This invention relates generally to structural frameworks. More particularly, disclosed herein is a novel and improved structure of elongate compression members placed within a membrane in tension to create a self supporting structure with the compression members separated from one other and retained by the membrane.
The present invention forms part of a well established class of structures often referred to as tensegrity structures, possessing characteristics of discontinuous compression and continuous tension, where elongate members are separately placed either in tension or compression to form a self-supporting lattice. These types of structures achieve significant weight-to-strength ratios by eliminating compression members from the structural framework and replacing them with tension members wherever possible. Tensegrity structures take advantage of the high strengths that are possible for certain materials in tension and the fact that materials in pure tension do not require additional mass or added dimension in cross section to resist buckling in compression. As a result, tensegrity structures also achieve significant visual lightness as a substantial portion of the framework comprises rods, cables, or thread with diameters significantly less than the diameters or cross sectional dimensions of the compression members. A further lightness of appearance is achieved in these systems where the compression members are truly discontinuous, with no overlaps or contact, appearing to float within a continuous network of attenuated tension members.
The several continuous tension, discontinuous compression systems known to us comprise basic modules which combine to create larger structural forms, such as columns, beams, arches, planes and domes, to name a few. The basic modules of the larger aggregate structures comprise structures of their own in the form of polygons—when the compression members and the tension members are more or less co-planar—and polyhedra or prisms—when the members define the edges of a volume in space—with rigid compression struts supported in space and separated entirely from each other by a network of tension members anchored to and pulling from the ends of adjacent compression members. In these cases of existing art, the tension and compression members of the module structures are linear, an expression of the forces within the system resolved as pure axial loads. When the structural modules comprise polyhedra and prisms, the tension and, additionally or alternatively, the compression members of the structure define the linear edges and the faces of the tensegrity module.
Planar or spherical aggregates of these modules, or planar aggregates that join to create curved forms, can be construed as a lattice membrane, the weave of the membrane comprising both the continuous tension network and the discontinuous compression members, with the dimensions of the module determining the minimum thickness of the membrane. On the scale of the individual modules, however, the linear tension and compression members of the structure define the edges of a space, and the faces of the structure so defined are open and do not constitute an enclosing membrane. At scales where an aggregate of tensegrity modules is not construed as a continuous woven fabric, the tensegrity module functions as a three-dimensional frame, and additional material must be supplied to the structural framework to enclose the defined space, possibly as exterior panels or curved or triangulated infill panels attached to the tension and compression members of the structure. An alternative to panels or modular infill at the building scale is to provide enclosed volumes as independent objects nested and supported inside of the structural frame. These techniques of providing enclosure, however, are common practices utilizing many types of structural frames for support, and are not unique to frameworks comprising discontinuous elongated compression members and networks of elongated, articulated tension members.
In another example of existing art, tension membrane panels replace a number of the linear tension members of the tensegrity structure. The tension membrane panels lie in the same plane or face typically defined by the tension and compression members, or, in cases where the tension member defines the edge of two adjacent triangular faces, the tension membrane panel forms a hyperbolic paraboloid panel. The corners or apexes of these panels anchor to the ends of the compression members, pulling the ends of the members together in a fashion similar to the substituted linear tension members. With the requirement that all areas of the panel surface experience tension, the edges of these panels assume a catenary curvature between the anchor points. The panels attenuate toward the corners and assume a more or less cruxiform shape of catenary curves.
While a network of such panels can be considered a continuous tension network in the same fashion as a network of linear tension elements, substantial gaps exist between adjacent panels and between panels and compression members in examples of art utilizing this system. Consequently, the proliferation of edges renders a discontinuous surface. Further disadvantage results from the phenomena of flutter where vibrations are created by the steady flow of air or liquid over these edges.
Prior art structures utilizing a continuous tension membrane for enclosure include a class of freestanding tent. In such structures, discontinuous elongated flexible members are combined end to end to create substantially longer members. Those longer members are then used in bending to combine the properties of compression and tension to provide pre-stressing and arch support to the structure.
The invention disclosed herein, while similar in its use of a membrane to provide structure and enclosure, differs significantly from these prior art tent and related structures. As taught herein, for example, elongate members are configured purely for axial compression and not for bending. Therefore, they have significantly less flexibility and smaller ratios of slenderness. Furthermore, pre-stressing of the system does not occur as a result of energy stored in the elongate compression members through bending of the members.
