WO2014170650A2

WO2014170650A2 - Folded shell structures

Info

Publication number: WO2014170650A2
Application number: PCT/GB2014/051161
Authority: WO
Inventors: Zhong You; Joseph GATTAS
Original assignee: Isis Innovation Limited
Priority date: 2013-04-19
Filing date: 2014-04-14
Publication date: 2014-10-23
Also published as: GB201307113D0; WO2014170650A3

Abstract

A shell structure is disclosed that comprises one or more shell modules. The shell modules each comprise a core module and a face module. The core module comprises a plurality of planar core plates having a geometry that allows them to fold relative to each other when unconstrained from a flat state to an expanded state having curvature. The face module comprises a plurality of planar face plates that are connected together at non-zero angles relative to each other. When the structure is assembled, the core module is in the expanded state and at least one of the face plates is connected along a continuous line to a corresponding core plate on a radially inner or radially outer side of the core module.

Description

FOLDED SHELL STRUCTURES

The present invention relates to shell structures, particularly curved shell structures that can be used to form sandwich panels having a lightweight core formed from folded planar elements.

Sandwich panels are known in which two stiff skins are attached to a lightweight core. Sandwich panels are used for example in modern aircrafts, for example using an aluminium honeycomb design, because of their high bending stiffness, high impact resistance, and low weight.

The lightweight core can also be formed by folding a flat sheet of material. A sandwich panel comprising such a core may be referred to as a foldcore sandwich panel. The core may be formed by folding the flat sheet into a tessellated pattern (e.g. an origami or origami-like pattern). Such a foldcore is sometimes referred to as a double-corrugated core because the resulting folds form corrugations that repeat in two, perpendicular directions.

Foldcore sandwich panels are advantageous over other types of sandwich panel for several reasons. For example, the core is simple to continuously manufacture from any sheet material (Zakirov and Alekseev, 2007; Basily and Elsayed, 2004), less sensitive or insensitive to manufacturing defects (Heimbs et al., 2007), and can be designed to have isotropic strength coefficients (Miura, 1972). Numerical and experimental studies have also shown that foldcores have comparable strength, stiffness, and energy-absorbing capabilities to an equivalent honeycomb core under lateral impact, due to the formation of an efficient plate buckling failure mode (Nguyen et al., 2005; Heimbs et al, 2010).

The bulk of existing engineering research has been conducted for planar sandwich panel geometries. A comprehensive literature review of existing planar foldcores can be found in Heimbs (2013).

Several academic articles and patent applications have suggested the possibility of developing curved lightweight sandwich panel core geometry using origami design techniques (Miura, 1972; Nojima and Saito, 2006; Fischer et al, 2009; Talakov, 2010; Alekseev, 2011; Kunstler and Trautz, 2011). However, curved foldcores tend to have jagged inner and outer edges which make it difficult to connect the inner and outer skins in order to manufacture a sandwich panel. Curved foldcore sandwich panels may therefore be difficult to manufacture efficiently and/or the resulting structure may be relatively weak and/or unreliable, at least for use in practical engineering or construction applications.

Several origami shell structures have recently been constructed for architectural and shelter applications. In general, these have been for emergency deployable structures. The benefit of using origami techniques in the design of these structures ensures that they are deployable, have a continuous watertight surface, are lightweight, and have a purely geometric mechanism, meaning their function is independent of the material used (Tachi, 2009). De Temmerman et al. (2007) and Buri and Weinand (Buri and Weinand) have shown foldable cylindrical shelters based on the so-called "Arc" and "Arc-Miura" patterns (discussed further below), and Gioia et al. (2012) has shown a similar shelter based on the so-called "Non-Developable Miura pattern" (also discussed further below). All these use a single-layer construction (i.e. without outer skins), and so suffer from extreme stress-concentration at the joints and correspondingly poor mechanical performance.

It is an object of the present application to at least partially address one or more of the problems with the prior art discussed above.

According to an aspect, there is provided a shell structure, comprising: a shell module comprising a core module and a face module, wherein: the core module comprises a plurality of planar core plates that are connected together via a plurality of core hinges so that, if the face module were absent, the core module would be capable of being transformed from a flat state in which the core plates are coplanar to an expanded state in which the core plates are not coplanar, via rotations of the core plates about the core hinges;

the geometry of the core module in the expanded state is such that additional, identical core modules can be connected to the core module to form a tessellated structure that extends along a curved path having a constant radius of curvature relative to a longitudinal axis of the core module; the face module comprises a first plurality of planar face plates that are connected together so that at least two of the face plates are at a non-zero angle relative to each other; and the core module is in the expanded state and at least one of the face plates is connected along a continuous line to a corresponding core plate on a radially inner or radially outer side of the core module.

Thus, a geometry is provided in which the inner and/or outer faces, formed by the face module(s), are faceted (each of the face plates forming one of the facets) and shaped so that a strong, continuous line bond can be made between the facets and the core. The core is formed from a tessellatable geometry, which is easily manufactured, for example by folding a flat sheet (with or without holes in the sheet). The core may be formed using origami or kirigami patterns for example. The core comprises planar core plates that are connected together at hinges (e.g. by folding of a material along a line) and thus encompasses foldcore geometries.

The core hinges may be interrelated so that when the core module is not constrained by the face module or face modules (as it would be in the completed shell structure when the face plates are attached to the core module) the core module can be transformed by rotations of the core plates in a manner that has only a single degree of freedom. Thus, in such an embodiment, for each angle of rotation of any given core plate relative to any other core plate, the angles of rotation about all other core hinges are uniquely defined. It is not possible to rotate any given core plate about a hinge in an independent manner. The use of such a mechanism makes the shell structure easy and reliable to deploy and/or manufacture.

The shell structure can be configured to have energy absorbing and/or structural properties. Varying the design of the shell structure can emphasize one or the other of these properties, or both. Accordingly, the shell structure can be used effectively in contexts that require different combinations of energy absorbing and structural properties. For example, in the context of an aircraft the shell structure may be useful as an energy absorbing component where failure (crushing) of the shell structure could be used to absorb and limit impact damage to the aircraft structure and occupants, for example after crash landings or bird strike. The shell structure may be configured to provide structural functionality in parts of the aircraft where high strength and stiffness is required, which is relevant to many parts of the aircraft frame. These two categories overlap, for example the aircraft fuselage will require structural properties in typical use, but will be expected also to behave as an energy-absorbing component in the event of a crash landing. Examples of positions on an aircraft where a shell structure according to an embodiment may be used are shown in Figure 1 : a) nosecone, b) wing leading edge, c) engine nacelle, d) and e) vertical and horizontal stabiliser leading edges; and structural components f) fuselage structure, g) and h) front and rear pressure bulkheads.

