In space geometry
A sphere without edges and corners
Is the most perfect!
The surface potential energy of a sphere is the smallest, which is why bubbles, balloons, inflatable structures and even celestial bodies become spherical.
Space windsurfing ball of "Beijing Institute of Technology 1" satellite
Space sail ball: After the satellite enters the orbit normally, it releases flexible materials and unfolds into a sphere, just like opening a "sail", which can be used as a solar panel of the satellite and a large antenna for satellite communication.
In mechanics, when a sphere is subjected to uniform tension or pressure, it only bears axial tension or pressure. Spherical shell is a very efficient structural form, just as it is difficult for us to break a thin eggshell with our hands.
American Pavilion at the Montreal World Expo, Space Sphere, 1967.
The pressure vessel for storing gas and liquid is always spherical. Because of the same surface area, the spherical shell has the largest volume, which has the characteristics of light weight and high efficiency.
Spherical storage tank
Under the same diameter and working pressure, the plate thickness is only half of that of a cylindrical storage tank.
Because of the unique shape, efficient stress and charm of the sphere, there are also many excellent cases in architectural design. The small I team is designing a spherical structure recently. This article takes this opportunity to share with you the cases we collected.
Spherical shell grid form
The grid forms of spherical reticulated shells are: geodesic grid dome, ribbed dome with ribbed ring, joint thin plate dome, Schwedler dome, Kewitt dome and so on.
Ribbed dome with ribbed ring
Lian Fang thin-plate dome
Schwedler Dome (No Oblique Weft)
Fuller and geodesic dome
Around 1927, Fuller developed a new spherical measurement and projection mapping strategy called Dymaxion map, which transformed spherical terrain into a series of planar triangles and squares. "By controlling the distortion caused by projection drawing, the size of the land on the map can keep a more accurate proportion with reality. Because these geometric elements can be rearranged, we can "peel off" the earth in countless different ways. "
Map of Fuller and Demaxian (1945)
Kyle Van Hemert's fuller illustration.
Fuller combined the idea of Dymaxion map with energy geometry and invented geodesic dome. Geodesic is the shortest straight line connecting two points on a surface.
Fuller-geodesic dome patent
At the 1967 Montreal International Expo, Fuller and Shoji Sadao designed a 3/4 spherical building with a diameter of 76m, and its outer surface was covered with transparent acrylic board. This exhibition hall has become a symbol of American advanced technology, attracting worldwide attention.
Fuller and Montreal World Expo USA Pavilion (1967)
1976, the dome was caught in a fire during reconstruction.
The exterior decoration was burned and the exposed structure became clearer.
In addition to the USA Pavilion in Montreal, Fuller also designed many spherical structures, including fly-eye domes and tensegrity spherical structures.
The fly's eye dome designed and built by Fuller, 1965.
Icosahedron based on geodesic dome structure
Fuller believes that "there is a system in nature that can provide maximum strength with the least materials, and the basic units of quadrangular pyramid and octahedron will become the most efficient spatial structure".
Coincidentally, in 1985, H.W. Kroto and R.E.Smalley discovered the third crystal form of carbon (the first two are diamond and graphite). To commemorate Fuller's early conjecture, he named it "Fullerene"-C60. Its molecular structure is spherical with 32 faces, and its carbon atoms are connected by 20 six-membered rings and 12 five-membered rings, which has strong molecular stability.
Fullerenes, soccer balls and grid balls all have similar structures.
Spheres can be composed of regular hexagons and regular pentagons.
And the number of pentagons must be 12.
Orlando Disney's earth spacecraft is designed for passengers to travel through the time machine, and it also adopts the form of short-distance grid.
Spacecraft earth
The difference is that the spaceship earth is a complete sphere, with a single-layer structure instead of a double-layer structure, with a diameter of 50m and supported by three huge inclined columns. The surface of the sphere is covered with a folding aluminum plate, which makes the sphere look more textured.
Spherically covered folded aluminum plate
***3840 node, 1 1324 aluminum plate.
Amazon sphere
Amazon spent a lot of money to build three glass balls in Seattle headquarters, which are called Amazon spheres. Hundreds of lush plants are planted inside the spherical building, creating an indoor version of the "Amazon Rainforest" in the core area of the metropolis.
