ARC20001 Eddy de Leon Nick Aylward Sean Yu
KOI
MINIMAL SURFACE In mathematics, a minimal surface is a surface that locally minimizes its area.
CONTENTS *
PRECEDENT STUDY
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DEVELOPABLE SURFACES
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ORIGINAL DESIGN
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INITIAL PROTOTYPES
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NEW PROTOTYPE
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SITE SELECTION
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DESIGN DEVELOPMENT
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ITERATIONS
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FINAL RENDERS
The term is used because these surfaces originally arose as surfaces that minimized total surfaces area subject to some constraint.
TENSILE STRUCTURE In mathematics, a minimal surface is a surface that locally minimizes its area. The term is used because these surfaces originally arose as surfaces that minimized total surfaces area subject to some constraint.
PR EC EDENT STUDY CRITICAL ANALYSIS
DIGITAL ARCHITECTURE LAB
UNIVERSITY OF STUTTGART
FREI OTTO
AGGREGATED POROSITY
DEEP SURFACE PROTOTYPE
MUNICH OLYMPIC STADIUM
Chasha, China
Stuttgart, Germany
Munich, Germany
Tensile
Tensile
Tensile
2011
2013
1972
DIGITAL ARCHITECTURE LAB Canopy Design
01
02
03
FABRICATION
CONSTRUCTION
MATERIALS
Within the dynamic form, curvature
Panels are doubly curved in most area of
A steel cable mesh is designed as an
varies across the surface. Such a
the surface, and in between panels lack
immediate support structure between
curvature variation provides a basic
any openings. Considering the available
the primary frame and the hexagonal
input for the propagated component to
panel fabrication technique and material
panels. A customized joint is designed
create differentiated openings. Several
being laser-cut plywood, it’s essential to
to fix the panels on the cable meshes,
steps of optimization have been taken
ensure that all panels are flat.
while it also gives enough flexibility
to subdivide the surface: by looking for a balanced point between the most dynamic grid which result in drastic variation in the shape/size of grid cells and the most identical grid cells’ shape that breaks the grid continuity at some high curvature areas. An orthogonal surface grid is chosen to generate a hexagonal array of panels. Extensive panels are automatically eliminated when they fall out of the surface domain.
After the propagation stategy, all hexagonal panels are flattened by projection in a manner to keep 3 points constraint to their original location and projecting the other 3 to a flat plane. This provides a method to constrain the hexagonal panels at 3 of its vertices, while freeing up the other 3 to produce openings where the surface curvature becomes radical. A second stream of triangular holes on the panels are deployed where the panels are very large.
between panels to absorb the construction tolerance and natural deformation due to gravity. The joint is made from using cable clamps, bolts and custom fabricated like 9mm MDF spacers and 0.4mm steel plates. The slots cut out from the plywood panels align perpendicularly to the slot on the stainless steel plate. When combined with the flexibility of the panel itself, they provide a joint that is flexible and manipulatable in 3 axes.
UNIVERSITY OF STUTTGARD Deep Surface Prototype
01
02
03
FABRICATION
CONSTRUCTION
MATERIALS
The Hyper-Torodial Deep Surface
Use of anchorage points and mesh within
Provided the computer generated
Prototype shows the investigation of
different locations it creates a baseline
design, the use of algorithms has
computer generated design. It illustrates
and boundary for which the surface is
been incorporated in the template to
cell-based membranes morphologies
constrained within. As the tension and
ensure that the structure is able to be
created as purely tensioned structure
anchorage points dictate and warp the
constructed physically in a practical
with the distributed anchorage points
surface to show some basic behaviours
manner within specifications for the
and interconnected elements. As
of meshes and tensioned surfaces.
acquired material performances and
tension has a continuous flow through the structure of multiple surfaces and
The origin of this structure’s design
limitations.
and orientation is processed by a
The final structure boasts surfaces and
cables and mesh materials.
simulation engine highly based on
geometry that are manufactured on a
particles and springs. Based highly
large scale plotter providing an easy
As the geometry’s surfaces diversify
through the evolution of both physical
process creating the essential surface.
throughout the structure, the tension and
and computational studies with a basic
surface behaviour greatly varies.
central origin. The inclusion of cable
cylindrical geometries made through
loading points within the geometries provides more centered locations it backs further tension and allows the creation of more extreme components.
