Novel method of construction using a geodesic honeycomb skeleton

Abstract

A method of construction by which the framework of various structures can be erected in a Geodesic manner is proposed. These structures are Geodesic in that they are comprised of a large number of a few identical parts and such that the pressure on the structure is distributed throughout the structure: In this case, the thicker the Dimensions of the parts the greater the strength of the structure. This method uses Hexagonal and Pentagonal cylinders as the main parts of the Geodesic structure, and similar Geodesic structures were proposed and built by the American Architect, the late R. Buckminster Fuller in the early 1960's. and many variations of Geodesics have been proposed and built since then. The concept has a mirror in the Molecular World, Specifically, the Carbon-60 Molecule discovered in 1985; The parent of a new family of molecular structures known as fullerenes named in honor of R. Buckminster Fuller. It is of special interest to note that R. Buckminster Fuller proposed that Domes assembled in a Geodesic manner would be extremely strong: These Domes mirror the molecular World, the Carbon-60 molecule, and it has transpired that the carbon-60 molecule is the strongest molecule known for it's size. Thus, this proposed method of construction would provide structures that are immensely strong; such a structure given a superior quality rating by this method would be immune from the destructive effects of Tornadoes, Hurricanes, and earthquakes.

Description

BACKGROUND OF THE INVENTION

During the time since the first dome structure was constructed, that could be called “Geodesic”; on top of the roof of the Carl Zeiss Optical Company in Jena Germany in 1922, the Science of Geodesic domes and structures has grown and evolved substantially. Shwam in U.S. Pat. No. 4,907,382 provides a categorization of various systems of Geodesic Domes and types of Fabrication. Shwam defines “Geodesic Domes” as being characterized such that “the outer surfaces of all Geodesic Domes are (either actual or implied) subdivided into triangles” In Mathematical terms “Geodesic” is defined as being “the shortest path between two points on any surface”. In Civil Engineering terms “Geodesic Structures” are defined to be “structures consisting of a large number of a few identical parts and therefore simple to erect; and whose pressure is loadshed throughout the structure, so that the larger it is the greater it's strength”. The Geodesic Dome is known to a very strong structure and the only structure that becomes stronger as it's becomes larger

SUMMARY OF THE INVENTION

The main component of this invention is a honeycomb skeleton made up of hexagonal and pentagonal Cylinders. (FIG. 1a & FIG. 1b) Many spheres and tubular corridors constructed in the manner described herein, could be linked together, thus forming a structural continuum. This skeleton is based on the closed cage highly symmetrical Carbon-60 molecule; a complete sphere known as buckminsterfullerene or simply as a “Buckyball”, in honor of R. Buckminster Fuller This molecule has attracted a lot of interest since it's discovery in 1985; by chemists and also mathematicians have been interested in the symmetry properties of C₆₀ and related closed cage molecules. (FIG. 2)

This honeycomb skeleton formed from Pentagonal and Hexagonal Cylinders differs from previously proposed Geodesic structures such as the polyhedral structure proposed by Yacoe in U.S. Pat. No. 4,679,361 in that this skeleton is formed from a network of joined polygon cylinders which approximate hollow cones (FIGS. 3a & 3b) the thickness and length of the cylinders and therefore the thickness and length of the hollow cones can be chosen, such that, for a material of given tensile strength, a Geodesic honeycomb skeleton can be erected which would be the strongest structure formed, and which could be formed using this material. (see 0090)

The skeletal spheres referred to herein and that form parts of the proposed structural continuum are truncated spheres and when consisting exclusively 1^st level Hexagonal and Pentagonal cylinders (see 0040) are described by mathematical terminology as “Truncated Icosahedrons” but will be referred to herein onwards as ¾ spheres.

These cylinders are best suited to be manufactured by methods of sand-casting, however, depending upon the choice of material and dimensional tolerances required for the cylinders, Die-Casting could be the preferred choice for manufacturing them. For a Sand Casting method of manufacture, Tooling would be needed and this tooling could be made from Aluminum or Timber. These polygon cylinders could be cast from Iron, however, a strong aluminum alloy might be more suitable. A polymer of superior tensile strength might also be suitable.