In an embodiment, particularly where the shell structure is configured for use in an aircraft, the shell structure may be provided with a faceted inner surface (i.e. a surface formed from planar face plate elements) and a smoothly curved outer surface (e.g. not comprising planar elements). As the required faceting can be configured to be very slight for the curvatures typically required in the context of aircraft panels (i.e. the angle between adjacent face plates is relatively small), manufacture by folding of typical aircraft materials such as aluminium and composite materials can easily be achieved.

In an embodiment, the shell structure may be used to manufacture shelters. In comparison to the origami shell structures discussed above (which do not have separate face layers), shell structures disclosed herein provide a superior load-bearing mechanism because the faces transmit bending loads, and the core modules carry shear and brace the face modules against buckling, similar to a planar sandwich panel load bearing mechanism. A range of shell structure geometries can be formed, including rigid structures in which rigid face plates are attached to the core and morphing shelters whereby a secondary origami pattern can be incorporated into the faceted faces.

In an embodiment, the face modules are configured to cooperate with core modules conforming to one of four types of pattern, referred to respectively as: Arc, Arc-Miura, Non-Developable Miura, and Flat- Foldable Miura patterns. Each of these patterns represents respectively a single modification of a property of a planar Miura-Ori pattern (discussed below): crease arrangement, crease alignment, developability, and flat- foldability respectively.

In an embodiment, the shell structure is built up from repeating identical shell modules. The use of such repeating units facilitates efficient manufacture and allows a wide range of shell structures to be created by varying the number of cell units (shell modules) included and/or the properties of each cell unit (shell module).

According to an alternative aspect, there is provided a kit for forming a shell structure, comprising: a core module and a face module, wherein: the core module comprises a plurality of planar core plates that are connected together via a plurality of core hinges in such a way that the core module can be transformed from a flat state in which the core plates are coplanar to an expanded state in which the core plates are not coplanar, via rotations of the core plates about the core hinges; the geometry of the core module in the expanded state is such that additional, identical core modules can be connected to the core module to form a tessellated structure that extends along a curved path having a constant radius of curvature relative to a longitudinal axis of the core module; the face module comprises a plurality of planar face plates that are connected together so that at least two of the face plates are at a non-zero angle relative to each other; and at least one of the face plates is connectable along a continuous line to a corresponding core plate on a radially inner or radially outer side of the core module when the core module is in the expanded state.

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings in which corresponding reference symbols represent corresponding parts, and in which:

Figure 1 depicts regions of an aircraft in which shell structures according to embodiments may be used;

Figure 2 is a perspective view of a prior art shell structure in which point contacts are made between the core and curved outer sheets;

Figure 3 is a sectional view along a longitudinal axis of the structure of Figure 2;

Figure 4 is a perspective view of a shell structure in which line contacts are made between interconnected face plates and core modules;

Figure 5 is a sectional view along a longitudinal axis of the structure of Figure 4;

Figure 6 depicts an unfolded core of a planar Miura pattern to illustrate pattern constants;

Figure 7 depicts a folded core of the planar Miura pattern of Figure 6 to illustrate pattern variables;

Figure 8 depicts an unfolded core module of an Arc-Miura type;

Figure 9 depicts a face module adapted to engage with the core module of Figure 8, when folded, on a radially inner side;

Figure 10 depicts a face module adapted to engage with the core module of Figure 8, when folded, on a radially outer side;

Figure 11 is an exploded view showing how the core module of Figure 8 and the face modules of Figures 9 and 10 fold in order to form the shell module;

Figure 12 depicts the shell module formed by engagement of the core and face modules of Figures

8-11;

Figure 13 depicts an unfolded example core module of the Arc Miura type to show pattern constants; Figure 14 depicts a folded example core module of the type shown in Figure 13 to show pattern variables;

Figure 15 depicts the core of a portion of a shell structure comprising shell modules of the Arc-Miura type in the unfolded state;

Figure 16 is a sectional view along the longitudinal direction of the portion of a shell structure corresponding to the core of Figure 15;

Figure 17 is a perspective view of the portion of a shell structure of Figure 16;

Figure 18 depicts in the unfolded state tessellated Arc-Miura core modules (top) and corresponding tessellated face modules for the radially inner (middle) and outer (bottom) sides;

Figure 19 depicts a shell structure built up from folded versions of the modules depicted in Figure

18;

Figure 20 depicts a folding sequence for multiple interconnected core modules of a Non-Developable Miura pattern type;

Figure 21 depicts an unfolded core module of a Non-Developable Miura type;

Figure 22 depicts a face module adapted to engage with the unfolded core module of Figure 21 on a radially inner side;

Figure 23 depicts a face module adapted to engage with the unfolded core module of Figure 21 on a radially outer side;

Figure 24 is an exploded view showing how the core module of Figure 21 and the face modules of Figures 22 and 23 fold in order to form the shell module;

Figure 25 depicts the shell module formed by engagement of the core and face modules of Figures

21-24;

Figure 26 depicts an unfolded example core module of the Non-Developable Miura type to show pattern constants;

Figure 27 depicts a folded example core module of the type shown in Figure 26 to show pattern variables;

Figure 28 depicts a sectional view along a longitudinal direction of core modules of the type shown in Figures 26 and 27 tessellated in a circumferential direction;

Figure 29 depicts a sectional view along the circumferential direction of the core modules shown in Figure 28;

Figure 30 depicts the core of a portion of a shell structure comprising shell modules of the Non- Developable Miura type in the unfolded state;

Figure 31 is a sectional view along the longitudinal direction of the portion of a shell structure corresponding to the core of Figure 30;

Figure 32 is a perspective view of the portion of a shell structure of Figure 31;

Figure 33 depicts a further example of an unfolded core module of the Non-Developable Miura type;

Figure 34 depicts a face module adapted to engage with the unfolded core module of Figure 33 on a radially inner side;

Figure 35 depicts a face module adapted to engage with the unfolded core module of Figure 33 on a radially outer side; Figure 36 is an exploded view showing how the core module of Figure 33 and the face modules of Figures 34 and 35 fold in order to form the shell module;

Figure 37 depicts the shell module formed by engagement of the core and face modules of Figures

33-36;

Figure 38 depicts in the unfolded state tessellated Non-Developable Miura core modules (top) and corresponding tessellated face modules for the radially inner (bottom left) and outer (bottom right) sides;

Figure 39 depicts a shell structure build up from folded versions of the modules depicted in Figure

38;

Figure 40 depicts in the unfolded state the same modules as Figure 38 but highlights an alternative tessellating unit cell;

Figure 41 depicts the shell structure of Figure 39 with the unit cell of Figure 40 highlighted;

Figure 42 depicts a folding sequence for multiple interconnected core modules of the Non-Flat- Folding Miura type;

Figure 43 depicts an unfolded core module of the Non-Flat-Folding Miura type;

