriate scale that could be suitable for architecture. With the toothpick scale, even though the structures constructed were potentially structurally self-stable but due to the small scale of aggregate, covering vast expanses and area would become time-consuming and unfeasible. When the same experiments were conduted with chopsticks, there were two clear advantages; 1) the scale of the chopsticks allowed to fabricate areas with greater effeciency and greater spans in shorter periods of time. 2) the adhesive friction was well suited for the scale as it provided greater area for the adhesive to apply on the surface and also provided a better surface contact. These samples when compared to the toothpick model scale took 1/3 of the time to fabricate and were far more rigid and self stable when compared to previous models. From these experiments it was concluded that the chopstick scale was suitable for architectural application as because of its scale it was appropriate for logistical reasons and also for human accessibility reasons.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.31 - 1:3 Model made by Chopsticks and Wood Glue

Figure 2.32 - Fabrication Process

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2.6

PRECEDENT â&#x20AC;&#x201C; T_ADS PAVILION 2014

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.33 - STIK Pavilion 2014

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2.6.1

MATERIAL STUDIES

The Linear Aggregate system was further explored and developed in the DFL Stik Pavilion 2014 by th Digital Fabrication Lab of University of Tokyo. The same chopsticks that were finalized in the previous section of the research for its appropriate scale for architecture were then continued in this next phase of research. Multiple mockup studies were done to study the mechanical properties of the material system with its geometrical constraints. In the model shown in Fig.2.35 the cantilever of the chopsticks were tested as in to test how much the structure could cantilever out without any sort of formwork or scaffolding. It was observed for a height of 1.60 meters the cantilever could stretch out by 60 centimeters. These constraints further informed the form finding process that took mechanical properties to constrain the geometrical development.

Figure 2.34 - Fabrication Process

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

1.60 m

Figure 2.35 - 1:1 Mockup - Curvature Studies

0.60 m

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Figure 2.36 - Fabrication Process

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.37 - 1:1 Mockup

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2.6.2

FORMAL EXPLORATION

The form finding process involved in the Stik Pavilion was a natural derivation of the fabrication process. The curves generated through the harmonograph were representative of the path the material was distributed on and by controlling the parameter of the curve generation several shapes were tested out in order to test out its structural potential.

Figure 2.38 - Harmonograph

By utilizing pendulums and weights, a harmonograph has the ability to generate different curves. This process was then digitized and transformed into a 3-D generating process. By having the liberty to automatically generate these curves by changing the parameters, the research could test out a variety of forms which were within the constraints defined by its mechanical properties. In the next section the pavilion research is summarized in the complications that arose within the process and how further research aims to tackle with those issues.

Figure 2.39 - 2-D Curves drawn by Harmonograph

Figure 2.40 - Harmonograph Curves in 3d by Processing

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.41 - Iterations of 3-d Scaled Models through Harmonograph Logic 65

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Figure 2.43 - Detail - STIK Pavilion

n 2014

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

Figure 2.42 - STIK Pavilion 2014

Figure 2.44 - Detail - STIK Pavilion 2014

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2.6.3

COMPLICATIONS/ FURTHER EXPLORATIONS The T_ADS STIK Pavilion 2014 was a coming together of the research from previous sections but the method of aggregation was one fundamental parameter that was always kept constant and this research could be gauged and analyzed by keeping that one parameter consistent. - The formal exploration employed for the STIK Pavilion by using the Harmonograph logic was compliant with the method of fabrication and assembly but it disregarded the structural dynamics of the material system. Consequently the process from form to structure was not smooth and had to go through a lot of trial and error to arrive at a structural shape that was within the defined safety factor. One way of resolving the difference was to understand the mechanical properties of the material system and derive a form finding logic that would embed the constraints within its framework. - The method of aggregation of the sticks was kept uncontrolled throughout the Pavilion research as it had the ability to use less material, was more porous and had the capacity to aggregate up till a considerable height without any sort of formwork. However, with uncontrolled aggregation there was a lot of contingencies in terms of its organization and the contact surfaces which determined their main structural strength were too few for it to be seriously considered as a potent structural material. The closes material comparable to the aggregated sticks was Styrofoam in terms of its Youngâ&#x20AC;&#x2122;s Modulus and Yield Strength which too happened to be stronger. In order to further explore qualities of this system alternate methods of aggregation must be further developed that would ensure more surface contacts between the sticks. - The material system exhibited anisotropic qualities as its mechanical properties showed differentiations in performances due to direction of the applied force. Further studies should take this factor into consideration as it could ensure better structural efficiency.

chapter 2 - MATERIAL SYSTEM DEVELOPMENT

- The material systems inherently lacks resistance to tensile force making it extremely weak. With the addition of tensile membrane within the formal investigation could possible address such issues.

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chapter 3:

Development of Tools for Formal Development and Structural Analysis

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3.1

ANISOTROPIC MATERIALITY The culmination of the STIK Pavilion 2014 brought about an important set of trajectories that could be explored in order to fully realize the potential of the linear aggregate system. The most significant of those future explorations which dealt with the directionality of the linear aggregates is explored in length in this chapter. At the atomic level of materials, the physical and mechanical properties of the materials can be subjected to the difference in orientation of fibers. In the event that the properties of the material vary with different fiber orientations the material is understood to be anisotropic. On the other hand, if the material properties remain the same despite differentiation in orientation then it is considered to be isotropic. Isotropic and Anisotropic materials both exist abundantly in the natural environment. The orientation of wood fibers in trees is fundamental in determining the structural character of the trees against gravity and wind loads. It is understood that wood has ‘extreme anisotropy’ where in trees 90-95% of their cells elongated or vertical (i.e. aligned parallel to the tree trunk) which help it sustain its immense weight by its trunk (Ferdinand, 2012). Understanding it at the microscopic level, the formation of the plant’s wood fibres are seen to be aligned to the flow of forces within a tree. Since the direction of the fibers is oriented perpendicular to the contact surface it leaves room for adjustment for all the unnecessary material at each contact point and all new growing wooden fibers (Ferdinand, 2012). This effect reduces the shear forces on the inner part of the trunk due to the characteristic ‘interlocking between the technical component and the growing wood taking place.’ (Ferdinand, 2012). The aggregated sticks have an anisotropic nature due to their linear geometry, and thus produce differentiations in mechanical properties in accordance with differentiations in the direction of applied force. The hypothesis set forth in this research was to subject the linear elements to the orientation of the applied force and to study the results acquired from the varying structural tests to get a holistic view of the mechanical potential of the linear aggregate system.