The Hexagonal and Pentagonal cylinders will require a Taper on the outer surfaces such that if the longitudinal dimensions were extended they would become cones. It is explained in paragraphs 0060 & 0065 that this angle of Taper on “2^nd lower level cylinders” would need to be 9 degrees to the perpendicular edge of the cylinders for a curvature approximating that of a sphere to be formed.

The formation of tubular corridors (0085) would be similar to the formation of Carbon-60 molecules in Carbon-60 nano-tubes. A unique aspect to this structural continuum is than a section of it could be seen to be a macroscopic representation of the molecular world.

An assessment can be made of a Structural Continuum erected from these Hexagonal and Pentagonal Cylinders, in that, this assessment provides an overall Quality rating of the structure; due to two aspects; Firstly; the tensile strength of the material from which the cylinders are cast and secondly; the heat resistance of the material used to create the skin that protects the skeleton (0120). The Structural Continuum is referred to as comprising of two embodiments discussed herein; The Honeycomb skeleton and also the skin protecting the skeleton. It is this combination of a Honeycomb Skeleton and Skin which will provide the Structural Continuum it's overall Quality rating Q_sc. It is suggested that Q_sc be a number assigned between 1 and 10; the higher the number assigned to a structure the higher it's quality. Ideally, a material of high tensile strength would be used to create the honeycomb Skeleton and a material that is highly heat resistant would be used to create the skin that covers the skeleton. These superior materials would create a Structure of Superior Q_sc; a superior Q_sc would be interpreted to indicate a structure being immune from the devastating effects of earthquakes, tornadoes and possibly, also, bushfire.

A unique aspect of this structural innovation is that the hexagonal cylinders can be formed from a lower level of hexagonal and polygonal cylinders and these lower level hexagonal cylinders could also be formed from a lower level of hexagonal cylinders and the same for the pentagonal cylinders. These cylinders are in fact sections of hollow cones and the overall strength of the skeleton will be a function of;

• • a) the volume of mass forming the identical hollow cones
  • b) the tensile strength of the material of which the cylinders are cast
  • c) a constant for the lowest level of hollow cones (cylinders) forming the skeleton.In the hypothetical case where the dimensions of these cylinders are extended to make them into solid cones then the structure will no longer resemble a skeleton but a solid enclosure of mass and will thus be of ultimate strength. In the other extreme in which the dimensions of the cylinders are as small as realistically possibly; the skeleton will only be a thin mesh outline, and thus, be of minimal strength. However, between these two extremes, there will exist dimensions for the cylinders, such that, the strongest skeleton can be erected for a particular material of given tensile strength.

Besides it's inherent strength, the proposed structural continuum has another advantage; this is that it is easy to assemble; Once tooling for the manufacture of the polygon cylinders has been designed and built, and it is seen that prototype parts connect together correctly, the continuum can be easily expanded upon.

A huge number of spheres, and tubular corridors and circular tubular corridors could be linked together over a flat land mass thus forming a structural continuum . . . only limited by the extent of flat land available. But, in the case where this structural continuum is used to erect a space station or space dwelling; the continuum can expand out into the infinity of space indefinitely.

There are four main components needed in the construction of this Novel Geodesic structure described herein; which will result in a viable alternative to conventional structures, being erected, which can be used as a dwelling space or as Civil Defense shelters. With the prevailing predicament on our planet, and in recent years, with tornadoes, hurricanes and earthquakes bringing devastation upon communities of people, especially in the United States, structures built up from the method described herein would be a viable and practical alternative to current methods of construction. This Structural continuum could be a viable option in the building of space stations or space dwellings as the continuum could easily be assembled in space.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a and 1b; The outer surfaces of the cylinders tapering to a point