Figure 44 depicts a face module adapted to engage with the core module of Figure 43, when folded, on a radially outer side;

Figure 45 depicts a face module adapted to engage with the core module of Figure 43, when folded, on a radially inner side;

Figure 46 is an exploded view showing how the core module of Figure 43 and the face modules of Figures 44 and 45 fold in order to form the shell module;

Figure 47 depicts the shell module formed by engagement of the core and face modules of Figures

43-44;

Figure 48 depicts an unfolded example core module of the Non-Flat-Folding Miura type;

Figure 49 depicts a folded example core module of the type shown in Figure 48;

Figure 50 depicts a sectional view along a longitudinal direction of core modules of the type shown in Figures 48 and 49 tessellated in a circumferential direction;

Figure 51 depicts a sectional view along the circumferential direction of the core modules shown in Figure 50;

Figure 52 depicts the core of a portion of a shell structure comprising shell modules of the Non-Flat- Folding Miura type in the unfolded state;

Figure 53 is a sectional view along the longitudinal direction of the portion of a shell structure corresponding to the core of Figure 52;

Figure 54 is a perspective view of the portion of a shell structure of Figure 53;

Figure 55 is an exploded view showing how a core module of the Arc type and face modules adapted to connect to radially inner and outer sides of the core module fold in order to form the shell module; Figure 56 depicts the shell module formed by engagement of the core and face modules of Figure 55; Figure 57 depicts the core of a portion of a shell structure comprising shell modules of the Arc type in the unfolded state;

Figure 58 is a sectional view along the longitudinal direction of the portion of a shell structure corresponding to the core of Figure 57;

Figure 59 is a perspective view of the portion of a shell structure of Figure 58;

Figure 60 depicts in the unfolded state, two Arc-Miura core modules and a half of an Arc core module that are configured to tessellate with each other;

Figure 61 is an exploded perspective view of a shell structure comprising folded versions of the modules depicted in Figure 60, together with appropriate face modules;

Figure 62 is an exploded sectional view along the longitudinal direction of the shell structure of Figure 61 ;

Figure 63 is a perspective view of a shell structure formed from the dissimilar core modules of Figure 60 with bridging face plates to achieve a continuous radially inner face surface;

Figure 64 is a sectional view along the longitudinal direction of the shell structure of Figure 63;

Figure 65 is a perspective view of a shell structure formed from the dissimilar core modules of Figure 60 with extending face plates to achieve a continuous radially inner face surface;

Figure 66 is a sectional view along the longitudinal direction of the shell structure of Figure 65;

Figure 67 depicts in the unfolded state, two planar Miura core modules and a curved Arc-Miura core module that are configured to tessellate with each other;

Figure 68 comprises exploded perspective (top) and longitudinal sectional (bottom) views showing how the modules of Figure 67 fit together in the folded state, together with suitable continuous radially inner and outer face surfaces;

Figure 69 comprises perspective (top) and longitudinal sectional (bottom) views of a shell structure according to Figure 68 in the assembled state;

Figure 70 depicts a core module of complex geometry in the unfolded state;

Figure 71 is an exploded perspective view showing how the core module of Figure 70 can be folded and attached to radially inner and outer face modules to form a shell structure;

Figure 72 is a longitudinal sectional view of the exploded shell structure of Figure 71 ;

Figure 73 is a perspective view of the shell structure of Figures 71 and 72 in the assembled state;

Figure 74 is a longitudinal sectional view of the assembled shell structure of Figure 73;

Figure 75 depicts an unfolded core module (top) and inner (middle) and outer (bottom) face modules of a shell structure comprising a void;

Figure 76 is a perspective view of an assembled, folded shell module formed from the modules of Figure 75; Figure 77 is a radially outward view of the shell structure of Figure 76;

Figure 78 is a perspective view of a shell structure comprising core modules that are stacked in the radial direction;

Figure 79 is a longitudinal sectional view of the shell structure of Figure 78.

In an embodiment, as illustrated in the perspective and longitudinal sectional views of Figures 4 and 5 for example, there is provided a shell structure 2 that comprises a shell module comprising a core module (formed from core plates 4A-4D in the example shown) and a face module (formed from portions of the plates 8 and 14 that are adjacent to the core module in the example shown). The shell structure 2 may further comprise one or more further core modules, face modules, or portions of either, which may be identical or non-identical. In the example of Figures 4 and 5, the shell structure 2 comprises three further shell modules, tessellated longitudinally and circumferentially.

Each core module comprises a plurality of planar core plates that can be hinged relative to each other to form an expanded structure having a finite radius of curvature relative to a longitudinal axis X (into the page in the example of Figure 5) of the shell module. In the example shown the radius of curvature is marked "R" on Figure 5. The curvature can be seen most clearly when a plurality of the core modules are connected together to form a tessellated structure that extends along a curved path that is longer than that associated with a single core module, as shown in Figure 5. In the example of Figures 4 and 5, the core plates 4A-4D may be considered to belong to a first core module. One core module may be considered as a unit cell that can be tessellated with other core modules or portions of core modules to form a larger structure. In the example shown, the core module of core plates 4A-4D is tessellated in a direction parallel to the longitudinal axis with one identical core module and in the circumferential direction with another identical core module. The tessellated core modules may be connected to each along hinge lines for example.

In an embodiment, the core plates are interconnected via hinges 6 in the sense that each core plate is connected to at least one other core plate via a hinge 6. The hinges 6 allow the relative orientations of adjacent connected core plates to be changed. Various methods for implementing the hinges 6 may be used. For example the hinges 6 may comprise lines along which the material of the core plates has been folded. The hinges 6 may comprise lines of reduced rigidity, achieved for example by folding along the lines or by reducing the thickness of the core plate material along the lines. Alternatively or additionally, the hinges 6 may be formed by attaching plates, material, or other elements of finite thickness to the core plates, for example in the style of a piano hinge or cloth tape. As will be discussed below, the face plates may also be connected together by hinges and any or all of these hinges may also be implemented by any of the methods described above or by other methods.

In an embodiment, the interconnected core plates form a folding mechanism that has a single degree of freedom. In an embodiment, the core plates may be connected to each other in such a way that, in the absence of any constraint, they can be folded from a sheet like state in which the core plates are coplanar into an expanded state, such as that shown in Figures 4 and 5, in which the core plates are not co-planar. In an embodiment, the core plates may also be foldable into a flat-folded state in which the core plates are substantially parallel to each other with at least a subset of the core plates lying on top of each other.