It will also be known to one skilled in the art that fully enclosed structures exist wherein elongated compression members of uniform or slightly variable length radiate more or less from a common intermediate point or from several intermediate points along and generally towards the ends of a single axial compression member. The compression members of these structures support a continuous closed, anticlastic membrane with peaks corresponding to the ends of the compression members that are held in place by the uniform pull of the membrane. The intersecting compression members in such structures cannot be characterized properly as discontinuous. The resulting structures describe star-like, radiating forms of combined conical double curved surfaces, resembling complex polyhydra. Likewise, as proven out by prior art structures, each module is a closed system unto itself. The usefulness of these structures is further undermined by the density of the compression members at their centers, which effectively fills instead of creating space at the center of the enclosure. The present inventor has recognized that similar volumes of space can be achieved with more efficient use of material and space and better volume-to-weight ratios using discontinuous compression members.
Other notable examples exist in prior art wherein a continuous membrane is stretched or draped over a pre-stressed scaffolding comprising a single structural module. The scaffolding comprises a framework of discontinuous elongate members held in compression by a continuous lattice of attenuated, linear tension members. In prior art disclosures by Anne Niemetz and Andrew Pelling (The dark side of the cell, audio-visual installation, 2004, United States) and more recently by Florian Idenburg and Jing Liu (In Tension, Installation, 2010, United States) a membrane or mesh wrapper induces catenary curvature in linear tensile members in scaffolding. The membrane or mesh assumes anticlastic double curvature while contributing additional pre-stress and embodied energy to the structure. This assertedly provides increased stability.
Lasse West disclosed a freestanding display structure utilizing a single tripod of discontinuous, elongate compression members held in compression by a continuous band of tensile membrane (Trinex, Construction, 2004, Germany). The West disclosure represents a recent development in the substitution of a tensile membrane for the continuous lattice of elongated tension members in pre-stressed continuous tension, discontinuous compression structural systems. As disclosed by West, a prestressed, anticlastic membrane directs tensile forces to the ends of the discontinuous compression members as axial compressive loads. Evidencing the still further attempts of prior art inventors to devise elegant and effective tensegrity structures, Mizuki Shigematsu, Masato Tanaka and Hirohisa Noguchi have disclosed a similar module of tensegrity membrane structure based on a variational method (Form finding analysis of tensegrity membrane structures, Conference Paper, 2008, United States and Japan). Under their teachings, a single layer of a diamond-pattern system of continuous tension, discontinuous compression construction is employed. Following the prismatic model, the tensile membrane in this module engages the discontinuous compression members along their entire length. Each compression member is incorporated into the exterior surface as the edge of a linear crease. This condition induces bending loads in the compression member and requires design for bending and for axial loads yielding a resulting loss in the weight and material efficiencies of the system. The compression member must assume the function not only of a tent pole but also that of a ridge beam under uniform loads. Furthermore, the edge of the membrane at the continuous attachment to the linear compression member also panelizes the membrane, in such a way that it no longer assumes the form of a minimal surface spanning the outermost edges of the structure. This increases the surface-to-volume ratio of the structure and reduces the efficiency of material used relative to the volume of enclosed space. These shortcomings are compounded when the diamond-pattern system is utilized to create multi-layered tubular figures employing tension membranes as disclosed by Mizuki Shigematsu et al. The resulting panelization of the membrane creates discontinuities, invaginating the membrane surface while interfering with the even distribution of loads. This effectively reduces the area of the membrane engaged with loads applied to the structure.
With an awareness of the disclosures of the prior art and the shortcomings thereof, the present inventor has appreciated that there remains a need for improved tensegrity structures that exhibit desirable structural integrity while providing for efficiency in the use of material and enclosure of space and improved volume-to-weight and volume-to-surface ratios.
With a knowledge of the state of the art as summarized above, the present inventor set forth with the basic object of devising of tensegrity structures and methods for exploiting the same that exhibit desirable structural integrity while providing for efficiency in the use of material and enclosure of space while providing opportunities for improved volume-to-weight and volume-to-surface ratios.
A further object of embodiments of the invention is to provide tensegrity structures that can pursue widely variable shapes and sizes.
In certain embodiments, an object of the invention is to provide an essentially self-enclosing, generally tubular structure of variable length and diameter formed by multiple, potentially consecutive, units of discontinuous compression members in combination with a continuous tension membrane.
An underlying object of the invention is to provide tensegrity structures and methods for using the same that are adaptable to numerous applications, including but not limited to, tubular column and beam constructions, the design and construction of free standing buildings, the design and fabrication of free-standing fixtures, such as floor lamps and other structures, that require structure and shading, the design and construction of kites, and the design and construction of sculptures. Of course, other structures are contemplated and well within the scope of the invention except as it might be expressly limited.