Fig 3.1 - Orientation of Wooden Fibers in a Tree

Fig 3.2 - Detail - Orientation of Wooden Fibers in a Tree

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3.1.1

STRUCTURAL CHARACTERISTICS OF MATERIAL SYSTEM The mechanical properties of the waribashi (disposable chopsticks) were thoroughly tested during the research development building up to the DFL STIK Pavilion. In order to forecast its structural stability for the pavilion, a number of compression tests and bending tests were conducted. The bending test demonstrated material strength that was significantly greater than the results observed in the compression tests. The mode of aggregation maintained throughout the tests was uncontrolled for the reasons that were explained in the previous chapter. The sticks demonstrating highly anisotropic nature in those tests produced differentiations in mechanical properties in accordance with the direction of the applied force (Yoshida 2015). Several other factors were also seen to affect the results such as the strength of the binding agent, the number of chopsticks within the sample, the drying period allowed for the glue/water mixture to completely be absorbed by the sticks.

Online Submission ID: 0328 266 267 268 269 270 271 272 273 274 275 276

277 278

angle (Figure 7). The feed roller feeds 10 sticks a slit, and then passes the sticks to glue coaters, ev sticks with wood glue. Both feed and coating roll by a DC motor with variable speed control. When wood glue, it was important to determine the visco tor in the pumping pressure required, friction enc the hose, and glue drying speed. In particular, gl affects the aggregation mode (as described in Sec glue dries faster and thus holds the sticks where th but makes it difficult to control the dropping angl takes more time to dry (and thus hold the sticks allows precise control in terms of dropping angle results indicated the optimum glue viscosity is 2.0

0.028 0.024

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0.020 0.016

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0.012

Sa Sa Sa Sa Sa Sa Sa

0.008 0.004 0.000 0

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Stress-strain curves from compressions tests. Fig 3.3 - Compression Tests for the 30 cm x 40 cm Sticks Sample

1.000 0.900 0.800 0.700

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0.600

at once through a 0.500 venly coating the lers are 0.400 powered Yield Stress n considering 0.300 the osity of glue, fac0.200 countered within lue drying speed 0.100 ction 3). Thicker hey are dropped, 0.000 0 50 100 150 200 250 300 350 le. Thinner glue in place), but it Displacement [mm] Fig 3.4 - Bending Tests for the 30 cm x 40 cm Sticks Sample and speed. AOur 75 Bending Load-Deformation Curve from a 3-points Bend-test P a Âˇ s, with wa-

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Figure 3.5 - Sample #08 undergoing a Crush Test at Sato Lab, University of Tokyo

Density (t / m^3)

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Stick Aggregation

0.060

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Styrene Foam

0.013

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0.140

150

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0.140

4000

Cedar Wood (with the grain)

0.380

8000

Steel (SS400)

7.800

205000

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Fig 3.6 - Comparison of Mechanical Properties of Uncontrolled Aggregation with other Standard Materials

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Figure 3.7 - Sample #05 undergoing a Crush Test at Sato Lab, University of Tokyo

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In this research similar test samples were reproduced but this time the direction of the sticks was controlled to be along the direction of the applied force in the compression tests. A conscious effort was made to align the sticks as closely packed as parallel to the vertical force exerted by the Crush test machine. The three test samples shown in Fig ( -- ) had variations in the order of organization of sticks; Sample #08 and Sample #09 had all layers homogenously packed amongst each other while Sample #10 had the layers closely packed but divided in two layers. Along with the organization the drying time for the samples was also varied to test how it would impact the mechanical properties of the material system.

Figure 3.8 - Revised Crush Test Samples with Sticks Aligned Parallel to Applied Force

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Figure 3.9 - Crush Test to evaluate Compressive Strength

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Figure 3.10 - Crush Test to evaluate Compressive Strength

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Figure 3.11 - Crush Test to evaluate Compressive Strength

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The mechanical properties of the waribashi (disposable chopsticks) were thoroughly tested during the research development building up to the DFL STIK Pavilion. In order to forecast its structural stability for the pavilion, a number of compression tests and bending tests were conducted. The bending test demonstrated material strength that was significantly greater than the results observed in the compression tests. The mode of aggregation maintained throughout the tests was uncontrolled for the reasons that were explained in the previous chapter. The sticks demonstrating highly anisotropic nature in those tests produced differentiations in mechanical properties in accordance with the direction of the applied force (Yoshida 2015). Several other factors were also seen to affect the results such as the strength of the binding agent, the number of chopsticks within the sample, the drying period allowed for the glue/water mixture to completely be absorbed by the sticks.