A Miura-Ori (literally, "Miura fold") is a rigid fold pattern development by Miura (Miura, K. (1993), "Map Fold a La Miura Style, Its Physical Characteristics and Application to the Space Science", Research of Pattern Formation, pp. 77-90). Miura-Ori patterns are examples of folding mechanisms with a single degree of freedom and can be folded and unfolded in a simple and convenient manner. For example a geographical map folded according to a Miura-Ori pattern can be deployed simply by pulling on opposite corners, in contrast to conventional orthogonally folded maps that require a complex sequence of movements to unfold. Furthermore, once unfolded the non-right-angled corners of a Miura-Ori map are much more stable and less prone to folding "inside out" .

Figures 6 and 7 illustrate how the geometry of a Miura base pattern can be parameterized. Figure 6 depicts the pattern in the unfolded state and Figure 7 depicts the pattern in the folded or "expanded" state. In this case, the Miura base parameterisation given in Wu (2010) is used. In this parameterisation, the unfolded Miura geometry is determined generally by five pattern constants: side lengths a and b, pattern angle φ , and the number of crease lines in the longitudinal (y), and lateral (x) directions, m and n respectively. Crease lines (hinges) are marked by dot-dashed lines for valley folds and dashed lines for mountain folds. One of seven pattern variables is also required to determine the folded configuration. The seven pattern variables are dihedral angles or θ_ζ , edge angles or r _z , or pattern length l_a, width 4, or height l_h as illustrated in

Figure 7. A total of six independent parameters is required to completely define the Miura pattern.

In an embodiment, the core modules are formed from a geometry that is a modification of the Miura base pattern that results, for example, in the core module having a finite global curvature when the core plates are in the "expanded" (i.e. not flat) state.

In an embodiment, the modification is to the alignment of the hinges 6 and is termed "Arc-Miura". The arrangement of Figures 4 and 5 comprises a core formed from tessellation of core modules of the Arc- Miura type in the expanded state. Core modules forming patterns of the Arc-Miura type may retain the "flat- foldability" of the Miura base pattern in the sense that the core plates can be folded into a "flat-folded" state in which the core plates are all substantially parallel to each other with at least some of the plates lying on top of each other. The core modules may also retain the "rigid foldability" of the Miura base pattern in the sense that the structure formed from the core modules can be folded into different shapes without any bending of the core plates themselves (which can thus be completely rigid). Core modules of the Arc-Miura type may also retain the "developability" of the Miura base pattern. This is discussed in further detail below.

In an embodiment, there is provided a plurality of planar face plates 8 that can be hinged relative to each other about one or more hinges 10 which, in an embodiment, are parallel to the longitudinal axis X of the shell module 2. The hinges 10 may be formed in the same way as the hinges 6 between the core plates 4 or in a different way. The face plates 8 are dimensioned so as to be connectable along a continuous line 12 (marked by thicker lines for emphasis in Figures 4 and 5) to a corresponding core plate (for example via an edge or hinge of the core plate) on a radially inner or radially outer side of the core plates. In an

embodiment, the continuous line connection spans a face plate, for example extending continuously from one hinge 10 to a different hinge 10 of the face module.

In the example shown, the face plates 8 are formed on a radially outer side of the core plates. In the example shown the "edges" of the core plates correspond to hinges 6 between the core plates.

In an embodiment, a further plurality of face plates 14 are provided on an opposite side of the core plates so that face plates are present on both the radially inner and radially outer sides of the core plates. Again, the face plates 14 may be dimensioned so that they can be brought into contact with the core plates along continuous lines 12 (marked by thicker lines for emphasis in Figure 4).

The provision of a connection that is made along a continuous line 12, 16 is stronger and more reliable than prior art arrangements that use curved inner and/or outer face units on either side of the core in combination with point contacts. An example of a prior art approach to attaching face units 20 to a core structure of the type illustrated in Figures 4 and 5 is shown in Figures 2 and 3. As can be seen the curved face units 20 are only able to be brought into contact with the core at isolated points 22, which is why the connection tends to be weaker and/or less reliable.

In the example of Figures 4 and 5, the outer face plates 8 do not all have the same length L in a direction perpendicular to the longitudinal axis X (i.e. at a tangent to the circumferential direction). In the example shown, the inner face plates 14 also do not have the same length. However, this is not essential. In other embodiments the face plates may have the same length on one side (on either or both of the inner and outer sides).

Figure 8 shows a core module 24 of the Arc-Miura type comprising four core plates 4A-4D in the unfolded state (i.e. lying flat within the plane of the page). Figures 9 and 10 show corresponding radially inner and outer face modules 28 and 30 in the unfolded state. Figure 11 is an exploded view showing how the core and face modules fold and fit together to form the shell module 40. The folded state adopted by the core module 24 may be referred to as an expanded state to distinguish over the flat state adopted in Figure 8. Figure 12 illustrates the shell module 40 in the assembled state.

The modification of the core module relative to the base Miura pattern in this example can be seen by inspecting Figures 6 and 8 for example. The angle made by the hinges 6A with the hinges 6B is no longer the same as the angle made by the hinges 6C and the hinges 6B.

The radially inner face module 28 comprises two face plates 30A and 30B which are hinged together by hinge 32. The hinge 32 may lie parallel to the longitudinal axis in the assembled state. The radially outer face module 30 comprises two face plates 34A and 34B which are hinged together by hinge 36. The lengths /_{; 1} and /_{; 2} of the face plates 3 OA and 3 OB in the circumferential direction need to be different to allow the continuous line connection 12 to be made. Similarly, the lengths iff and iff of the face plates 34A and

34B in the circumferential direction also need to be different to achieve the continuous line connection 12.

In an embodiment, the shell structure 2 can be made up from a plurality of the core modules 24 and radially inner and/or outer face modules 28,30 that are tessellated either in the circumferential direction, perpendicular to the longitudinal axis of the core modules, and/or in a direction parallel to the longitudinal axis of the core modules. In an embodiment, the tessellation is such that the core modules form a continuous structure, for example of an Arc-Miura type. In an embodiment, the face modules form continuous radially inner and/or radially outer surface(s). This would be the case where the shell modules of Figures 8-12 are tessellated in this manner, for example.

The construction of a shell structure 2 using repeating shell module 40 units facilitates use in engineering or architecture because the repetitive geometry considerably simplifies manufacture and assembly of structures.

Figures 13 and 14 depict in detail the geometry of an example core module of the Arc-Miura type. Figure 13 depicts the core module 24 in the unfolded state and illustrates the pattern constants a a₂, b b₂, φ₁ , and φ₂ . Figure 14 depicts the core module 24 in the folded (expanded) state and illustrates the pattern variables ,θ^ ,Θ _Ζ , \_VA , \_ΜΑ , , and η _Ζ .

Figures 15-17 illustrate the geometry of a shell structure 2 formed from tessellating core and face modules of the Arc-Miura type.