These and in all likelihood further objects and advantages of the present invention will become obvious not only to one who reviews the present specification and drawings but also to those who have an opportunity to examine, use, and witness the structure and performance of the compression systems and methods disclosed herein. Although the accomplishment of each of the foregoing objects in a single embodiment of the invention may be possible and indeed preferred, not all embodiments will seek or need to accomplish each and every potential advantage and function. Nonetheless, all such embodiments should be considered within the scope of the present invention.
In carrying forth the aforementioned objects, a tensegrity structure according to the invention has a pre-stressed membrane that can comprise a substantially continuous, resilient material with an inner surface and an outer surface. At least a first tensegrity unit is formed by the membrane in combination with at least three elongate compression members. With that, the membrane can be considered to act as a sheath in the broadest use of the term in that it encases the compression members when the tensegrity structure is assembled. The membrane can be substantially tubular, and the resulting tensegrity can approximate a tubular configuration. It will be understood, however, that the concept of a tubular configuration or the like as used herein shall not require that the structure be round or smooth in cross section.
The elongate compression members are obliquely disposed in compression within the membrane to establish an open inner volume therein. Each compression member has a first end that applies force to the membrane at a first location and a second end that applies force to the membrane at a second location spaced from the first location. The ends of the compression members are not in contact with one another whereby the compression members can be considered to be discontinuous. Compression members that are not in contact with one another and not in contact with any other supporting structure apart from the membrane are supported entirely by the membrane, which in turn they support. The membrane and the several compression members thus cooperate to provide a mutually supportive structure.
The tensegrity structure can be considered to have a longitudinal axis, and the compression members of each tensegrity unit can be crossed between their ends in a spiral in relation to the longitudinal axis. Within the present specification and claims, reference to a longitudinal axis shall not be considered to require that the tensegrity structure or the longitudinal axis be straight. Indeed, resulting tensegrity structures can be curved, straight, or otherwise formed. Furthermore, as used herein, the term discontinuous shall not necessarily require that the bodies or mid-portions of the compression members be out of contact, and the claims should not be interpreted to require the same except as they might be expressly limited. As shown in the drawings, however, embodiments of the invention are contemplated where the entire mid-portions of the compression members within each tensegrity unit and as between adjacent compression units are also not in contact.
Embodiments of the invention can have multiple tensegrity units so formed. The multiple tensegrity units can have the same or different numbers of compression members. The compression members of adjacent tensegrity units can also not be in contact so that they too are discontinuous. Where the tensegrity structure is considered to have a longitudinal dimension and a lateral dimension, compression members of adjacent tensegrity units can overlap along the longitudinal dimension. With the tensegrity structure so formed, the membrane can form anticlastic curves and can have variable double curvature between ends of compression members.
Whether the tensegrity units have three, four, or more compression members, the compression members of adjacent tensegrity units can spiral in common or opposite orientations. For example, all compression members can spiral clockwise or all compression members can spiral counter-clockwise around the longitudinal axis. In other embodiments, the compression members of one or more tensegrity units can spiral in a clockwise direction while one or more others can spiral in a counter-clockwise direction.
Where the compression members are crossed in a spiral between the ends of the compression members and in relation to the longitudinal axis, the compression members can establish a gap β about the longitudinal axis. That gap β can be exploited in certain manifestations of the invention, such as for the retention of articles and other structures. Where the tensegrity structure comprises a building structure, for example, a column, such as an elevator column, can communicate within the gap β.
Means can be provided for selectively adjusting a length of the compression members. With that, the membrane can be selectively pretensioned by a selective lengthening of the compression members.
Where plural tensegrity units are each formed by the membrane in combination with at least three elongate compression members, the elongate compression members will again be obliquely disposed in compression within the membrane to establish an open inner volume therein. The ends of the compression members of each tensegrity unit will preferably not be in contact with one another so that they are discontinuous and supported by the membrane. Likewise, the compression members of adjacent tensegrity units are preferably not in contact whereby they too are discontinuous. Within each tensegrity unit, the compression members of each tensegrity unit will again be crossed in a spiral between the ends of the compression members and in relation to the longitudinal axis of the tensegrity structure.
