20.301 Material Computation: Advanced Topics in Geometry and Matter Design Report

M AT E R I A L C O M P U TAT I O N C L I F F O R D

M A R I O

DESIGN

K O S A S I H

| SPRING 2015

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All pictures are taken by : Clifford Mario Kosasih, Chen Yutong, Lee Fu Hui, Ng Yi Jin, Tay Jenn Chong, Chow Man Yee, Goh Yi Qian, and Melissa Estella Lim

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introduction: material computation frame analysis shell analysis shell and frame analysis brick fabrication robotic fabrication

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This design report documents 7 weeks of exploration and investigation involving structural analysis, digital fabrication and material optimization, applied using various computational tools. By evaluating the possibilities of material computation, we formulate design problems using computational methods and technologies and decide to further explore the design of a staircase. This design project aims to re-think and redefine how staircase is designed with respect to its structural stability and material distribution, contributing to new design typology

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This design exploration focuses on the effect of material distribution of a canopy design on its structural strength and a b i l i t y. T h e c a n o p y f r a m e n e e d s t o b e c a n t i l e v e r e d 1 0 m e t e r s f r o m a w a l l a n d t h e r e i s o n l y 3 . 5 6 m e t e r s o f a l l o w a n c e

f o r t h e c a n o p y f r a m e t o h a v e e x t r a s u p p o r t v e r t i c a l l y.

Diagram 001 Setting up condition for canopy frame design

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Looking at simple moment diagrams for both loading conditions, it can be interpreted that more material needs to be d i s t r i b u t e d n e a r e r t o t h e w a l l i n s t e a d o f f u r t h e r a w a y. C o m p a r i n g t h e p o i n t l o a d c o n d i t i o n a n d t h e c o n t i n u o u s l o a d condition, it can be seen that the moment diagram for the former condition is a linear graph, while the latter condition i s c u r v e d . B y u n d e r s t a n d i n g t h e m o m e n t d i a g r a m f o r a c a n t i l e v e r, w e c a n b e b e t t e r i n f o r m e d i n c o n c e p t u a l i z i n g t h e canopy frame design.

Diagram 002 Moment diagram for point load condition

Diagram 003 Moment diagram for continuous load condition

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The design tries to simulate the condition shown by the moment diagrams above. Along the longer side of the canopy frame, the longer members of the frame alternates in its origin, from the top and bottom. This provides the structural support as shown by the moment

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Image 001 Render view

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Image 002 Plan view

Image 003 Side elevation view

Material: Steel Radius: 0.1 m Maximum deflection: 1.688 mm

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Image 004 Front elevation view

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The shell canopy needs to cover a span of 10m between two buildings. It can be supported from both sides of the

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building. Furthermore, this canopy needs to have deflection less than 5mm.

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Similar to the cantilever frame canopy before, it is structurally better for the shell canopy to have a variation in hight a l o n g t h e z - a x i s . S i n c e w e h a v e t w o s i d e s o f t h e b u i l d i n g n o w, t h e e s s e n t i a l p a r t t o t a k e n o t e o f i s t h e m i d d l e p o r t i o n o f t h e c a n o p y, w h e r e t h e m o s t d e f l e c t i o n w i l l b e m o s t l i k e l y t o o c c u r. T h e r e f o r e , b y m i r r o r i n g t h e p r o f i l e o f t h e c a n o p y f r o m o n e t o t h e o t h e r, i t i s a b l e t o p r o v i d e e x t r a s u p p o r t f o r t h e d e f l e c t i o n .

Higher positive amplitude Lower positive amplitude Higher negative amplitude

Higher positive amplitude Lower positive amplitude Higher negative amplitude

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I m a g e 0 0 5 R e n d e r v i 14 ew

The canopy is formed by lofting two curves together and creating intertwining shell. With thickness of 0.411m, the deflection stands at 0.277mm, which is far below the allowable deflection of 5mm.

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Image 006 Plan view

Image 007 Front elevation view

Material: Concrete Thickness: 0.411m Maximum deflection: 0.277mm

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Image 008 Side elevation view

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The shell and frame canopy needs to cover the space between two 50m long buildings separated 12m apart. The coverage needs to be at least 80% and the boundary condition needs to be â&#x20AC;&#x153;simply supportedâ&#x20AC;?. Furthermore, the m a x i m u m a l l o w a b l e d e f l e c t i o n s h o u l d b e c a l c u l a t e d f r o m s p a n / 3 0 0 . A d d i t i o n a l l y, t h e m a x i m u m a l l o w a b l e s t r e s s i s

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12MPa for steel, 30MPa for concrete and 15MPa for wood.