Sample No. 1 3

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Youngâ&#x20AC;&#x2122;s Modulus [N/mm ] 88

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Deformation [mm] Figure 3.13 - Structural Evaluation after Revised Crush Tests

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3.1.2

CONCLUSIONS

- The orientation of sticks in the direction of the applied force increases the Yield Strength of the material system by an average of 10 – 12 times compared to uncontrolled aggregation. This means greater strength compared to the previous material systems which could enable us to design large span shell structures that were not previously possible. - The nature of structural systems based on this material system has seen to fail under tension but has performed relatively better in terms of compression. With revised and much stronger values, the material system would be suitable for compression based shell structures by minimizing tension as much as possible with the global geometry. - Information extracted through varying Young’s modulus values explain deformation within test samples which could be helpful to understand how to maintain organization of sticks within global geometry. The homogenous stick samples proved to have much higher Young’s Modulus reaching up till 73.028 kgf/cm2 which give us new insight on how to deal with structure of the material. - The Striated Panels ere also able to keep their shape and did not go under deformation whereas the uncontrolled sample was irreversibly transformed. - The last three samples had chopsticks twice the amount used by the previous samples but the results obtained from the results show strength values going much higher demonstrating the significance of the orientation of the sticks. The strength of the samples is proportional to the points or surfaces in contact between the local components. It is fundamental to understand how fabrication of the sticks would use more knowledge about how the distribution of sticks is controlled. By controlling the distribution process the structural values could also benefit to provide a stable global geometry.

Applied Force

Uncontrolled Aggregation

Points/Surfaces in Contact Applied Force

Striated Aggregation Figure 3.14 - Evaluating Differences in Mechanical Properties through difference in aggregation patterns

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3.2

GENERATING DESIGN FRAMEWORK

The previous section dealt in depth with changes in the material’s mechanical properties with the consideration of orientation of linear aggregates within the spatial framework. To realize the potential of the material system within the structural requirements of event structures, this research will try to employ the use of computational tools to maximize the use of its mechanical properties. This section particularly deals with setting up a design feedback framework that can ensure the material system’s adaptability to the form finding processes through the use of geometry, then by software using the finite element analysis, the specific material values are run through the surfaces to ensure structural integrity and material optimization. The last step is to consider the fabrication process of the geometry and analyzing it the geometry through the lens of fabrication constraints. Any geometry that does not comply with those constraints is sent back in the loop to the ‘Shape Design’ section where appropriate changes are iterated until the final output fulfils maximum design and structural considerations.

Identifying regions falling in critical areas due to fabrication constraints

3 - Fabri

Subdiv Geometry t Flow Di

1- Shape Design Generating Furnicular Surfaces through RhinoVault

Design Loop

ication

vision of through Force istribution

ModiďŹ cation of Force Density Method to Generate Self-Supporting Surfaces

2 - Structural/Material Analysis F.E.A using Karamba with Material Properties

Analyzing Compression and Tension in Self-Supporting Surfaces

Figure 3.15 - Generating a Design Feedback Loop for Form Finding and Structural Evaluation

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3.2.1

COMPRESSION BASED SHELL STRUCTURES

With greater insight on the mechanical properties of the material system, the direction ahead for this research was to choose an appropriate structural system for the material that could maximize its compressive potential and minimize its tensile potential. Shell Structures, often a popular choice for compressive based material such as concrete, stone or brick masonry, was one structural system that complied with the potential of the material system of linear aggregates. Shell structures defined by Philippe Block and co-researchers in their book “Shell Structures for Architecture” are ‘constructed systems described by three-dimensional surfaces, in which one dimension is significantly smaller compared to the other two. They are form-passive and resist external loads predominantly through membrane stresses’ (Adriaenssens, 2014). The shell structures are dealt with in greater detail in the book where they are sub-divided into multiple hierarchies in reference to the method of their generation. In this research the objective was to take a specific typology of shell structures that are classified as ‘Freeform, free-curved or sculptural shells that are generated without taking into consideration structural performance. If they are shaped digitally, then they are often described by higher degree polynomials’ (Adriaenssens, 2014). The freeform surfaces are generated by the Thrust Network Analysis (TNA) which is a ‘graphic statics-based approach to the equilibrium design and analysis of compression-only vaulted structures with complex geometry’ (Rippmann, 2012).

Fig. 3.15 - Bundesgartenschau Pavilion, with a 12mm fibre reinforced concrete shell, Stuttgart, 1977

In the next section multiple digital tools would be employed to acquire digital forms which are self-supporting and are adaptable to different force-density load settings. However, it should be noted that shells explored in the next sections are fundamentally form-passive which have specific properties and differ to form-active tensile systems in three ways (Adriaenssens, 2014): - The shell is unable to actively change its shape due to varying loading conditions. - Due to elasticity and contingency in materials, the form undergoes deformation through undesirable additional bending moments. - The shell always maintains an unstable equilibrium due to external loading conditions.

Fig. 3.16 - Multihalle in Manheim by Frei Otto

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3.2.2

FORM FINDING WITH THE FORCE DENSITY METHOD

Perform

Socialize

Exhibit

This research explores form finding keeping in consideration of the design criteria set out by the program and the event guidelines discussed in the first chapter. Consequently it also considers the constraints, possibilities and limitations as expressed in the previous concluded section about the mechanical properties of the material system which inform on a large part the constructability of the geometry according to its mechanical and fabrication limitations. The form finding process as explained in the previous sections is divided into four sections, this section will deal with the first part which employs RhinoVault (Rippman, 2012) as a dynamic form finding tool. The process involves working with parameters that controlled to find an ‘optimal’ geometry within a structural framework which is in static equilibrium with a design loading (Rippman, 2014). For passive-form shell structures the design loading is mainly contributed by their self-weight. As explained by Rippman and Block (2014), these form finding processes can be identified by

Area Req. = 180 m

Event Space

Design Space

1 – Supports; or boundary conditions 2 – Topology of the Model 3 – Internal forces, and their relationship to the geometry (Force Density Method) The Fig 3.17 explain how by manipulating these three conditions it is possible to navigate through the different variations of forms that control the furnicular form finding process. The RhinoVault method uses two geometrically linked form and force diagrams. The force density method which is explored in detail in the figure on the next page shows the multiple possibilities of geometries achieved through the controlling parameters iteratively. Force densities do not require the specific material information required to generate a furnicular geometry through which the research can employ extremely accurate results later to acquire the thickness of the shell and the specific structural considerations. This allows the geometry to be introduced with material information according to each and every individual member rather than one homogenous shell.