In Figures 15-17, points A-H have been marked to show the correspondence between the figures. Figure 15 shows the tessellated core modules in the unfolded state. As can be seen, the tessellated core modules in this example comprise one complete core module formed from core plates 4A-4D, one half of a core module tessellated in the circumferential direction comprising core plates 4E and 4F, and one half of a core module tessellated in the longitudinal direction comprising core plates 4G and 4H. Figure 16 is a longitudinal sectional view showing the assembled shell structure 2 complete with face modules. Figure 17 is a perspective view of the assembled shell structure 2.

As can be seen, the core modules do not provide an edge that is continuous along a constant radius, either on the inner or outer radii. However, inner and outer face modules can still be attached effectively by faceting the face modules (forming the face modules from multiple interconnected face plates that are hinged together) via the continuous line connections that are made with every other one of the face plates (along the zig-zag edges 12 of the core modules). The continuous line connections are marked by thicker lines in Figure 17.

As discussed above with reference to Figures 8-12, two face lengths are required for both inner and outer face plates: if , iff , iff and iff . Equations for Arc-Miura pattern parameters ξ,ξ_Μ ,ξ_α2 ,Ri and R₂ are given in Wu, and they can be used in the following equations to calculate the face lengths:

/_{ο !2} = ?₁ /2 - 2 οο8(ξ - ξ_Μ )

Ι_ιίΛ = ^_{2 Λ}/2 - 2 οο8(ξ_Μ + 2ξ_α2 - ξ) hf* = ^_{2 Λ}/2 - 2 οο8(2ξ - ξ_Μ - 2ξ_α2 ) . Note that in this embodiment the inner and outer face lengths

l span unsupported between core- face bonds, and so would be expected to be important for determining face compressive capacity. In alternative embodiments, the Arc-Miura core geometry is adapted to remove or reduce the length of such unsupported face plates.

In Figures 18 and 19, a shell structure 2 comprising four complete shell modules 40 is depicted. Figure 18 shows the four core modules in the unfolded state (top) with one of them highlighted by shading, the inner face plates in the unfolded state (middle) with the face plates corresponding to one shell module highlighted by darker shading, and the outer face plates in the unfolded state (bottom) with the face plates corresponding to one shell module highlighted by darker shading. Figure 19 depicts in perspective view the corresponding assembled structure.

In an embodiment, the core modules are formed from a geometry that is a different modification of the Miura base pattern that results in the pattern no longer being developable. This means that the plurality of interconnecting core plates making up the core modules are no longer connected together in such a way that the pattern can be formed from a continuous sheet without any cavities (as in Figures 15 and 18 for example). The resulting pattern may be referred to as a Non-Developable Miura pattern. Developability is not a requirement for folded plate structures used in engineering applications. Without this requirement, a much larger range of rigid folded plate geometry is possible. The Non-Developable Miura pattern retains flat-foldability and rigid foldability characteristics, but is not developable. The pattern must be constructed by joining separate patterns along a common edge. Once joined, the edge is able to transfer the rigid plate folding motion across the joined edge, to create a whole pattern with a single degree of freedom. After this joining, the Non-Developable Miura pattern will also lose the ability to fold flat into the planar state (with all core plates in the same plane), but will be foldable into the state where all the core plates are parallel with each other with a subset lying on top of each other. An example folding sequence for a Non-Developable Miura pattern is shown in Figure 20. Specific examples are discussed below in further detail with reference to Figures 21-41.

Figure 21 depicts a core module 24 of the Non-Developable Miura type comprising four core plates 4A-4D in the unfolded state. Figures 22 and 23 show corresponding radially inner and outer face modules 28 and 30 in the unfolded state. Figure 24 is an exploded view showing how the core and face modules fold and fit together to form the shell module 40. The folded state adopted by the core module 24 may be referred to as an expanded state to distinguish over the flat state adopted in Figure 21. Figure 25 illustrates the shell module 40 in the assembled state.

The radially inner face module 28 comprises two face plates 30A and 30B which are hinged together by hinge 32. The hinge 32 may lie parallel to the longitudinal axis in the assembled state. The radially outer face module 30 comprises two face plates 34A and 34B which are hinged together by hinge 36. As in the examples discussed above, the dimensions of the face plates are chosen so as to allow them to make continuous line contacts 12 with the edges of the core plates.

Figures 26-29 illustrate how the geometry of a core module 24 of the Non-Developable Miura type can be parameterized. Figure 26 depicts the core module 24 in the unfolded state and Figure 27 depicts the core module 24 in the folded or "expanded" state, ready for connection with one or more face modules to form a shell module. As can be seen, the crease pattern is obtained by adding or subtracting length

Ab = (b₀ - b_x ) / 2 to alternating zig-zags on a base Miura pattern, where b_t and b₀ are the inner and outer zig-zag side lengths. The unfolded configuration shown in Figure 26 is therefore determined by the same five parameters of the Miura pattern, a, b φ , m, and n, plus one additional constant b₀ or Ab . The folded geometry can be parameterised using cylindrical co-ordinates, which are found with three additional pattern variables: lateral panel rotation angle pattern γ , and radii ?_¾ and R₀k, as illustrated in Figures 27-29.

Figures 30-32 illustrate the geometry of a shell structure 2 formed from tessellating core and face modules of the type illustrated in Figures 21-29. Points A-H have been marked to show the correspondence between the figures. Figure 30 shows the tessellated core modules in the unfolded state. As can be seen, the tessellated core modules comprise one complete core module formed from core plates 4A-4D, one half of a core module tessellated in the circumferential direction comprising core plates 4E and 4F, and one half of a core module tessellated in the longitudinal direction comprising core plates 4G and 4H. Figure 31 is a longitudinal sectional view showing the assembled shell structure 2 complete with face modules. Figure 32 is a perspective view of the assembled shell structure 2.

As can be seen, the Non-Developable pattern has nodes 42 located at kinks along the inner and outer edges, so bending (hinging) face plates around these kinks (i.e. with the hinges between face plates effectively running along a line of the nodes 42) allows them to be attached continuously along core zigzag lines. This is illustrated in Figures 31 and 32. There is one facet length required for the inner face, l ^D , and one facet length required for the outer face, l ^D , given by the following equations:

In the embodiment discussed above, a shell structure may be formed by tessellating shell modules 40 acting as unit cells and formed as shown in Figures 21-25. However, the same shell structure may be seen as being formed by tessellating a differently defined shell module. An example of such an alternative shell module 40 is shown in Figures 33-37, which respectively depict unfolded versions of a core module, an inner face module and an outer face module, and an exploded perspective view of a folded version of the shell module and a non-exploded perspective view of a folded version of the shell module, corresponding to Figures 21-25. Corresponding parts are marked with corresponding reference numerals. Figures 38 and 39 show how four whole shell modules 40 of the type shown in Figures 21-25 can be tessellated to form an example shell structure 2. Figures 40 and 41 show how four of the shell modules 40 of Figures 33-37 can be tessellated to form the same shell structure 2 as that shown in Figure 39. Figures 38 and 40 depict unfolded versions of tessellated core modules (top), tessellated inner face plates (bottom left) and tessellated outer face plates (bottom right). Face plates of one of the shell modules 40 are shown in darker shade.