In such embodiments, the tensegrity structure can take the form of a tapered column achieved, for example, by a sequential reduction in length of the elongate compression members of adjacent tensegrity units. In further embodiments, the tensegrity structure can comprise a curved structure. This can be realized by, for example, a curvature induced by a variation in length of elongate compression members within each compression unit or by a variation in overlap between adjacent tensegrity units. In each embodiment, reinforcements can be disposed at the ends of the compression members to prevent a piercing of the membrane.
One will appreciate that the foregoing discussion broadly outlines the more important goals and features of the invention to enable a better understanding of the detailed description that follows and to instill a better appreciation of the inventor's contribution to the art. Before any particular embodiment or aspect thereof is explained in detail, it must be made clear that the following details of construction and illustrations of inventive concepts are mere examples of the many possible manifestations of the invention.
In the accompanying drawings:
The tensegrity structures and methods disclosed herein can pursue numerous embodiments within the scope of the invention. However, to ensure that one skilled in the art will be able to understand and, in appropriate cases, practice the invention, certain preferred embodiments of the broader invention revealed herein are described below and shown in the accompanying drawing figures.
The present invention was made in view of the present inventor's discovery that a continuous membrane can replace the network of linear tension members as a structural component for a particular class of continuous tension, discontinuous compression structures. Under embodiments of the present invention, for example, a continuous pre-stressed membrane can be combined with repetitive, overlapping, and interweaving arrangements of discontinuous compression members to create tubular structures of variable length. The structures and methods disclosed herein substitute a continuous surface for the open faces or edges of the continuous tension, discontinuous compression lattice networks of the prior art to create enclosed and continuous interior spaces. Structures according to the invention realize efficiencies of material use and improved volume-to-weight ratios by utilizing the tension membrane as an integral component of the structural system. Elongate, multi-tiered structures according to the invention provide improvements in flexibility and utility over prior art systems previously comprising a single module. The pretensioned membrane of the disclosed structure assumes an anticlastic form of continual curvature and efficient, minimal surface area. The tension and the curvature of the membrane contribute stiffness to the structure while minimizing both the ratio of surface to volume and the energy that must be embodied in the system.
A basic module of embodiments of the invention creates a volume through the retention of three compression members crossed in a spiral intermediate to their ends and held to be self supporting by a continuous sheath of tension membrane. This tripod arrangement of struts can be situated in a network of linear tension members to constitute the basic compression unit of self-supporting linear tensegrity structures. Variations on this basic unit are found in the addition of compression members in a spiral arrangement.
A continuous sheath of tension membrane can effectively replace the lattice of linear tension members in the module, contacting only the ends of the discontinuous compression members and connecting these ends within a pre-stressed membrane. It is a further characteristic of the module that the continuous membrane sheathing assumes a unique form determined by its connections to the ends of the compression members. The form is anticlastic and of continually changing double curvature specific to the disposition of the compression members of the module thereby assuming a shape indicative of the approximately even distribution of stress throughout the membrane. Advantageously, the continuous membrane avoids edges along its length that are relatively unsupported in relation to external forces perpendicular to its surface.
Pursuant to the present invention as described further below, one can create a self-supporting structure of variable length founded on the described module through a combination of extending the continuous, pretensioned membrane sheathing at intervals that can correspond to the longitudinal dimension of the unit arrangement of compression members while adding compression units in support of the extended membrane tube. The added compression units can potentially correspond in number and length of compression members to the previous units, or the compression members can vary in number, size, and otherwise. Particularly where the compression members are of consistent number and size, the resulting structure can be considered analogous to a helical ladder with a pre-tensioned membrane tube substituted for the rails and an arrangement of oblique rungs suspended inside of the tube.
While potentially constructed in a linear, modular fashion, structures according to the invention typically will not comprise an assembly of discreet modules. As an approximation of a minimal surface, the continuous tension membrane that encloses and supports iterative, mutually supporting unit arrangements of compression members assumes a repetitive form related to the basic module while effecting, in a distinctive way, the transmission of forces between the successive units. The resulting structure is to be distinguished from the basic module as a result of, among other things, the overlapping adjacency of two unit arrangements of compression members bound together by the continuous tension membrane. The disclosed structure further distinguishes from those taught by the prior art in that the continuous tension membrane directs forces only to the ends of the compression members. Consequently, only axial loads are imparted on the discontinuous structural elements. The form and disposition of the integrated components resulting from this adjacency are among the unique features of the invention.