Generating Mesh for Shell Structures

Supports and Boundary

Aperture Bonuding Line Aperture

Aperture + Support

Base Surface Force Density Diagram Force Density =

force in a bar stressed length of a bar

Fig 3.17 - Generating Furnicular Shell Surfaces by Force Density Method.

#0 1

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id Sol rface Su Fig 3.19 - Generating Elliptical Vaults by consideration of Program and Site through the exploration of Force Density Method (FDM)

101

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3.2.3

EVALUATING STRUCTURE WITH FINITE ELEMENT ANALYSIS As concluded in the previous section, RhinoVault (Rippmann, 2012) provides a suitable platform to develop the furnicular shell geometry for a compression leaning material system. However, due to the lack of any material information within the furnicular shell, the geometries require to be tested with precise material values that were acquired in the start of Chapter 3 regarding the anisotropic nature of the material system. In order to do that, this research employed the same computational tools that were employed by the DFL STIK Pavilion 20141 to structurally evaluate the pavilion geometry by the Grasshopper component, Karamba (Presinger 2013) for the preliminary evaluation. Karamba is a finite element analysis (F.E.A) software that is plugged into the Rhinoceros 3D Modelling platform to structurally evaluate complex geometries by dividing the geometry into multiple elements and solving the partial differential equations resulting from the subsequent elements. The form finding logic behind the pavilion geometry was in consideration of the fabrication process of the then linear aggregation process as discussed earlier in chapter 2. The principles behind creating a Harmonograph was mimicked and by gradually elevating the height a 3-D geometry was achieved (Yoshida, 2014) that was in compliance with how the fabrication process was practiced. However, after running the geometry through the material information provided to Karamba, it was observed due to the lack of any structural considerations within the form-finding logic, the results of the analysis showed tension (shown in red) in fig. 3.12 which was undesirable to the very nature of the aggregate material system. In order to compensate for the inherent tension in the geometry, a secondary structural network of steel cables ran vertically and horizontally throughout the structure. The cables were spaced 500 mm from each other and there were concrete weights added to the base to the keep the network of cables intact and in tension throughout the geometry. This system, however effective was something that this research attempted to avoid and utilize the form finding logic that was structurally driven and kept the mechanical constraints of the material in consideration.

Fig 3.20 - Harmonograph

Fig 3.21 - Processing 2D to 3D Curves

Fig 3.22 - Analysing Curvature

[1] - The Script was developed by Masaki Miki from Sato Lab, The University of Tokyo

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Fig 3.23 - STIK Pavilion 2014

Compression (kN/cm ) < 0.001 > 0.001 2

Tension (kN/cm ) Fig 3.25 - STIK Pavilion FEM Analysis

< 0.0011 > 0.0011

Tensioned Steel Cable Network

Fig 3.26 - Steel Tension Cable Network to resist Tension Forces

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Compression (kN/cm ) < 0.001 Fig 3.27 - Finite Element Analysis Comparative Analysis to Structurally Evaluate the Surfaces

> 0.001 2

Tension (kN/cm ) < 0.0011 > 0.0011

It was observed that the furnicular shells that were generated by RhinoVault through the use of force density method displayed far acceptable compression and tension values than the results achieved by Harmonograph geometry. The compression-only vaulted structures achieved by RhinoVault gives the material system a suitable structurally dynamic shape that can withstand the self-weight and loading by compression only minimizing the tension elements in the process. The Finite element analysis through Karamba shows the range of elements that fall within the compression and tension balance (compression in blue and tension in magenta), wherever the values show red or dark blue, they go beyond the safety factor and require the geometry to be adjusted for the a more coherent structural shape. The boundary conditions and thickness of the shell in both cases are extremely significant parameters that define the results of the analysis.

104

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The furnicular geometries that were generated through the multiple iterations in the previous chapter all tend to show similar results with the analysis validating the RhinoVault process of generating compression only vault structures. The next step would be to explore the maximum span of unreinforced linear aggregate shell structures that can be achieved within the current material system properties.

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Compression (kN/cm ) < 0.001 > 0.001 2

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Plan Fig 3.28 - Finite Element Analysis Comparative Analysis to Structurally Evaluate the Elliptical Surfaces generated through

106

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Note: The Values in Tension (shown in red) are at the supports as the model does not have a bounding base which is imperative for integrity in structural considerations 107

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3.3

FORCE FLOW OPTIMIZATION IN SHELL STRUCTURES Force flow lines as used in this research are a representation of the load paths distributed within a structure. In this section of the research, there is an attempt to understand how particular forces can be visualized within a geometrical framework in order to affiliate the anisotropic natures of material systems into the design scheme. The figure on the right represents a flat cantilever shell with one support which is also displayed and through using the Grasshopper Plugin; Karamba the force lines are visualized within the cantilever shell. The results show that the direction of the force lines visualize where the normal stresses are dominant (at both ends) and where the shear stresses are dominant (at the middle), so basically it can be concluded that the force lines will always show the direction of the resultant force of either dominant force.

Fig 3.29 - Force lines in a plate with a hole

Force flow lines can help identify distributing patterns for an anisotropic material where the direction of the force is key in determining an effective structural layout. In case of strengthening a structure with linear elements, it is always recommended to orient the fibers/linear elements along the direction of the major resultant force (Presinger 2013). Another key determining factor is to understand how the concentration of the force lines can sometimes indicate the concentration of stresses which can be detrimental to the structural layout as can be seen on the figures on the right. When a hole is introduced in flat plate, the flow lines start concentrating on the periphery of the hole increasing the stress. It is worth considering when designing in regards to force flow lines to understand the significance of the distribution of force lines and to align them as equally to each other as possible with least possible concentrated areas.