FIG. 2; A C-60 molecule

FIGS. 3 a & 3b; The cylinders extended to form Cones

FIGS. 4 a & 4b; Very thin 2^nd lower level Hexagonal and Pentagonal Cylinders forming larger 1^st level Cylinders

FIG. 5 A ¾ sphere formed only of 1^st level cylinders

FIG. 6; Cross-Sectional view of a cylinder

FIG. 7 a ; Plane through Soccer Ball with diagram showing the total angle formed by one cylinder through the plane of the diameter

FIG. 7 b; Piece of Soccer Ball Removed

FIG. 8; 2^nd lower level Hexagonal “sub-cylinders” within one 1^st level hexagonal cylinder, showing (in 2 directions)

4 angles contributing to the overall curvature

FIG. 9 a; A Tubular corridor, and FIG. 9b Cylinders showing the surfaces requiring a taper

FIG. 10; Approximating the polygon cylinders as circular cones of a set thickness

FIG. 11 a; A segment of circular tubular corridor and

FIG. 11 b; a Circular tubular corridor

FIG. 12; A ceramic U-Bar

FIG. 13 a and FIG. 13b Joining corridors; showing polygons designed to be the joining cylinders

FIG. 14; The 1^st level cylinders put into place to construct a skeleton

FIG. 15; the complete skeleton;

a “section” of the structural continuum

FIGS. 16 a & 16b; 1^st Level cylinders formed from 3^rd Lower Level cylinders

FIG. 17; Plan of a skeleton formed from 3^rd lower level cylinders

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The Embodiments comprising the invention are as follows;

POLYGON CYLINDERS FORMING THIS HONEYCOMB SKELETON

HEAT INSULATING GASKET

CERAMIC U-BAR AND WEATHER RESISTANT FILLER

SWITCHABLE PHOTOREFRACTIVE WINDOWS

Polygon Cylinders Forming this Honeycomb Skeleton

The cylinders forming this honeycomb skeleton referred to herein as the “1^st level of Cylinders”, could, and ideally would be formed from a smaller level of Hexagonal and Pentagonal cylinders . . . referred to herein as the “2^nd lower level of cylinders”. Each pentagonal cylinder would be formed from 6 smaller pentagonal cylinders and each Hexagonal cylinder would be formed from 3 smaller Hexagonal cylinders and 3 quadrilateral cylinders. (FIGS. 4a & 4b show cylinders formed from “very thin” 2^nd lower lever cylinders). These 2^nd lower level of cylinders could be formed from a network of smaller cylinders; a 3^rd lower level of cylinders, and these cylinders being formed from a 4^th lower level network of cylinders and so on. A Constant for a skeleton formed from an n_th-level cylinders is designated herein as; K_nth-level

For a ¾ sphere (FIG. 5a) formed from this honeycomb skeleton with only a 1^st level of Hexagonal and Pentagonal cylinders; there will be 15 Hexagonal cylinders (Hex-Cyl) and 11 Pentagonal Cylinders (Pent-Cyl) required; and in general , the number of cylinders contained in a skeleton formed from an nth-level of cylinders will be; (let a=n_th-level−1)

Σ Polygon Cylinders=Σ{15[3^a] Hex-Cyl.+11 [6^a] Pent-Cyl}

Of critical importance is the angle of Taper on the outer surfaces of the cylinders. From a cross-sectional view of the cylinders (FIG. 6 showing a sliced section of cylinder) the inner surfaces of the cylinders will be perpendicular to the inside edge of the cylinder, however the outer surface of the cylinder will require an angle of Taper. For a honeycomb skeleton formed from a 2^nd lower level of cylinders, this angle of Taper will need to be 9 degrees. This can be deduced from slicing a plane through the largest diameter on the Soccer Ball. (FIG. 7) It will be found that there will be a total of 10 angles around the circumference arising from joining the 1^st level cylinders. Thus each angle between adjacent sides on a 1^st level cylinder will be 360/10=36 degrees, and thus, the angle between one side of the same cylinder and the centre of this cylinder will be 18 degrees. (FIG. 7a and FIG. 7b showing the section of soccer ball removed)