FREI OTTO Munich Olympic Stadium
01
02
03
FABRICATION
CONSTRUCTION
MATERIALS
The roof of the Olympic Stadium in
The metal frame created numerous
Large pipes and steel cables have been
Munich was developed based on the
minimal surfaces and also provided
incorporated into the construction as an
use of computerized mathematical
minimal weight. The surface tension of
immediate support to the canopy. These
procedures in determining the form and
these forms are completely balanced,
cables range from 65 to 400 meters long.
behaviour of the structure, resulting in an
providing a very stable construction.
architectural form of “minimal surfaces”.
The cover membrane is suspended by
The metal frame created numerous minimal surfaces also provided minimal weight. The surface tension of these forms are completely balanced, providing a very stable construction. The cover membrane is suspended by a multitude of vertical masts enabling sharp bends winding surface draping dynamically changing flow through the space possessing scale and sectional characteristics.
a multitude of vertical masts enabling sharp bends winding surface draping dynamically changing flow through the space possessing scale and sectional characteristics. Because of the precision in calculations of the structural system and the membrane, these structural components were manufactured offsite. This level of high precision allows the easy assembly for one of the most innovative and complex structural systems that have been worked only with the premise of stress.
The enclosure of the structure consists of a sheet of of PVC-coated polyester, 2.9 x 29m and 4mm thick. To avoid deformations due to temperature, valves rest on neoprene. Structural members such as straps, parallel cords, knots, cast steel clamps, masts steel tubes, and acrylic (Plexiglas) have all been utilized for the construction.
D E VE LO PA B LE S UR FACES RESEARCH
DEVELOPABLE
DEFINITION:
SURFACES ALLOW
Forms are called ‘developable’ or ‘single curved’ when they can be created
ROUND FORMS TO BE CONST RUCTED WITH PLANAR
through ordinary bending of a planar surface without distortion of the material. These surfaces are characterized by only bending in one direction at a time, like a cylinder or cone. Developable surfaces are used for the construction of ships, tent sewing, fabrication of ventilation ducts, buildings, and all kinds of architectural structures.
MATERIALS SUCH AS: PLYWOOD SHEET METAL FABRIC
TYPES: Cylindrically Developable Conically Developable Poly-conically Developable Super-poly-conically Developable
ORIGINAL DESIGN
INITIAL PROTOTYPES
CONSTR UCTI ON PROTOTYPE II
CONSTRUCTING AND TESTING THE PROTOTYPE PROVIDED ABILITY TO ANALYSE AN ACCURATE PHYSICAL REPRESENTATION OF THE DIGITAL GEOMETRY.
RHS Steel Tubing 12.5mm thick 500mm x 500mm
Galvanised Wire 0.9mm thick
Washer 0.9mm Galvanised
CONSTR UCTI ON PROTOTYPE III
IN ORDER TO PUSH THE GEOMETRY EVEN FURTHER, THE APPLICATION OF TIMBER PANELS HAS BEEN INCORPORATED INTO THE 3RD PROTOTYPE AND EVENTUALLY, INTO THE FINAL DESIGN.
RHS Steel Tubing 12.5mm thick 500mm x 500mm
Galvanised Wire 0.9mm thick
Bamboo LaserPly - Natural 1mm thick 1200mm x 600mm
NEW PROTOTYPE
SITE SELECTION
Path Diagram
Se Se le lec ct te ed d ArAre ea a
Se le ct ed Ar ea
Site Project Project SiteProject Site
DESIGN DEVELOPMENT
Isometric View
Northeast
Southeast
Tension Simulation
Southwest
Northwest
Plan View Voronoi Mesh
Curving Voronoi Top Plate
Plan View Gravity Simulation
North Ele
Outer + Mesh + Inner
Pulling Curve
Plan View Pulling Curve
ew sh
ew on
Site Plan
Site Plan Re - Simulation (Final)
Re - Simulation (Final)
North Elev.
South Elev.
East Elev.
West Elev.
ITERATIONS