Despite the foregoing and further important structural and functional differences as compared to the prior art, tensegrity structures according to the invention may be considered to have certain characteristics in common with prior art methods of creating beams, columns, and arches from modules with a lattice of discontinuous compression members joined by a continuous network of linear tension members. A primary shared characteristic is that the structures as taught herein are pre-stressed, relying on energy stored in the system for stability. Accordingly, the tensile membrane of the disclosed structure shares elasticity properties with the tension networks of prior art, and the currently disclosed structures have a degree of flexibility proportionate to the degree of tension that can be stored in the structure and the elasticity of the pre-tensioned membrane. Embodiments of the structure disclosed herein can be collapsed to a fraction of their extended lengths, subject to the degree of elasticity in the membrane and other factors, while reassuming their full lengths when released. When resiliently compressed in this fashion, the energy input into and released by the structure is nonlinear as with a spring. Also similar to structures of the prior art, individual units composed of the spirally arranged compression members according to the invention possess left and right handed rotational characteristics in responding to external forces. These may be utilized to neutralize the distortion caused by such forces on a structure composed of two or more modules. This can be accomplished, for example, by mirroring the spiral arrangement of compression at each successive module.
Looking first to
Looking again to
In the basic module 10, the tendency of the membrane 11 to pull the ends 15 and 18 of legs 12 and 14 toward each other in the longitudinal direction is resisted by an equal force pulling the two ends 15 and 18 in the transverse direction. Thus, a transverse tensile force pulls end 15 toward ends 16 and 17 and another pulls end 18 toward ends 19 and 20. The distribution and equilibrium of these longitudinal and transverse tensile forces in the membrane 11 result in the anticlastic surfaces and catenary edges notable to the invention.
As with prior art discontinuous compression, continuous tension structural systems, the compression members 12, 13, and 14 may be considered to have a left or right handedness depending on the orientations of the compression members 12, 13, and 14. Consequently, the modules 10 defined by the compression members 12, 13, and 14 have a tendency to rotate in a clockwise or counter-clockwise direction when loaded laterally.
The basic module 10 can be altered by adding additional compression members crossing in a spiral arrangement as described. By way of example,
Turning additionally to
Returning to
As a result of the oblique arrangement of the compression struts, all stresses in the struts have horizontal and vertical components thereby linking the longitudinal stresses in the membrane 30 with the transverse, annular stresses. Longitudinal loads, such as loads originating with the weight of construction material, are transmitted to the ground from compression members in unit 28 to the compression members in unit 29 primarily through longitudinal tension in the membrane 30 between strut ends 34, 35 and 36 and strut ends 15, 16 and 17, and annular tension in the membrane that prevents the outward spreading of the strut ends 15, 16, 17, 34, 35, and 36.
It should be noted in relation to each embodiment that the distinct double curvature of the surface of the membranes 11, 26, and 30 is an expression of the simultaneous lateral and transverse tensile forces distributed evenly in the membranes 11, 26, and 30 in relationship to the attached ends of the compression members.
These anticlastic surface forms of constantly changing curvature can be considered to fall into four basic categories.
Finally,
A five-tiered vertical structure constructed according to the invention is indicated at 43 in
Exploiting the invention, the two-tiered structure 27 shown, for example, in
In a further alternative,
For example,
The present inventor has further realized that arches, hoops, and other curved structures 68 can be created utilizing the invention, including by varying the lengths of the individual compression struts within each compression unit and, additionally or alternatively, by differentially varying the degree of overlap between adjacent compression units so that one side of the tube formed has a greater or lesser length than the other. In one of the many possible examples,
The membrane that forms the tensile component and enclosure of structures according to the invention can be one or more layers of any flexible, permeable, impermeable, or semi-permeable material. The material can be resilient and can be selected based on the application. Chosen membrane materials will preferably withstand tension, not resist compression or bending, and attain stiffness when pretensioned. Among the possible suitable materials are plastic polymers, woven or knit fabrics made of natural or synthetic fibers, woven or welded wire meshes, knit wire meshes, cable nets, or a lattice of elongated tension members joined with flexible connections, designed to evenly distribute forces in tension only and to assume the characteristic continuous and constantly changing anticlastic form of the invention. Of course, multiple layers of different characteristics could be employed, and varied materials could be incorporated in any given layer.
In an example of the variability of the invention,
Still further,
With certain details of the present invention for continuous tension, discontinuous compression systems and methods disclosed, it will be appreciated by one skilled in the art that changes and additions could be made thereto without deviating from the spirit or scope of the invention. This is particularly true when one bears in mind that the presently preferred embodiments merely exemplify the broader invention revealed herein. Accordingly, it will be clear that those with certain major features of the invention in mind could craft embodiments that incorporate those major features while not incorporating all of the features included in the preferred embodiments.