It is also easily deduced that the diameter of a sphere built up from the honeycomb skeleton as a function of the Diameter of the 1^st level of polygon cylinders will be;

DIAMETER OF SPHERE=2*{Rad-Cyl/Tan(θ/2)}

Where Rad-Cyl is the radius of the polygon Cylinders and θ/2=18 degrees

From joining the 2^nd lower level sub-cylinders together to obtain a 1^st level Hexagonal cylinder (FIG. 8) it is seen that there will be four angles contributing to the overall Taper of the cylinder to form a cone. This can be seen from FIG. 8 where the contributing angles are formed from vectors [ab+{cd*2}+ef]. Thus, the angle of Taper on each 2^nd lower level cylinder will be; 36/4=9 degrees and in general, for a honeycomb skeleton made up of an nth level of polygonal cylinders the angle of taper required will be; (let a=n_th-level−1)

/angle=36/(4^a)°

It is suggested that the around both the outer and inner faces of the cylinders, on the outer edge (FIG. 6) that there be a indentation of approximately 20 mm by 5 mm and also, if possible, a small cavity within the outer edge of the cylinders. The outer indentation will be useful for fitting bus wiring to connect to the photorefractive window material, described in a following section. The inner indentation will be required for these sheets of photorefractive material to sit in.

It is suggested that a suitable length for the 2^nd lower level of cylinders be between 100 mm and 200 mm and the thickness of the cylinders be 20 mm at the outer edge. Depending on the tensile strength of the material that the cylinders are cast from the thickness of the cylinders could be as thin as 10 mm at the outer edge and still form a robust Honeycomb skeleton of immense strength.

The cylinders would be bolted together at two places at each joining face and thus, holes needing to be drilled in these places; identical places on each face of each cylinder and it is suggested that a stencil be made and used to mark the location of the holes. It is suggested that bolts of no less than M10 be used.

The formation of tubular corridors can be achieved by using only hexagonal cylinders and quadrilateral cylinders as indicated. (FIG. 9a) In this case, the cylinders will only require an angle of taper on 2 of the 6 outer surfaces of the cylinder edges (FIG. 9b; shows these cylinder surface edges marked ‘T”). In this case the overall diameter of the tubular corridor will be a function of the degree of taper on the 2 outer surface edges of the hexagonal cylinders; The steeper the degree of taper the smaller diameter of the resulting tubular corridor.

A method for Quantifying the Overall strength of a honeycomb skeleton built out of a material of known tensile strength is proposed by modeling the skeleton on a structure formed from hollow cones (FIG. 10) (in a special case, the sections of hollow cones can be approximated to circular cylinders). I will assume here that the strength of the Honeycomb skeleton is equivalent to the stress in Newtons/meterŝ2 applied at one point to deform the skeleton. It is a known property of Geodesics that any force acting at a particular location on the structure is distributed throughout the structure. I will thus assume the dimension meterŝ2 to be the entire surface area of a unit sphere or tubular corridor of which the stress is applied. With an either linear or logarithmic proportionality constant linking the property of a single cone to the Strength of a skeleton formed from an n_th-level of hollow cones (circular cylinders) the Overall Strength can now be approximated;

(for the special case in which the hollow cones approximate cylinders)

OVERALL STRENGTH=(τcyl)(K_nth-level)(π[C_out²−C_in²]. C_L)

Where (τcyl)(K_nth-level)(π[C_out²−C_in²])≦Stress needed to Deform the skeleton Subsequently, where the cylinders are to be designed to yield an overall strength, then [C_out²−C_in²]. C_L=(OVERALL STRENGTH)/π(τcyl)(K_nth-level) τcyl is the tensile strength of the cylinders; K_nth-level is the linear or logarithmic constant for a structure formed from an n_th level of polygonal cylinders; C_out & C_in denote the outer and inner radii of the cylinder, thus [C_out−C_in] denotes the cylinder thickness C_th and C_L denotes the cylinder depth and in the case where C_th and C_L approach maximum values, a sphere would approach a solid mass, but there will be values for C_th and C_L for which the sphere, or tubular corridor will be the strongest structure attainable for tensile strength of material.