Fig 3.30 - Force lines in a plate with a central crack.

108

Supports

Loads Fig 3.31 - Force Flow Analysis on Flat Cantilever Shell

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Fig 3.33 - Force Flow Analysis on Furnicular Shells

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In Figure (ellipse series) the series of elliptical forms generated through RhinoVault were analysed through the Finite Element Software and then their force flow distribution was analyzed to identify weak or potentially stress concentrated areas and to visualize how the effect of each iteration could somehow affect the layout of forces in a structure. This becomes a key determining factor which could potentially inform the form finding process to optimize the surfaces that can keep the orientation of the sticks along the direction of the loads distribution but also to assess the concentration of force lines and to avoid or reinforce areas that could potentially be vulnerable to the over bearing of stresses

Fig 3.34 - Evaluation of Structural Values and Force Lines

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Forc of th

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chapter 4:

Design Development and Implementation

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4.1

SITE AND PROGRAMMATIC CONTEXT The site to hold the events organized by the OtemachiMarunouchi-Yurakucho Area is proposed to be in Central Tokyo between the access from Tokyo Station to the Imperial Palace famously known as Gyoko-dori Avenue. It was a site that was famous for its use by the imperial family as a dedicated lane for the familyâ&#x20AC;&#x2122;s horse carriageway. Currently, as it stands the site was renovated and made into pedestrian walkway open for everyone. The site acts as an island between two major arteries and forms a public space between four famous attractions that have the Tokyo Station, the Imperial Palace and then Marunouchi and Shin-Marunouchi Buildings. Gyoko-dori Avenue acts as a thoroughfare for major pedestrian activity in between the buildings in the OMY area and it also becomes an open plaza for special seasonal events and commemoration events due to its proximity to Tokyo station and Imperial Palace. The site is ideal for the event structures as it is surrounded by 206 restaurants that can contribute to the collection of used disposable chopsticks as the main construction material. The underground passageway that connects Tokyo station to the key attractions also holds the seasonal markets weekly where farmers and crop producers come to Tokyo to market their produce from all parts of Japan. The programmable area as described by the event guidelines is taken in consideration with the amount of material that can be collected from within the dedicated restaurants by the OMY authority. The ellipses that were also tested out in the previous section are then adapted to the site and programmatic constraints and the base surface achieved from those considerations are then finally executed through the formal tools developed in Chapter 3.

Fig 4.01 - Evaluation of Structural Values and Force Lines

118

Shin-Marunouchi Building

Marunouchi Building

Thoroughfare

200 m

Thoroughfare

Site

Thoroughfare

Thoroughfare 35 m 119

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Perform

Socialize

Exhibit

Event Space Area Req. = 180 m Fig 4.01 - Programmable Area of the Event

120

Area Req. =

180 m

20.0m

Design Space

Design Mesh for Form Finding 121

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Underground Passageway

Pedestrian Circulation

Underground Passageway

Fig 4.02 - Site Features

122

14.0m

24.0m

Programmable Area

d Programmable Area

No.of clusters depended on the amount of material that can be collected from site.

123

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Bounding Lines Cutting Lines

Fig 4.03 - Elliptical Modifications to Shape according to site constraints.

Area of Programmable Areas scaled up to accomodate Programmatic Requirements 124

Programmable Area

No.of clusters depended on the amount of material that can be collected from site. 125

SYMBIOTICK LANDSCAPES

Form Diagram

Force Diagram

Cluster #01 Fig 4.04 - Generating Furnicular Shells through Manipulation of Force Density Method.

126

Form Diagram

Force Diagram

Cluster #02 127

SYMBIOTICK LANDSCAPES

Form Diagram

Force Diagram

Cluster #03

128

Form Diagram

Force Diagram

Cluster #04 Fig 4.05 - Generating Furnicular Shells through Manipulation of Force Density Method.

129

SYMBIOTICK LANDSCAPES

#01

Fig 4.06 - Evaluating Structural Values through Finite Element Analysis

130

#02

#03

#04

Compression (kN/cm )

Tension (kN/cm )

< 0.010

< 0.0011

> 0.010

> 0.0011 131

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Supports

#01

Fig 4.07 - Extracting Force Flow Lines on Resulting forms through Structural considerations.

132

#02

Supports

#03

#04

133

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Fig 4.08 - Extracting Force Flow Lines on R esulting forms through Structural considerations.

134

135

SYMBIOTICK LANDSCAPES

#01 Fig 4.09 - Surface Distribution of Material with respect to Force Flows.

136

#02

#03

#04

137

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Fig 4.10 - Material Distributed along Force Flow Lines

138

139

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Fig 4.09 - Comparing Force Flow Lines in Shell Structures to Steepest Vector Descent Lines

140

141

SYMBIOTICK LANDSCAPES

4.3

IDENTIFYING DISCREPANCIES BETWEEN FABRICATION AND FORM FINDING The geometries achieved through the Thrust Network Analysis (Rippmann, 2012) and RhinoVault adapted to the site run through the final stage of the Design Loop which evaluates the geometry from the considerations of fabrication (which is dealt in detail in Section 2) and takes the sub-divided panels from Section 2. The sub-divided panels are formulated along the direction of the force flow lines also known as the Steepest Vector Descent Lines that are generated specifically from each geometry. According to the fabrication constraints dealt in depth in Section 2, there is a minimum range on the inclination angle of each sub-divided panel beyond which the sticks cannot be distributed in a desired way according to the lines of the Force Flow. In that case minor adjustments to the geometry have to be done back in the Shape Design Section through RhinoVault.

