# Advanced Structures Group

Selected Publications

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 2016 Seffen K A (2016), "Inverted Cones and Their Elastic Creases", Physical Review E, 94, 063003 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We study the elastic inversion of a right circular cone, in particular, the uniform shape of the narrow crease that divides its upright and inverted parts. Our methodology considers a cylindrical shell analogy for simplicity where the crease is the boundary layer deformation. Solution of its governing equation of deformation requires careful crafting of the underlying assumptions and boundary conditions in order to reveal an expression for the crease shape in closed form. We can then define the characteristic width of crease exactly, which is compared to a geometrically nonlinear, large displacement finite element analysis. This width is shown to be accurately predicted for shallow and steep cones, which imparts confidence to our original assumptions. Using the shape of crease, we compute the strain energy stored in the inverted cone, in order to derive an expression for the applied force of inversion by a simple energy method. Again, our predictions match finite element data very well. This study may complement other studies of creases traditionally formed in a less controlled manner, for example, during crumpling of lightweight sheets. BibTeX: @article{seffen2016d, author = {K. A. Seffen}, title = {Inverted Cones and Their Elastic Creases}, journal = {Physical Review E}, year = {2016}, doi = {doi: /10.1103/PhysRevE.00.063002} }  Seffen K A (2016), "k-Cones and Kirigami Metamaterials", Physical Review E, 94, 033003 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We are inspired by the tensile buckling of a thin sheet with a slit to create a foldable planar metamaterial. The buckled shape comprises two pairs of identical e-cones connected to the slit, which we refer to as a k-cone. We approximate this shape as discrete vertices that can be folded out of plane as the slit is pulled apart. We determine their kinematics and we calculate generic shape properties using a simple elastic model of the folded shape. We then show how the folded sheet may be tessellated as a unit cell within a larger sheet, which may be constructed a priori by cutting and folding the latter in a regular way, in order to form a planar kirigami structure with a single degree of freedom. BibTeX: @article{seffen2016c, author = {K. A. Seffen}, title = {k-Cones and Kirigami Metamaterials}, journal = {Physical Review E}, year = {2016}, doi = {doi: /10.1103/PhysRevE.00.033003} }  Seffen K A (2016), "Fundamental Conical Defects: the d-Cone, its e-Cone, and its p-Cone", Physical Review E, 94, 013002 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We consider well-known surface disclinations by cutting, joining, and folding pieces of paper card. The resulting shapes have a discrete, folded vertex whose geometry is described easily by Gausss mapping, in particular, we can relate the degree of angular excess, or deficit, to the size of fold line rotations by the area enclosed by the vector diagram of these rotations. This is well known for the case of a so-called "d-cone" of zero angular deficit, and we formulate the same for a general disclination. This method allows us to observe kinematic properties in a meaningful way without needing to consider equilibrium. Importantly, the simple vector nature of our analysis shows that some disclinations are primitive; and that other types, such as d-cones, are amalgamations of them. BibTeX: @article{seffen2016b, author = {K. A. Seffen}, title = {Fundamental Conical Defects: the d-Cone, its e-Cone, and its p-Cone}, journal = {Physical Review E}, year = {2016}, doi = {doi: /10.1103/PhysRevE.00.013002} }  Fowler P W, Guest S D and Schulze B (2016), "Mobility of a Class of Perforated Polyhedra", International Journal of Solids and Structures 85-86: 105-113 [Abstract] [BibTeX] [DOI] [PDF] Abstract: A class of over-braced but typically flexible body-hinge frameworks is described. They are based on polyhedra with rigid faces where an independent subset of faces has been replaced by a set of holes. The contact polyhedron C describing the bodies (vertices of C) and their connecting joints (edges of C) is derived by subdivision of the edges of an underlying cubic polyhedron. Symmetry calculations detect flexibility not revealed by counting alone. A generic symmetry-extended version of the Grübler---Kutzbach mobility counting rule accounts for the net mobilities of infinite families of this type (based on subdivisions of prisms, wedges, barrels, and some general inflations of a parent polyhedron). The prisms with all faces even and all barrels are found to generate flexible perforated polyhedra under the subdivision construction. The investigation was inspired by a question raised by Walter Whiteley about a perforated polyhedron with a unique mechanism reducing octahedral to tetrahedral symmetry. It turns out that the perforated polyhedron with highest (Oh) point-group symmetry based on subdivision of the cube is