“Circular” tubular corridors can be achieved by again using Hexagonal cylinders but, in this case, 4 & 5-sided polygon cylinders (as seen in FIG. 11a) will also be needed. These 4 & 5-sided polygon cylinders are the joining cylinders to fit the space between hexagonal cylinders and connect and form the network of hexagonal cylinders into a circular corridor, The Hexagonal cylinders will need to have the same angle of taper on 2 of the 6 outer surfaces of the cylinders (same angle on same outer surfaces used for the Tubular corridor). The outer surfaces 1 & 3; 4 & 6 of the cylinders as shown in FIG. 11 will require a small angle of Taper between 2 and 4 degrees depending upon the “ROUND PATH LENGTH” that is desired. The “Round Path Length” of the circular tubular corridor will be a function of the size of the hexagonal cylinders and the angle they tilt towards the spokes radiating from C_x. (FIG. 11b)

It is seen looking down on the Circular Corridor (FIG. 11b) two Circular lines “Y” and “Z”; Line Z is the highest point on the roof of the Corridor and line Y is the inner horizon of the corridor. It is suggested that line Z be used as the measurement of the “ROUND PATH LENGTH”.

In Quantifying the strength of the corridor, it will not be correct to take the area over which the stress is applied to be the total surface area of the corridor. Instead it is suggested that;

(τcyl)(K_nth-level)(π[C_out²−C_in²]. C_L)

be calculated for the surface area at the cylinder where the stress is applied plus the surface area of the cylinders that are directly connected to it.

It is seen that the most practical method of assembling this structural continuum consisting of many ¾ spheres and tubular corridors linked together, is to assemble it starting from the top downwards; that is; the top cylinders are joined into position first and then the surrounding side cylinders are joined. An unconventional method of course when considering how most buildings are constructed. A problem arises when joining the tubular corridors into the ¾ spheres. Solving this problem requires polygon cylinders specially designed and Die-cast to fit the space in which two cylinder surfaces are to be joined. It can be seen in all cases, this is an easy engineering problem to solve: As stated, the continuum is constructed from the top first; The top cylinders of the ¾ sphere and the top cylinders of the tubular corridor need to placed in close proximity. Polygon cylinders are then designed and made from Timber that will fit this space and connect the surfaces; This wooden polygon cylinder is then used to make the cast (and kept to make more casts). Tubular corridors will, also, need to be joined with “Circular” tubular corridor using irregular shaped cylinders and this case is shown in FIG. 13;

Heat Insulating Gasket

Heat Insulating Gasket will be required to be placed between each joining surface of the cylinder. The properties of this gasket material should be such that it be heat insulating. Ceramic sheeting between 1 mm and 2 mm thick in thickness; such as silicon nitride which is known to withstand temperatures up to 1000 degrees Celsius would be a suitable choice. Silicon Carbide or Cubic Boron Nitride would also be ideal.

It is essential that the cylinders be insulated from each other by heat insulating gasket as in a circumstance where a fire erupts inside the structures; a vast amount of heat emanating from a fire inside the structure could weaken and eventually collapse the honeycomb skeleton. However, when each cylinder is insulated form it's neighboring cylinders in the skeleton, the heat energy required to weaken the entire structure would be much more substantial.

Ceramic U-Bar and Weather Resistant Filler

Ceramic U-Bar placed along the interior joining edges of the assembled honeycomb skeleton would provide additional protection to the skeleton in the scenario where a fire erupts inside the structure. These Ceramic U-Bars (FIG. 12) will form a continuous interior shell, thus protecting the skeleton and also adding a pleasant finish to the interior of the structure. This Ceramic U-Bar would be manufactured by common extrusion method. It is suggested that the Ceramic U-Bar be attached with bolts and spring washers with screw holes needing to be tapped into the edges of the cylinders. It is suggested that two holes be cut out of the length of each Ceramic U-Bar to place the Bolts through. These holes would be cut out using “Water Jet Cutting” which is now the preferred method for cutting shapes out of Ceramic and Glass.