Î¸

Angle of Inclination < 75 deg.

Î¸

The Figure on the right show the two typologies of panels that exist in terms of their fabrication constraints. Any angle which is beyond 75 degrees or below it are segregated in two categories which allows them to be fabricated positively and negatively.

Angle of Inclination > 75 deg. Fig 4.10 - Sub-divided Panels divided on the basis of Angles of Inclination

142

96.8

76.1 70.3 61.4 68.0

55.9

77.8

60.4

56.3

88.5

109.7

91.3 106.7 116.8 97.0103.3 114.0 91.8 101.3109.5 120.3123.0 96.9 104.9 115.7 112.0 100.4 87.2 93.5 105.8 119.2125.7 95.7 111.7

93.2 88.7 97.6 88.2

97.6

114.8

91.8

90.7 79.2

105.1 100.0 102.2

99.6

119.4

126.4

132.8

97.9 80.5

70.8 89.9 108.8 102.180.0 56.8 56.6 136.5 67.5 123.0 54.8 57.5 99.0 114.5 61.5 82.9 107.7 59.5 55.2 72.5 114.297.075.062.9 86.2 62.4 57.6 45.8 53.7 65.5 139.0 47.1 68.9 76.0 86.4 110.8 127.7 64.3 61.5 50.4 100.8 110.6 65.7 55.1 76.2 69.2 101.0 73.8 78.0 85.394.8 85.1 60.6 63.3 66.3 55.5 40.1 70.5 73.0 135.9142.7 76.0 78.0 82.6 98.0 99.7 118.2 57.9 65.9 71.7 74.3 84.5 78.3 74.9 76.6 79.2 71.9 97.9 78.3 53.5 48.8 33.536.4 45.2 56.3 64.8 76.1 86.5 83.6 103.6 139.4 72.6 96.5 64.8 61.3 44.3 56.0 95.4 35.7 46.4 83.6 107.1 134.5144.8 54.7

88.9

65.8

94.6

40.7 49.5 76.1

66.2 52.4

61.3

71.4

73.8 78.0 70.5 80.7 68.8

85.9

86.9 92.9

71.6 78.5 89.8

77.2

73.8

75.7

71.5 78.6

76.3 78.4

103.1

51.5

38.7

113.4 108.6 97.3

44.3

87.7 72.5

112.1

Fig 4.11 - Sub Divided Panels projecting Angle of Inclination on Entire Geometry

Total No. of Panels < 75 deg. = 129

138.8145.4 62.4 89.3 120.2 57.7 41.6 100.4 132.2 143.8 64.9

35.7

48.2

35.3 33.3 38.7

110.3 131.1 142.1

87.2 73.8

52.7

105.0

82.4 96.9 124.6 138.9

92.7109.4 74.8 85.3 100.9 125.1 65.7 109.1 42.2 98.7 119.4 134.4 31.3 31.3 72.7 85.9 127.1 78.8 98.0 114.4 52.1 122.3 40.1 36.2 72.7 85.8 108.2 128.0 93.7 129.0 64.3 79.4 115.7 90.5 56.5 101.1 121.9 74.8 51.6 123.4 87.7 106.1 71.9 112.6 70.4 83.1 94.8 117.4 65.8 81.3 89.4 103.8 81.0 86.2 77.1 96.0 91.2

Total No. of Panels > 75 deg. = 150

Fig 4.12 - Panels divided into two different typologies.

143

SYMBIOTICK LANDSCAPES

96.8

76.1

93.2 88.7 97.6 88.2

70.3 61.4 68.0

55.9

97.6

88.5

109.7

91.3 106.7 116.8 97.0103.3 114.0 91.8 101.3109.5 120.3123.0 96.9 104.9 115.7 112.0 100.4 87.2 93.5 105.8 119.2125.7 95.7 111.7 99.6 114.8

91.8 79.2

105.1 100.0 102.2

119.4

126.4

132.8

77.8 60.4 97.9 56.3 80.5 70.8 89.9 108.8 102.180.0 56.8 56.6 136.5 67.5 123.0 54.8 57.5 114.5 61.5 82.9 99.0 107.7 59.5 55.2 72.5 97.0 114.2 75.062.9 86.2 62.4 57.6 45.8 53.7 65.5 139.0 47.1 68.9 76.0 86.4 110.8 127.7 64.3 61.5 50.4 100.8 110.6 65.7 55.1 69.2 73.8 76.2 85.3 101.0 85.1 60.6 78.0 63.3 94.8 66.3 55.5 40.1 70.5 73.0 135.9 142.7 76.0 78.0 82.6 98.0 99.7 118.2 57.9 65.9 74.3 71.7 84.5 78.3 74.9 76.6 79.2 71.9 97.9 78.3 53.5 48.8 33.536.4 45.2 56.3 64.8 76.1 86.5 83.6 103.6 139.4 72.6 96.5 64.8 61.3 44.3 56.0 95.4 35.7 46.4 83.6 107.1 134.5144.8 88.9 138.8145.4 65.8 62.4 89.3 120.2 94.6 57.7 41.6 49.5 40.7 100.4 132.2 143.8 64.9 76.1 103.1 66.2 38.7 87.7 51.5 61.3 110.3 85.9 52.4 72.5 71.4 131.1 142.1 112.1 48.2 87.2 77.2 73.8 35.7 113.4 44.3 73.8 105.0 73.8 71.6 78.0 75.7 71.5 70.5 80.7 124.6 138.9 78.5 52.7 82.4 96.9 108.6 68.8 86.9 35.3 76.3 78.6 92.7109.4 33.3 74.8 85.3 89.8 78.4 97.3 38.7 100.9 125.1 92.9 65.7 109.1 42.2 98.7 119.4 134.4 31.3 31.3 72.7 85.9 127.1 78.8 98.0 114.4 52.1 122.3 40.1 36.2 72.7 85.8 108.2 128.0 93.7 129.0 64.3 79.4 115.7 90.5 56.5 101.1 121.9 74.8 51.6 123.4 106.1 87.7 71.9 112.6 70.4 83.1 94.8 117.4 65.8 81.3 89.4 103.8 81.0 86.2 77.1 96.0 91.2 54.7