In an alternative embodiment, the core modules are formed from a geometry that is a different type of modification of the Miura base pattern that results in the pattern no longer being flat-foldable. The resulting pattern may be referred to as a Non-Flat-Foldable Miura pattern. The Non-Flat-Foldable Miura pattern is similar to the Non-Developable Miura pattern, except that where portions of the Miura base are removed in the Non-Developable Miura pattern, these sections are instead retained as triangular plates in the Non-Flat-Foldable Miura pattern. This creates a pattern that is the converse of the Non-Developable Miura pattern, in that it retains developability, but loses flat-foldability. Linear combinations of the Non- Developable and Non-Flat-Foldable Miura patterns can be used to create more complex, yet still repetitive folded plate geometries for core modules. An example folding sequence for a Non-Flat-Foldable Miura pattern is shown in Figure 42.

Figure 43 depicts a core module 24 of the Non-Flat-Foldable Miura type comprising larger core plates 4A-4D and smaller core plates 4E-4J in the unfolded state. Figures 44 and 45 show corresponding radially outer and inner face modules 30 and 28 in the unfolded state. Figure 46 is an exploded view showing how the core and face modules fold and fit together to form the shell module 40. The folded state adopted by the core module 24 may be referred to as an expanded state to distinguish over the flat state adopted in Figure 43. Figure 47 illustrates the shell module 40 in the assembled state.

The radially outer face module 30 comprises five face plates 34A-34E in this example, which are hinged together by hinges 36. The hinges 36 may lie parallel to the longitudinal axis in the assembled state. The radially inner face module 28 comprises two face plates 30A and 30B which are hinged together by hinge 32. As in the examples discussed above, the dimensions of the face plates are chosen so that one or more of them form a continuous line contact 12 with one or more edges of the core plates.

Figures 48-51 illustrate how the geometry of a core module 24 of the Non-Flat-Foldable Miura type can be parameterized. Figure 48 depicts the core module 24 in the unfolded state and Figure 49 depicts the core module 24 in the folded or "expanded" state, ready for connection with one or more face modules to form a shell module. The unfolded pattern can be completely defined by specifying a width

w = (b_j - b_o ) είηφ / 2 on alternating zig-zags on a normal Miura pattern, or by specifying the side length change Ab = w / είηφ , as illustrated in Figure 48. The unfolded configuration is then determined by the five pattern constants of the Miura pattern, a, b₀, § , m and n, plus one additional constant bj, Ab or w.

The folded geometry can be parameterised using cylindrical coordinates, which are found with seven additional pattern variables: global panel rotation angles p and p_k , local panel rotation angles γ and α , inner radius i?„ and outer radii R_ow and R₀k, as depicted in Figures 49-51.

Figures 52-54 illustrate the geometry of a shell structure 2 formed from tessellating core and face modules of the type illustrated in Figures 43-51. Points A-L have been marked to show the correspondence between the figures. Figure 52 shows the tessellated core modules in the unfolded state. As can be seen, the tessellated core modules comprise one complete core module formed from core plates 4A-4J, one half of a core module tessellated in the circumferential direction comprising core plates 4K-4P, and one half of a core module tessellated in the longitudinal direction comprising core plates 4Q-4V. Figure 53 is a longitudinal sectional view showing the assembled shell structure 2 complete with face modules. Figure 54 is a perspective view of the assembled shell structure 2. Selected ones of the continuous lines of connection 12 between the face plates and the core plates have been shown in thicker lines.

Attachment of face modules to a Non-Flat-Foldable Miura pattern is similar to the process used for the Non-Developable Miura pattern. The only difference is that two face plate lengths are required along the outer edge, Ιζ and Ιζ . Note that, if desired, it is possible to define an additional geometry constraint 2w = b_o sin(r|_z / 2) , such that these two lengths are equal. There is still only one facet length required along the inner edge, l ^F . These lengths are given by the following equations:

II = ^R _ok V2(l - cos(2p - 2pJ)

Figures 55 and 56 are exploded and non-exploded perspective views of a shell module 40 according to a further embodiment. Figure 57 shows the core module of the shell module 40 of Figures 55 and 56 in the unfolded state (comprising core plates 4A-4D) tessellated with a half of an identical shell module (comprising core plates 4E and 4F) in the circumferential direction and a half of an identical shell module (comprising core plates 4G and 4H) in the longitudinal direction. Figures 58 and 59 depict a shell structure formed using the shell module 40 of Figures 55 and 56 tessellated according to the geometry of Figure 57. As can be seen most clearly in Figure 57, the geometry of the core modules is similar to that of the Miura pattern except that alternate zig-zag creases are flipped relative to each other in polarity. The geometry may be referred to as an "Arc" pattern or geometry, although certain forms of the Arc pattern are also sometimes referred to as the Yoshimura pattern. To attach face modules to the Arc pattern, a different method to those used for other single-curved patterns is required. This is because the alternating zig-zag pattern causes all zig-zag creases to be of the same polarity, and therefore to lie along the same outer radius. The outer face module 30 can therefore be continuously connected along both the core zig-zag (marked 12A) and the straight mountain-crease lines (marked 12B). The inner face plate 28, on the other hand, is attached only along straight valley-crease pattern lines (marked 12C).

Two face plate lengths are required for the outer face, lf_l , lf₂ , and one face plate length for the inner face length if . These can be related to existing Arc parameters R, Θ_Α , ξ₁ and ξ₂ , with the following equations:

In an embodiment (such as one of the embodiments described above), shell modules are tessellated with other shell modules, or portions of shell modules, that are nominally identical (or similar). This approach can be used for example to create a structure in which multiple shell modules in the circumferential direction define an arc of constant radius of curvature. However, the tessellation of identical units is not essential. In other embodiments, shell modules having compatible but different ("dissimilar" or "non- identical") geometries may be connected together.

In an embodiment, non-identical shell modules of compatible geometry are connected together (tessellated) in a circumferential direction in order to define an arc having a non-uniform radius of curvature. For example, non-identical shell modules each having a finite radius of curvature may be connected together in the arc.

Figure 60-62 depicts an example in which non-identical shell modules are connected together. In this particular example, two Arc-Miura type shell modules 50 are connected via a fragment of a non-identical shell module 52. In this embodiment, the fragment comprises half of an Arc pattern shell structure

(comprising two core plates 56 connected together along a hinge 6). Figure 60 depicts the core modules 54 of the two shell modules 50 and plates 56 of the fragment 52 in the unfolded state (with each plate 4,56 flat in the plane of the page). Figure 61 is an exploded perspective view showing the shell modules 50 and fragment 52 in their folded states, together with inner and outer face modules 28 and 30, ready for connection to produce a shell structure 2. Face plates 58 of the fragment 52 are also shown. Figure 62 is a longitudinal sectional view of the configuration of Figure 61.