It is possible that other heat resistant materials will also be suitable for this U-Bar to form a continuous protective shell covering the interior of the skeleton.

Ceramic would have one disadvantage in that; in the event of an earthquake or similar severe shock to the structure, a ceramic shell could crack in places with parts falling down. Thus, it is strongly recommended that the manufacturing process of the Ceramic U-Bar include encasing it in a polymer sheet/film of approximately 0.2 mm thick

WEATHER RESISTANT FILLER will be needed to cover the gap at the exterior joining edges of the Geodesic skeleton. These joins would need to be filled over using a corrosion resistant filler. For this I suggest that an industrial grade silicon sealant be used. It is suggested that the gasket material be cut to be a few millimeters narrower than the sides of the cylinders.

Switchable Photorefractive Windows

Switchable Photorefractive window material is suggested for the structure. Sheets of this material would need to be specially molded to fit, and to sit inside the outer interior step of the cylinders. Switchable Photorefractive sheet is opaque in it's natural state but when a voltage is applied across it, the material becomes transparent to light. This Switchable Photorefractive Sheet is known more precisely as Polymer Dispersed Liquid Crystal (PDLC) film. PDLC film is made by dissolving a liquid Crystal material into a two part fluid mixture of polymer and cross-linking agent. With sheets of this Photorefractive window installed as the window material in the Geodesic structure, each cylinder forming the skeleton then becomes a Switchable “photorefractive cell”

It is recommended that these sheets of photorefractive window material be molded such that the sheets will have a degree of curvature. Thus, the curvature of these sheets will contribute towards the end result of the this Geodesic structure more closely resembling a Dome

This purpose of these Switchable photorefractive windows are to replace the need for curtains as used in conventional dwellings. All photorefractive cells would be controlled by a central voltage network; This feature will provide the occupants inside the dwelling the freedom to select the “cells” they wish to turn on to become transparent.

In planning for the construction of a continuum by the method disclosed herein, there is one aspect that needs to be stressed; the honeycomb skeleton is to be constructed from the top downwards. This is essential because the tooling to make polygon Casts for the joining cylinders need to be designed while the parts of the “prototype” skeleton are being assembled. Current methods of CAD modeling will provide a method to design the tooling without first needing to assemble parts of the skeleton, but the problem is still a complex one even using CAD. Shown in FIG. 14 are the first level polygon cylinders connected to construct a skeleton consisting of one circular tubular corridor connected to a straight tubular corridor connected to a sphere. Shown in FIG. 15 is the completed skeleton. Shown in FIG. 17 is a view looking down onto the top surface of a Dome; straight tubular corridor; section of tubular circular corridor made up of 3^rd lower level polygon cylinders shown in FIG. 16

Claims

1. A structural continuum comprising a plurality of polygon cylinders, the outer surfaces of these polygon cylinders having an ‘angle of taper’ such that the cylinders can be assembled to form a larger level of Hexagonal and Pentagonal cylinders and these polygon cylinders being used to assemble a larger level of Hexagonal and Pentagonal cylinders and so on.

2. A structural continuum of claim 1 comprising a plurality of polygon cylinders the outer surfaces of these polygon cylinders having an ‘angle of taper’ such that the diameter of the so formed part of the continuum is a function of the angel of taper of these smallest level of polygon cylinders

3. A structural continuum of claim 1 comprising a plurality of polygon cylinders formed in a geodesic manner, the resulting parts of the structural continuum so formed being either a Dome, a tubular corridor or a circular tubular corridor.

4. A structural continuum of claim 1 formed from unit polygon cylinders, the dimensions of which can be chosen such that the resulting structural continuum of claim 1 will form the strongest structure that can be formed for a given material of given tensile strength.