Fabrication Orientation = Positiv No of Panels = 129 Panels beyond Critical Range of Fabrication = 13

Amongst these panels some of these panels are right at the ends of the spectrum where fabricating them becomes a complication. In order to identify those panels beyond the critical range a script is generated in grasshopper that evaluates the angle of inclination on each panel by extracting the tangent on the center point of their maximum curvature and then calculates the angle by the normal value from that point. Those angles are then projected at each individual panel of the geometry and highlights them in a specific shade of red according to their position in the spectrum of desirable range. This gives us a way of evaluating the geometry through the lens of fabrication possibilities. Minor adjustments to the geometry can let the panels fall in the range of desirable value which is between 20 â&#x20AC;&#x201C; 75 degrees.

96.8

76.1 70.3 61.4 68.0

88.5

109.7

91.3 106.7 116.8 97.0103.3 114.0 91.8 101.3109.5 120.3123.0 96.9 104.9 115.7 112.0 100.4 87.2 93.5 105.8 119.2125.7 95.7 111.7

93.2 88.7 97.6 88.2

97.6

99.6 114.8

126.4

91.8

132.8 55.9 119.4 105.1 102.2 79.2 77.8 100.0 60.4 97.9 56.3 80.5 70.8 89.9 108.8 102.180.0 56.8 56.6 136.5 67.5 123.0 54.8 57.5 114.5 61.5 54.7 82.9 99.0 107.7 59.5 55.2 72.5 114.297.075.062.9 86.2 62.4 57.6 45.8 53.7 65.5 139.0 47.1 68.9 76.0 86.4 110.8 127.7 64.3 61.5 50.4 100.8 110.6 65.7 55.1 69.2 73.8 76.2 85.3 101.0 85.1 60.6 78.0 94.8 63.3 66.3 55.5 40.1 70.5 73.0 135.9 142.7 78.0 82.6 76.0 118.2 57.9 65.9 98.0 99.7 71.7 74.3 84.5 78.3 74.9 76.6 79.2 71.9 97.9 78.3 53.5 48.8 33.536.4 45.2 56.3 64.8 76.1 139.4 86.5 83.6 103.6 72.6 96.5 64.8 61.3 44.3 56.0 95.4 35.7 46.4 83.6 107.1 134.5144.8 88.9

65.8

94.6

40.7 49.5 76.1

66.2 52.4

61.3

73.8 78.0 70.5 80.7 68.8

85.9

71.4

86.9 92.9

71.6 78.5 89.8

73.8 71.5 78.6

77.2 75.7 76.3 78.4

103.1

138.8145.4 62.4 89.3 120.2 57.7 41.6 100.4 132.2 143.8 64.9 51.5

38.7

113.4 108.6 97.3

44.3

87.7 72.5

112.1 35.7

48.2

No of Panels = 150 Panels beyond Critical Range of Fabrication = 15

110.3 131.1 142.1

87.2

105.0

73.8

35.3 33.3 38.7

Fabrication Orientation = Negative

52.7

82.4 96.9 124.6 138.9

77.1

70.4 81.3

81.0 86.2

83.1 94.8 89.4

112.6 117.4

103.8

96.0

91.2

Fig 4.13 - Critical Range Identified based on Angle of Inclination of Panels

Angle of Inclination > 75 deg. 20 144

No of Panels = 279 Panels beyond Critical Range of Fabrication = 28 No of Panels = 232 Panels beyond Critical Range of Fabrication = 5 Fig 4.14 - Evaluating different geometries on the basis of the difference in their fabrication constraints

The same script can also be used to evaluate the optimum curvature of the surface between the different geometries generated as seen by figure on the top. The script identifies the number of panels that fall outside the critical range and can differentiate geometries which are sensitive the fabrication possibilities from the ones that become problematic. The design scheme tries to keep a holistic view of all possible structural, mechanical, fabrication constraints within the development of formal tools and attempts to create a system that would allow self-supporting furnicular geometries to be generated and evaluated according to specific material conditions that allow for a dynamic structurally driven shape.

145

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Fig 4.15 - Top View of Cluster #01 populated with Sticks Distributed along the force Lines

146

Fig 4.16 - Detail A

Fig 4.16 - Detail B

147

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148

26.4 m Fig 4.18 - Plan

15.0m

149

3000mm

SYMBIOTICK LANDSCAPES

150

5100mm Fig 4.19 - Elevation

151

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154

155

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CONCLUSION

The Linear Aggregate System is a novel construction and architectural prototypical system that is in response to the current economic, environmental and social conditions of Japan and could also contribute to the larger context of the developing countries of the world. This material system possesses solutions to crucial problems that the current construction industry is facing. This system addresses problems such as the shortage of skilled labor in the times of increasing depopulation of developed countries such as Japan and creates space to allow such material systems to synthesize with crafts based and completely automated systems to create new hybrids where the use of craft is embedded within the material and technology that allows the system to be aware of the material intelligence and explores the complexities in form and material behavior by constantly evaluating and regenerating the solutions it provides. By creating a feedback evaluation process, it is easy to integrate considerations that arise from structure, fabrication, program, material behavior and create one platform to address all the issues that parametrically feedback to optimize the resulting geometry. This research deals with issues of eliminating formwork in the first part where by employing uncontrolled aggregation, it is possible to achieve complex geometries without the need of any formwork. This reduces the cost that results from putting in place the formwork required to conventionally to support complex geometries. With the uncontrolled aggregation logic, it is possible to achieve considerable heights of the system without relying on any sort of scaffold or framework. However in the second part, where the force flow distribution is introduced, a limited amount of formwork has to be put in place for the sticks to fall freely under gravity to achieve the desired striated patterns. Ideally, one aspect that needs to be further explored is to devise a fabrication system that could reduce the amount of formwork that is employed in the fabrication and assembly part or at least bring it back to the same amount of formwork that was employed with the uncontrolled aggregation.