In embodiments where a plurality of shell modules are tessellated in the circumferential direction, the face plates of the face modules from different shell modules may be configured to connect together to form a continuous surface spanning the plurality of shell modules that are tessellated in the circumferential direction. A continuous surface may be provided on the radially inner side and/or on the radially outer side. Examples are described above, for example with reference to Figures 19, 39, 41, 54 and 59.

In other embodiments, tessellation of the shell modules may not naturally provide such continuous face surfaces. This is particularly likely to be the case where the shell structure is formed by tessellating non-identical shell modules. However, a continuous inner and/or outer surface can still be achieved. In an embodiment, a continuous face surface is provided by adding additional face plates to the structure that connect together face plates from different shell modules. These additional face plates may resemble extensions of shell module face plates or may bridge across a portion of the shell structure. Examples are given in Figures 63-66.

Figures 63 and 64 are perspective and longitudinal sectional views of a shell structure 2 having the same core structure as the embodiment described above with reference to Figures 60-62: namely, comprising two Arc-Miura type shell modules 50 connected together via a fragment 52 comprising half of an Arc pattern shell structure. In this embodiment, a continuous inner surface is provided by means of an additional face plate 60 that spans across from one of the Arc-Miura shell modules 50 to the other. In this example, this requires a relatively long additional face plate 60, marked by distance Bl .

Figures 65 and 66 are perspective and longitudinal sectional views of a shell structure of the type of Figures 63 and 64 except that instead of the bridging additional face plate 60 two extending additional face plates 62 are provided that each extend from face plates of respective Arc-Miura shell modules 50. The extending face plates 62 are at least approximately aligned with the face plates of the shell modules 50 to which they are connected and, in this example, are significantly shorter than the additional face plate 60 of Figures 63 and 64, marked by distance B2.

The differences in orientation and length of the example additional face plates lend correspondingly different structural and impact resistant properties to the shell structures and can be selected according to the requirements of the application in question. Indeed, the arrangements depicted in Figures 63-66 represent just two examples of how continuous surfaces can be achieved. In general there will be many options for configuring the additional face plates and, as a consequence, considerable flexibility for tuning the properties of the shell structure 2.

In another embodiment, a shell module having a finite radius of curvature may be connected to one or more units that have no curvature (infinite radius of curvature). The units having no curvature may be referred to as planar structures. The planar structures may comprise a core structure formed from a Miura- Ori pattern or an adaptation thereof. The planar structures may each comprise one or more face plates on the inner and/or outer surfaces. Examples of arrangements comprising such planar structures are described below with reference to Figures 67-69.

Figure 67 depicts unfolded cores 65 of two planar structures 64 and of a core module 24 of a shell module 40 connecting the two planar structures 64. Figure 68 depicts exploded perspective and longitudinal sectional views of the shell structure 2. Figure 69 depicts non-exploded perspective and longitudinal sectional views of the shell structure 2. In this example, the planar structures 64 are connected together by a curved shell module 40. In this example, each of the planar structures 64 comprises a core formed from a planar Miura-Ori pattern with planar face plates 66 and the shell module 40 is of the Arc-Miura type.

Figures 70-74 depict a shell module having a complex core geometry. Figure 70 depicts two core modules 24 tessellated in the circumferential direction and in the unfolded state. The core modules 24 each comprise core plates 4 connected together by hinges. In this embodiment a first subset of the hinges 6A are configured to lie in planes that are perpendicular the longitudinal axis of the core modules in the folded (expanded) state and a second subset of the hinges 6B are configured to lie in planes that are parallel with the longitudinal axis. Figures 71 and 72 are exploded perspective and longitudinal sectional views showing how the core modules 24 can be folded and face modules 28 and 30 attached on the inner and outer sides to form the shell structure 2. Figures 73 and 74 are non-exploded perspective and longitudinal sectional views of the shell structure 2. This embodiment illustrates the wide range of core geometries to which the invention can be applied. The key requirement for this type of embodiment is that at least a subset of the hinges (in this case hinges 6B) are oriented so that a planar face plate can be connected to the hinge on an inner or outer side of the core module in order to form a continuous line connection 12. In this embodiment, a plurality of hinges 6B satisfy this requirement and lie in a common plane, thus providing for a continuous line of connection 12 to the face plates along a plurality of hinges 6B.

In an embodiment, a shell structure is formed by tessellating identical or non-identical shell modules and/or planar structures to form a continuous structure without cavities in either or both of the inner and outer surfaces and/or in the core structure. However, other arrangements are possible. In particular, one or more cavities or voids may be incorporated into one or more of the core structure and the inner and outer faces. An example of such an arrangement is shown in Figures 75-77.

Figure 75 shows an unfolded core structure (top) formed by tessellating a plurality of core modules 24, in this example of the Arc-Miura type, with a void 70 formed in a central region, a corresponding unfolded plurality of inner face modules 28 with a further void 72 formed therein, and a corresponding unfolded plurality of outer face modules 30 with a further void 74 formed therein. Figure 76 shows the shell structure 2 formed from folding and assembling the modules depicted in Figure 75. Figure 77 is a radial view of the shell structure 2 of Figure 76. As can be seen, in this example the void traverses the whole shell structure 2 in the radial direction. Other arrangements are possible in which the void does not completely traverse the shell structure. One or plurality of voids may be provided. This may be convenient for certain applications, for example shelters requiring penetrations for windows and doors. In an embodiment, a void is defined by one or more fragments of shell modules that are provided around at least a portion of the edge of the void.

In the embodiments discussed above, the shell structures comprise shell modules that are tessellated in either or both of the circumferential or longitudinal directions only. However, it is also (or alternatively) possible to connect shell modules together in the radial direction to create a radially multilayered structure. Such structures provide a further opportunity to tune the properties of the shell modules, for example the structural and/or impact resistant properties, so that they are best suited to the application in question.

In an embodiment, shell modules that are connected together in the radial direction share a face plate, such that a radially outer face plate of one of the shell modules is a radially inner face plate of the other of the shell modules. An example of such an arrangement is shown in Figures 78 and 79.

Figures 78 and 79 are perspective and longitudinal sectional views of a shell structure 2 comprising shell modules that are tessellated in a radial direction. In this embodiment, face plates 76 positioned radially between two shell modules are shared between the two shell modules. In this embodiment, the two core modules also have aligned edges, although in other embodiments this may not be the case.

As discussed above, a shell structure according to an embodiment of the invention may be used as a panel in an aircraft. In this case, the shell module may comprise face modules having planar (faceted) elements on the radially inner side (the side which will not be exposed to air flowing past the aircraft in use) and a smoothly curved outer surface on the radially outer side.