Therefore, the following claims are intended to define the scope of protection to be afforded to the inventor. Those claims shall be deemed to include equivalent constructions insofar as they do not depart from the spirit and scope of the invention. It must be further noted that a plurality of the following claims may express certain elements as means for performing a specific function, at times without the recital of structure or material. As the law demands, these claims shall be construed to cover not only the corresponding structure and material expressly described in this specification but also all equivalents thereof that might be now known or hereafter discovered.
This application is a continuation of application Ser. No. 13/340,474, filed Dec. 29, 2011, which issued as U.S. Pat. No. 8,833,000 on Sep. 16, 2014 and which claimed priority to Provisional Application No. 61/427,890, filed Dec. 29, 2010, both of which being incorporated herein by reference.
Number | Name | Date | Kind |
---|---|---|---|
3063521 | Buckminster | Nov 1962 | A |
3169611 | Snelson | Feb 1965 | A |
3745777 | Blenkarn | Jul 1973 | A |
3901551 | Wiesner | Aug 1975 | A |
4207715 | Kitrick | Jun 1980 | A |
4655022 | Natori | Apr 1987 | A |
4711062 | Gwilliam | Dec 1987 | A |
4731962 | Kittner | Mar 1988 | A |
5642590 | Skelton | Jul 1997 | A |
6868640 | Barber | Mar 2005 | B2 |
6901714 | Liapi | Jun 2005 | B2 |
6931812 | Lipscomb | Aug 2005 | B1 |
7278245 | Rouse | Oct 2007 | B2 |
7578307 | Ung | Aug 2009 | B2 |
8826602 | Lipscomb | Sep 2014 | B1 |
20020002807 | Newland | Jan 2002 | A1 |
20030009974 | Liapi | Jan 2003 | A1 |
20030182874 | Barber | Oct 2003 | A1 |
20040068940 | Amir | Apr 2004 | A1 |
20040134141 | Hebbelinck | Jul 2004 | A1 |
20040261351 | Ung | Dec 2004 | A1 |
20110005160 | Nihei | Jan 2011 | A1 |
Entry |
---|
Val Stavrev, Tensile Stars, Internet Publication http://www.visign.org/pdf/TensiStars.pdf, 2007, 3 pages, Helium ET, Bulgaria. |
Hugh Thompson, Tensegrity: Membranes, Internet Publication http://spatialgeometrix.blogspot.com/2010/10/tensegrity-membranes.html, Oct. 4, 2010, 3 pages, Hugh Thompson, United Kingdom. |
Toby Burgess, Phase 2 Gallery Exhibition / Internet Publication http://www.digitalhinterlands.com/exhibitor/toby-burgess, Sep. 8, 2009, 3 pages, United Kingdom. |
Anne Niemetz & Andrew Pelling, The Dark Side of the Cell Los Angeles County Museum of Art Concert & Exhibition / Internet Publication http://www.darksideofcell.info/installation.html, Jun. 2, 2004, 3 pages, Los Angeles, California. |
Lasse West, Culm and Cover, Design Competition / Internet Publication http://www.conbam.de/halmundhuelle.html?&L=1%22%20onfocus%3D%22blurLink%28this%29%3B, CONBAM, TRINEX, Aug. 9, 2005, 4 pages, Jteichen, Germany. |
Florian Idendburg & Jing Liu, In Tention, Sukkah City, Exhibition / Internet Publication http://so-il.org/artifact/66, http://img.sukkahcity.com/1600s/343—1600.jpg, Sep. 19, 2010, 4 pages, New York, New York. |
Mizuki Shigematsu et al., Form finding analysis of tensegrity membrane structures based on variational method, Proceedings of the 6th International Conference on Computation of Shell & Spatial Stuctures / Internet Publication http://ecommons.cornell.edu/handle/1813/11521, May 28, 2008, 4 pages, Ithaca, New York. |
Tristan D-Estree Sterk, Orambra Ultra-Lightweight Skyscrapers / Internet Publication http://www.orambra.com/˜filamentosa.html, Orambra, Approx. 2004, Chicago, Illinois. |
Trinex—WayBack machine Mar. 25, 2008. |
Number | Date | Country | |
---|---|---|---|
20150000213 A1 | Jan 2015 | US |
Number | Date | Country | |
---|---|---|---|
61427890 | Dec 2010 | US |
Number | Date | Country | |
---|---|---|---|
Parent | 13340474 | Dec 2011 | US |
Child | 14486333 | US |