156

Generating compression only surfaces for the linear aggregate system is a successful way of minimizing the unwanted tension from the geometry. This allows the material system to be used in surfaces that can stretch to spans up to 25 meters which could not have been possible from the old material values. Different aggregates need to be tested with this material system and to ascertain how by the use of different geometries, different lengths of each members, the parameters or the mechanical properties could change.

157

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158

BIBLIOGRAPHY

Chapter 2 Tibbits, Skylar. “4D Printing: Multi-Material Shape Change.” High Definition Zero Tolerance in Design and Production AD. Ed. Bob Sheil. Wiley, 2014. Print. Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities, and Software. New York: Scribner, 2001. Print Bagnold, R. A. The Physics of Blown Sand and Desert Dunes. London: Chapman & Hall, 1971. Print Cambou, Bernard. Behaviour of Granular Materials. Wien: Springer, 1998. Print Hensel, Michael, and Achim Menges. “Aggregates.” Versatility and Vicissitude: Performance in Morpho-ecological Design. London: Wiley, 2008. Print. Yoshida, Hiro. STIK: Architecture-Scale Additive Manufacturing with Chopsticks, Hand-Held Dispenser, and Projection Mapping. The University of Tokyo. 2015. Paper Chapter 3 Ludwig, Ferdinand, and Hannes Schwertfeger. “Living Systems Designing Growth in Baubotanik.” Architectural Design. 2nd ed. Vol. 82. Wiley, 2012. 82. Print. Yoshida, Hiro. STIK: Architecture-Scale Additive Manufacturing with Chopsticks, Hand-Held Dispenser, and Projection Mapping. The University of Tokyo. 2015. Paper Adriaenssens, Sigrid, Philippe Block, Diederik Veenendaal, and Chris Williams, eds. Shell Structures for Architecture: Form Finding and Optimization. Routledge, 2014. Print. Rippmann Matthias, Philippe Block. Rethinking Structural masonry: unreinforced, stone-cut shells. ICE, 2012. Rippmann Matthias, Lorenz Lachauer, Philippe Block. Interactive Vault Design. International Journal of Space Structures. Vol 27 Number 4. 2012

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FIGURE CITATIONS:

Chapter 1: Figure 1.4 - OMY Road-Map - Source: http://www.ecozzeria.jp/images/english/index/pdf/csr2009en.pdf Chapter 2: Figure 2.1 - Man vs. Machine – Source: Figure 2.2 – Forest and the City – Source: http://image.haosou.com/i?src=360baike_sidepicmore&q=%E6%A3%A E%E6%9E%97%E7%94%9F%E7%89%A9 Source: http://www.factrange.com/11-countries-with-worlds-fastest-internet-speeds/ Figure 2.3 – Robots 3-d printing a bridge: Source: http://www.businessinsider.com/robots-to-build-a-3d-printed-bridge-in-amsterdam-2015-6 Figure 2.4 – Contour Crafting - Source: https://homes.yahoo.com/blogs/spaces/3d-printing-homes-223421156. html Figure 2.5 – FabClay – Barcalona - Source: http://www.scoop.it/t/rhizome-thoughts/p/3996739559/2013/02/12/ fabclay-by-sasha-jokic-starsk-lara-and-nasim-fashami-the-method-case Figure 2.6 – Ant Bridge - https://6legs2many.wordpress.com/2011/07/08/ant-bridge/ Figure 2.8 – Desert Formations – Source: http://www.nationalgeographic.com/wallpaper/photography/photos/mysterious-earth/empty-quarter-dunes/ Figure 2.9 – Detail from Circus Sideshow – Source: File:Seurat-La_Parade_detail.jpg

https://en.wikipedia.org/wiki/Georges_Seurat#/media/

Fig 2.10 – Emergence in Pointilism – Source: https://en.wikipedia.org/wiki/Georges_Seurat#/media/File:SeuratLa_Parade_detail.jpg Fig 2.11 – Frei Otto - Source: http://galleryhip.com/frei-otto-book.html Fig 2.16 – Aggregates Installation Rice University 2009 – Source: http://www.achimmenges.net/?p=4419 Fig 2.17 – Detail - Aggregates Installation Rice University - Source: http://www.achimmenges.net/?p=4419 Chapter 3: Fig 3.1 – Wooden Bark Source: https://ndktravels.wordpress.com/page/12/

160

Fig 3.2 – Detail Wooden Fiber Orientation Source: https://ndktravels.wordpress.com/page/12/ Fig 3.15 - Bundesgartenschau Pavilion, with a 12mm fibre reinforced concrete shell, Stuttgart, 1977 Source: Adriaenssens, Sigrid, Philippe Block, Diederik Veenendaal, and Chris Williams, eds. Shell Structures for Architecture: Form Finding and Optimization. Routledge, 2014. Print. Fig 3.16 – Multihalle in Mannheim Source: http://www.wikiwand.com/de/Multihalle Fig 3.29 – Force Lines in a Shell. Source: https://en.wikipedia.org/wiki/Stress_concentration Fig 3.30 - Force lines in a plate with a central crack. Source: https://en.wikipedia.org/wiki/Stress_concentration#/media/File:HoleForceLines.svg

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162