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Through form-finding from past precedents, the most efficient way for forces to run through matter is to form a c a t e n a r y s t r u c t u r e . T h e r e f o r e , t h i s d e s i g n e x p l o r a t i o n f o c u s e s o n t h e c a t e n a r y f o r m o f a s h e l l c a n o p y. K n o w i n g a b o u t t h e c a t e n a r y f u n c t i o n i s e s s e n t i a l i n t h i s d e s i g n e x e r c i s e a s t h a t i s t h e m a i n d r i v i n g f o r c e o f t h e f o r m o f t h e c a n o p y.

The parametric catenary function is as follows:

‫ݔ‬ሺ‫ݐ‬ሻ ൌ ‫ݐ‬ ͳ ‫ݕ‬ሺ‫ݐ‬ሻ ൌ ܽሺ݁ ௧Τ௔ ൅ ݁ ି௧Τ௔ ሻ ʹ where t = 0 corresponds to the vertex and a equals to the parameter that determines how quickly a catenary graph opens up.

Catenary shape forms the cross section of the canopy and through the long section, the parameter a changes so as to give different spatial experience. The entrance and the exit will have higher parameter a so as to create a larger v o l u m e s p a c e a s c o m p a r e d t o t h e m i d d l e p o r t i o n . L a s t l y, t o c r e a t e h o l e s i n o r d e r t o p r o v i d e v e n t i l a t i o n t o t h e s p a c e u n d e r t h e c a n o p y, t h e f o r m i s i n f l u e n c e d b y s i n e c u r v e i n t h e p l a n v i e w s o a s t o c r e a t e t h i s m e a n d e r i n g f o r m .

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Image 010 Plan view

Image 011 Front elevation view

Frame material: Steel

Maximum stress on frame: 70.688

Shell material: Concrete

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Radius: 0.1 m

Maxmium stress on shell: 13.877MPa

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Image 012 Side elevation view

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Bricks of different quality (i.e. hard, medium and soft) are needed to visualize topology optimization in the physical world. A group of 11 students explored different materials and methods of production to end up with concrete and casting. Here are the documentations of different bricks produced as experimentation as well as the actual mass

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production of the concrete bricks.

To p r o d u c e a s o f t o r t r a n s l u c e n t c u b e , w e d e c i d e d t o m e l t g l u e stick and mold them into a cube. We needed about less than 10 glue sticks in order to fill up 5cm x 5cm x 5cm cube. It is a tedious and long process to melt the glue stick first then pour it into the mold. It takes almost 2 days to harden, after which the soft or translucent quality is not really successful since the cube turns more opaque as it hardens. Also, it is

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very difficult to remove the mold after it hardens.

To p r o d u c e a c u b e w i t h f u l l o p a c i t y , w e d e c i d e d t o m e l t c a n d l e wax and mold them into a cube. The result is pretty successful w i t h t h e c u b e s t i l l i n t a c t a f t e r t h e m o l d i s r e m o v e d . H o w e v e r, the options of varying its opacity or quality are very limited as it can only represent the hard cube.

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W e e x p e r i m e n t e d w i t h s t y r o f o a m c u b e s b y c u t t i n g h o l e s i n i t u s i n g t h e f o a m c u t t e r. T h e r e s u l t i s p r e t t y r a n d o m a n d chaotic, yet this is the beginning of the idea of creating holes on an opaque material to produce cubes with different

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quality (i.e. hard to soft) instead of varying the materials from hard to soft.

This is the latest iteration that we did before our concrete cubes. The design idea begins with creating holes in order

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t o a c h i e v e t h e v a r y i n g q u a l i t y. I n t h i s c a s e , i t i s t r a n s l a t e d i n t o t h e d i f f e r e n t t h i c k n e s s o f p a p e r i n o r d e r t o f i l l i n t h e

S t i l l s t i c k i n g t o t h e i d e a o f m o l d i n g , w e t r i e d t o m o l d d i f f e r e n t m a t e r i a l s n o w i n c l u d i n g n e w s p a p e r, p l a s t i c b a g a n d t i s s u e p a p e r. U s i n g a m i x t u r e o f e a c h m a t e r i a l a n d w h i t e g l u e ( p a p e r - m a c h e ) , w e p u t t h e m i n s i d e t h e m o l d f o r a f e w days in the hope that they will harden over time.

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We decided to carry on with casting concrete and mass produce our cubes. By varying the opening in the concrete, we can achieve the three different qualities needed for the cubes: soft, medium and hard. The following pages documents the process in which the concrete casting was done.

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soft

medium

3c

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x 3 cm

2c

m

x

hard

m 2c

x 2 c

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1c

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c x 1

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The design focuses on creating holes on the sides of the cubes.