Amazon Spheres*** has 2643 glass curtain walls. Four layers of ultra-white glass should not only reduce the thermal radiation of sunlight, but also ensure the light necessary for plant photosynthesis.
The total length of the building is about 40 meters, and the diameter of the sphere is about 24-29m, like three bubbles that interfere with each other. The structural material is a combination of glass and steel structure. The design team used a unique grid method to divide the spheres.
A future organic structure framework.
You can also vaguely see the traces of regular pentagons and hexagons.
Grid modeling seems complicated, but its generation logic comes from regular fullerene or football grid. The process of mesh generation is to divide the Pentagon into five parts and merge them with adjacent hexagons to form a basic unit; Then the basic unit is divided into five parts with the center point as the center, and the boundaries of adjacent basic units are fused to obtain the structural grid of Amazon sphere.
Structured Grid Generation Logic of Amazon Spheres
Although Amazon Spheres has become the new punching place for network celebrities in Seattle, we have to talk about its curtain wall plate design. As can be seen from the above figure, the steel structure grid not only has the organic sense of dynamic curve, but also has clear logical design. However, after covering the triangular glass curtain wall rudely, the architectural effect is greatly reduced.
The steel skeleton has smooth lines.
The main frame is connected by steel plates to enhance the integrity of the structure.
Detail drawing of steel structure skeleton module
Hanging bird's nest meeting room
The best place for lighting on the top floor is the rest area. Take a nap in the sun, wake up and go to work in high spirits.
Ribbed dome with ribbed ring
Rib ring is simple in form and structure, and there are many cases of this spherical building.
Ericsson Spherical Gymnasium
Ericsson Globe, Ericsson Spherical Gymnasium, 1989
Ericsson Globe in Stockholm, Sweden, designed by Svante Berg and Lars Fratblad, is probably the largest spherical building in the world. The diameter is110m, the internal height is 85m, and the volume is 600,000m2, which can accommodate 16000 spectators.
Profile of building structure
The performance venue and stands in the lower part of the building are reinforced concrete structures, and the hemispherical roof in the upper part is a double-layer grid structure in the form of rib rings. The surface is evenly covered with a white metal plate, just like a golf ball.
The cable car outside 20 10 has been opened, which is called Tianjing.
New German Parliament Building
The ribbed dome was also selected for the reconstruction of the German Reichstag designed by norman foster, which became an important city landmark in Berlin like a lighthouse on the city skyline.
Renovation draws inspiration from the original building. On the one hand, it retains the signboard of the old stonemason and the slogan left by the Soviet Red Army in 1945 as its own history museum; On the other hand, under the heavy shell is a light and transparent interior, and the 360-degree perspective reveals the beauty of Berlin, which is in sharp contrast with the old buildings. The public domain of the building extends from the roof to the terrace restaurant and dome, and the spiral passage leads people to the dome and observation deck.
The dome steel reticulated shell structure is as transparent as possible, and the expression of components and detailed nodes is also exquisite. Although the structure itself is not very difficult and innovative, it has achieved good results through the exquisite expression of the exposed steel structure itself.
Square spherical shell thin plate dome
In the early days of the Amazon Spheres project introduced earlier, the design scheme also considered using Lamella Dome, but it was not as expressive as the later scheme.
Initial square spherical shell scheme of Amazon ball
In the completed spherical buildings, Union Square is rarely used. The main reason is that the size of the cube grid is quite different, and the top rods of the sphere are densely connected, while the middle of the sphere is sparse, and the rods are different in length. Differentiated grids make it difficult to adopt uniform components for the structure and curtain wall, which increases the construction cost.
Concept scheme of Dubai science and technology ball
Limited by space, the following cases will not be developed in detail. In a word, spherical architecture is an architectural form with infinite design potential.
LaGéode is a spherical cinema designed by architect Adrien Fainsilber and engineer Gérard Chamayou. Mirror stainless steel reflects the beautiful city scenery of Paris on the building surface.
LaGéode mirror stainless steel spherical building
Mirror stainless steel spherical building of China Science and Technology Museum
Two spherical buildings of Shanghai International Conference Center
Together with the adjacent Oriental Pearl, it forms a scene in which pearls of all sizes are poured into a plate of jade.
Various ball screen cinema structures
Various radomes
Innovative spherical shell grid
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