The shell structure may also be used as all or part of a deployable shelter or other deployable structure. In this case, a kit may be provided that comprises the core modules and face modules disconnected from each other. In this case, the core modules and face modules may be configured to be "flat-foldable" in the sense that they can be folded into a state in which the constituent plates are substantially parallel to each other with at least a subset of the plates lying on top of each other. The flat-folded modules can therefore be transported to the site where they will be connected together to form the shell structure more efficiently and/or stored more efficiently

In the examples discussed above a continuous line connection is made between the core modules and the face modules. The line connection may be a width corresponding to the width of the edges or hinges of the core plates forming the line connection. Alternatively, the line connection may be part of an area connection where a core plate is parallel to the face plate to which it is to be connected. This type of arrangement can be achieved using core modules that form a Kirigami structure for example.

References

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Claims

1. A shell structure, comprising:

a shell module comprising a core module and a face module, wherein:

the core module comprises a plurality of planar core plates that are connected together via a plurality of core hinges so that, if the face module were absent, the core module would be capable of being transformed from a flat state in which the core plates are coplanar to an expanded state in which the core plates are not coplanar, via rotations of the core plates about the core hinges;

the geometry of the core module in the expanded state is such that additional, identical core modules can be connected to the core module to form a tessellated structure that extends along a curved path having a constant radius of curvature relative to a longitudinal axis of the core module;

the face module comprises a first plurality of planar face plates that are connected together so that at least two of the face plates are at a non-zero angle relative to each other; and

the core module is in the expanded state and at least one of the face plates is connected along a continuous line to a corresponding core plate on a radially inner or radially outer side of the core module.

2. A structure according to claim 1, wherein the rotations of the core plates about the core hinges are interrelated such that the transformation has a single degree of freedom;

3. A structure according to claim 1 or 2, wherein the face plates are connected together along hinge lines that are parallel to the longitudinal axis of the core module.

4. A structure according to any of the preceding claims, wherein the continuous line extends continuously across at least one of the face plates so as to span that face plate.

5. A structure according to any of the preceding claims, wherein the shell module further comprises a second plurality of planar face plates that are connectable on a radially opposite side of the core module to the first plurality of planar face plates.

6. A structure according to any of the preceding claims, wherein each face plate of the first plurality of face plates has the same length in a direction perpendicular to the longitudinal axis of the shell module and/or each face plate of the second plurality of face plates has the same length in a direction perpendicular to the longitudinal axis of the shell module.

7. A structure according to any of claims 1-5, wherein at least one face plate of the first plurality of face plates has a different length in a direction perpendicular to the longitudinal axis of the shell module than at least one other face plate of the first plurality of face plates and/or at least one face plate of the second plurality of face plates has a different length in a direction perpendicular to the longitudinal axis of the shell module than at least one other face plate of the second plurality of face plates.

8. A shell structure according to any of the preceding claims, further comprising one or more additional, identical shell modules connected to the shell module to form a tessellated structure that extends along a curved path of constant radius of curvature.

9. A shell structure according to claim 8, wherein all of the planar core plates of all of the identical core modules are connected together via a plurality of hinges so that, if the face modules were absent, the plurality of identical core modules would be capable of being transformed as a unit from a flat state in which all of the core plates are coplanar to an expanded state in which the core plates are not coplanar, via rotations of the core plates about the core hinges, the rotations of the core plates about the core hinges being interrelated such that the transformation has a single degree of freedom.

10. A shell structure according to any of claims 1-7, further comprising one or more additional, non- identical shell modules that are connected to the shell module to form a tessellated structure that extends along a path of non-constant radius of curvature.

11. A shell structure according to any of the preceding claims, comprising a plurality of the shell modules that are identical to each other, connected together to form a structure that is tessellated in a direction parallel to the longitudinal axis.

12. A shell structure according to any of claims 8-11, wherein face plates on the radially inner and/or outer side(s) of at least a subset of the tessellated shell modules are connected together along hinges to form a continuous surface(s) spanning those tessellated shell modules.

13. A structure according to any of the preceding claims, further comprising a planar structure having zero local curvature and connected to the shell module in the circumferential direction, the circumferential direction being defined relative to the longitudinal axis of the core module of the shell module.

14. A structure according to claim 13, wherein two of the planar structures are provided, connected together by one of the shell modules.

15. A structure according to claim 13 or 14, comprising a further shell module and wherein the planar structure connects together the two shell modules.

16. A structure according to any of the preceding claims, wherein the core plates are connected together via a plurality of hinges in such a way that, if the face module or face modules were absent, the core module or core modules formed by the core plates would be capable of being transformed from a flat state in which the core plates are coplanar to an expanded state in which the core plates are not coplanar and/or from the expanded state to a flat-folded state in which the core plates are substantially parallel with each other and at least a subset of the core plates are folded on top of each other.

17. A structure according to any of the preceding claims comprising a plurality of the shell modules that are connected together in the radial direction to form a radially multilayered structure.

18. A structure according to claim 17, wherein shell modules connected together in the radial direction share a face plate, such that a radially outer face plate of one of the shell modules is a radially inner face plate of the other of the shell modules.

19. A structure according to any of the preceding claims comprising a plurality of the shell modules and a plurality of shell module fragments, each comprising less than a full shell module, that are connected together so as to tessellate in directions parallel to either or both of the circumferential and longitudinal directions.

20. A structure according to claim 19, wherein one or more of the shell module fragments is/are connected to the structure on an outside edge of the structure and/or around the edge of a void in the structure.

21. A structure according to any of the preceding claims, wherein the core module comprises a core plate that is directly connected to a face plate that is parallel to the core plate such that the continuous line connection is part of an area connection between the core plate and face plate.

22. A kit for forming a shell structure, comprising:

a core module and a face module, wherein:

the core module comprises a plurality of planar core plates that are connected together via a plurality of core hinges in such a way that the core module can be transformed from a flat state in which the core plates are coplanar to an expanded state in which the core plates are not coplanar, via rotations of the core plates about the core hinges;

the face module comprises a plurality of planar face plates that are connected together so that at least two of the face plates are at a non-zero angle relative to each other; and

at least one of the face plates is connectable along a continuous line to a corresponding core plate on a radially inner or radially outer side of the core module when the core module is in the expanded state.

23. A panel for an aircraft comprising a shell structure according to any of claims 1-21.

24. A panel according to claim 23, wherein comprising a shell structure having face plates on a radially inner surface and a curved skin attached to a radially outer surface.

25. A shelter comprising a shell structure according to any of claims 1-21.

26. A shell structure, kit, panel or shelter arranged and/or configured to operate substantially as hereinbefore described with reference to and/or as illustrated in any one or more of Figures 4-79.