mechanically equivalent to the Hoberman Switch-Pitch toy. Both objects exhibit an exactly similar mechanism that preserves Td subgroup symmetry over a finite range; this mechanism survives in two variants suggested by Bob Connelly and Barbara Heys that have the same contact graph, but lower initial maximum symmetry. BibTeX: @article{guest2016a, author = {P. W. Fowler, S. D. Guest and B. Schulze}, title = {Mobility of a Class of Perforated Polyhedra}, journal = {International Journal of Solids and Structures}, year = {2016}, volume = {85-86}, pages = {105-113}, doi = {doi: /10.1016/j.ijsolstr.2016.02.006} }  Seffen K A and Vidoli S (2016), "Eversion of Bistable Shells Under Magnetic Actuation: a Model of Nonlinear Shapes", International Journal of Smart Materials and Structures, 25, 065010 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We model in closed form a proven bistable shell made from a magnetic rubber composite material. In particular, we incorporate a non-axisymmetrical displacement field, and we capture the nonlinear coupling between the actuated shape and the magnetic flux distribution around the shell. We are able to verify the bistable nature of the shell and we explore its eversion during magnetic actuation. We show that axisymmetrical eversion is natural for a perfect shell but that non-axisymmetrical eversion rapidly emerges under very small initial imperfections, as observed in experiments and in a computational analysis. We confirm the non-uniform shapes of shell and we study the stability of eversion by considering how the landscape of total potential and magnetic energies of the system changes during actuation. BibTeX: @article{seffen2016a, author = {K. A. Seffen and S. Vidoli}, title = {Eversion of Bistable Shells Under Magnetic Actuation: a Model of Nonlinear Shapes}, journal = {International Journal of Smart Materials and Structures}, year = {2016}, doi = {10.1088/0964-1726/25/6/065010} }  2015 Hodges T C and Seffen K A (2015), "Drag Manipulation Through Reversible Surface Dimpling and Ruffling", Technical Report, CUED/D-STRUCT/TR266 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We consider a novel yet simple compliant surface, which greatly changes, and sometimes enhances, the aerodynamic properties of a smooth cylinder. The surface is a close-fitting foil sleeve, wrapped around the cylinder but not attached to it. The sleeve can also be axially compressed to yield a textured surface, analogous to the cylinder being dimpled. This process is reversible upon decompression, and the original smooth sleeve is recovered. We measured the drag of the compliant surfaces for Reynolds numbers in the range 1X10^5 to 6X10^5. When textured, the surface behaves as a roughened cylinder, precipitating boundary layer transition at a lower Reynolds number than for a smooth cylinder. When not textured, the sleeve moves dynamically on the cylinder in response to the flow. This ruffling initiates turbulence at lower speeds, which lowers drag as expected; but sometimes we do not see a short-lived drag crisis, rather a gradual diminution of the drag force. The extent of all of these effects is controlled by the initial gap-size between the sleeve and cylinder: within limits the tighter the fit, the closer the performance approaches that of the cylinder, and vice versa. BibTeX: @article{seffen2015e, author = {T. C. Hodges and K. A. Seffen}, title = {Drag Manipulation Through Reversible Surface Dimpling and Ruffling}, journal = {Technical Report, CUED/D-STRUCT/TR266}, year = {2015}, }  Sareh P and Guest S D (2015), "Design of Non-isomorphic Symmetric Descendants of the Miura-ori", IOP Journal of Smart Materials and Structures, 24(8), 085002 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The Miura fold pattern, or the Miura-ori, is a flat-foldable origami pattern with various applications in engineering and architecture. In addition to free-form variations, scholars have proposed a number of symmetric derivatives for this classic fold pattern over recent years. In a previous work, the authors of this paper studied isomorphic variations on the Miura-ori which led to the development of an 'isomorphic family' for this fold pattern. In this paper, we study non-isomorphic variations on the Miura-ori in order to develop a 'non-isomorphic family' for this pattern. Again we start with the Miura-ori, but reduce the symmetry by migrating from the original symmetry group to its subgroups, which may also include the enlargement of its unit cell. We systematically design and classify the non-isomorphic symmetric descendants of the Miura-ori which are either globally planar, or globally curved, flat-foldable tessellations. BibTeX: @article{guest2015c, author = {P. Sareh and S. D. Guest}, title = {Design of Non-isomorphic Symmetric Descendants of the Miura-ori}, journal = {IOP Journal of Smart Materials and Structures}, year = {2015}, volume = {24}, number = {8}, doi = {doi: /10.1088/0964-1726/24/8/085002} }  Sareh P and Guest S D (2015), "Design of Isomorphic Symmetric Descendants of the Miura-ori", IOP Journal of Smart Materials and Structures, 24(8), 085001 