By changing the size of the hole from 3cm x 3cm to 1cm x 1cm, we h a v e m a n a g e d t o v a r y t h e q u a l i t y o f t h e c u b e s . A d d i t i o n a l l y, s m a l l e r

1c

m

x 1 cm

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m

c x 0

m

hole is added to the side of the cubes (with decreasing size as well) so as to add another dimension to the design.

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smaller side can fit in to the larger

the best concrete mix in order for it

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to harden promptly while maintaining

have

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with two openings of different sizes

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observed

to

at the two sides, it is important to

removal

stick in styrofoam in order to make

note that the styrofoam fillings need

from the above picture, we vary the

the hole, it is very difficult to do

t o f i t i n t o o n e a n o t h e r. T h e r e f o r e ,

proportion of concrete aggregates

1 0 h o l e s a t o n c e . A d d i t i o n a l l y, t o

tolerance is needed as well.

and

that

when

we

need

materiality

process.

water

remove the mold of 10 bricks side

different

b y s i d e i s h a r d e r t h a n 5 b r i c k s o n l y.

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during

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we

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Therefore, we decided to reduce to 2 rows of 5 cubes. Furthermore, the teeth need to be carefully designed with tolereance so that all the parts c a n f i t t o g e t h e r n i c e l y. I n t h e e n d , we still need to put masking tape all around the mold to secure them.

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casting

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right

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we To

mix

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In order to be able to remove the

of

After all the mold has been filled

started

with concrete, we need to wait for

hardens, we need to layer the inner

the

be

more

approximately one day for it to fully

side of the mold with oil. This is

efficient, this process needs to be

cure.

done before every batch of casting.

done in groups of 3-4 people. One

we can remove it slowly by firstly

person to continue mixing concrete

taking

w i t h t h e r i g h t a m o u n t o f w a t e r, a n d

removing the styrofoam filling. With

two to three people need to assist

the layer of oil, it is easier for the

with layering the mold with oil as

mold to be removed.

After out

the the

concrete masking

hardens, tape,

and

well as the casting process itself.

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A f t e r p r o d u c i n g t h e c u b e s t h r e e v a r y i n g o p a c i t y, w e c a n v i s u a l i z e p h y s i c a l l y a 3 D t o p o l o g y o p t i m i z a t i o n c o n d i t i o n b y a r r a n g i n g t h e c u b e s u s i n g r o b o t i c a r m s . F i r s t l y, w e n e e d t o d e t e r m i n e a s c e n a r i o w h e r e 3 D t o p o l o g y o p t i m i z a t i o n c a n be performed. In this case, we are experimenting with one support at the end and one load at the other end of the

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load

support

mesh 30

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After feeding the list of shades into the code to generate

the source plane, we match the number 0, 1 and 2 with the

respective origin planes of the cubes.

0

1

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To d e t e r m i n e t h e t a r g e t p l a n e , w e n e e d t o c o n s i d e r t h e

constraint of the robotic arms, where it can only extend

up to 1m radius. Therefore, we need to make sure that

when the robot is placing the cubes according to the

target plane, it must be within the range as well as on

the table.

33

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the

the cubes up.

A d d i t i o n a l l y,

solutions.

suction

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Suction system may not be strong enough to hold Improving

system other

is

one

system

of

the

such

as

g r a b i n g c a n b e c o n s i d e r e d . L a s t l y, f o r q u i c k f i x we can just hold it down with our hands or allow for more resting time for the suction system to properly grab the cubes and let them go.

Inaccuracies of the source cubes placement.

The

source

base

is

a

good

idea,

nonetheless

there needs to be some tolerance for the cubes, s o t h a t i t c a n b e l i f t e d u p e a s i l y.

A d j a c e n t c u b e s a r e h i t t i n g o n e a n o t h e r d u e t o To l e r a n c e o f 5 m m t o 1 0 m m i s n e e d e d f o r t h e r o b o t the

inaccuracies

of

the

robot

and

the

cubes to be able to safely place the adjacent cubes

fabrication.

w i t h o u t h i t t i n g o n e a n o t h e r.

Cubes are difficult to grab.

The design of the cubes needs to be light yet easily transportable using the suction system.

Our

concrete

cubes

are

not

suitable

for

this,

therefore the other design using wood is a better option.

Nonetheless,

the

design

of

the

least

opaque cube needs to be reconsidered as there is barely any surface for the suction to grab them.

Manual supply of the cubes to the robot.

This can be one by providing a simple incline storage of cubes where all the cubes move down by itself due to the inclinationwhen the first cube is removed.

35

M AT E R I A L C L I F F O R D

C O M P U TAT I O N M A R I O

K O S A S I H

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