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The Miura-ori is a classic flat-foldable tessellation which has its root in origami, but has been applied to the folding of reconfigurable structures for a variety of engineering and architectural applications. In recent years, researchers have introduced design variations on the Miura-ori which change both the form and the function of the pattern. This paper introduces the family of isomorphically generalized symmetric variations of the Miura-ori. We study the Miura crease pattern as a wallpaper pattern. We reduce the symmetry of the original crease pattern to design new patterns while at the same time preserving the symmetry group of the tessellation as well as the flat-foldability condition at each node. It will be shown that---through appropriate design variations on the original pattern---we are able to use the Miura-ori to design either globally planar, or globally curved, flat-foldable patterns. BibTeX: @article{guest2015b, author = {P. Sareh and S. D. Guest}, title = {Design of Isomorphic Symmetric Descendants of the Miura-ori}, journal = {IOP Journal of Smart Materials and Structures}, year = {2015}, volume = {24}, number = {8}, doi = {doi: /10.1088/0964-1726/24/8/085001} }  Sareh P and Guest S D (2015), "A Framework for the Symmetric Generalisation of the Miura-ori", International Journal of Space Structures, 30(2) 141-152 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The Miura fold pattern, or the Miura-ori, is a flat-foldable origami tessellation which has been applied to the folding of deployable structures for various engineering and architectural applications. In recent years, researchers have proposed systematic (see, e.g., [1] or [2]), and also free-form [3], variations on the Miura pattern. This paper develops a geometric framework for the symmetric generalisation of the Miura-ori while preserving the 'stacking while folding' behaviour of the pattern. We present a number of novel concepts and definitions which help us apply systematic variations on the original pattern. We study the Miura crease pattern as a pmg wallpaper pattern which is one of the seventeen distinct wallpaper groups. We reduce the symmetry of the Miura-ori to obtain new patterns while preserving the flat-foldability condition at each node. We conclude that we are able to use the Miura-ori, which is a globally planar pattern in its partially folded states, to systematically design either 'globally planar' or 'globally curved' patterns, through appropriate design variations on the original pattern. BibTeX: @article{guest2015a, author = {P. Sareh and S. D. Guest}, title = {A Framework for the Symmetric Generalisation of the Miura-ori}, journal = {International Journal of Space Structures}, year = {2015}, volume = {30}, number = {2}, pages = {141-152}, doi = {doi: 10.1260/0266-3511.30.2.141} }  Mertens J, Bowman R W, Willis J C W, Robinson A, Cotton D, White R, Seffen K A and Baumberg J J (2015), "Scalable Micro-Accordion Mesh for Stretchable Metallic Films", Physical Review Applied, 4(4), 044006 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Elastically deformable materials can be created from rigid sheets through patterning appropriate meshes which can locally bend and flex. We demonstrate how microaccordion patterns can be fabricated across large areas using three-beam interference lithography. Our resulting mesh induces a large and robust elasticity within any rigid material film. Gold coating the microaccordion produces stretchable conducting films. Conductivity changes are negligible when the sample is stretched reversibly up to 30% and no major defects are introduced, in comparison to continuous sheets which quickly tear. Scaling analysis shows that our method is suited to further miniaturization and large-scale fabrication of stretchable functional films. It thus opens routes to stretchable interconnects in electronic, photonic, and sensing applications, as well as a wide variety of other deformable structures. BibTeX: @article{seffen2015d, author = {J. Mertens, R. W. Bowman, J. C. W. Willis, A. Robinson, D. Cotton, R. White, K. A. Seffen and J. J. Baumberg}, title = {Scalable Microaccordion Mesh for Deformable and Stretchable Metallic Films}, journal = {Physical Review Applied}, year = {2015}, volume = {4}, doi = {10.1103/PhysRevApplied.4.044006} }  Loukaides E G and Seffen K A (2015), "Multistable Grid and Honeycomb Shells", International Journal of Solids and Structures, Vol. 59, pp. 46-57 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The manufacturing of multistable shells has been dominated by the use of pre-stressed and composite materials. Here we advocate the use of common materials through a simple design that requires no pre-stressing and has an initially developable geometry. A rudimentary demonstrator is constructed and serves as the starting point for further study. An existing homogenisation model for a lattice structure is combined with an analytical strain energy model from the literature to show the mechanical properties needed to construct an initially developable, bistable grid shell. The concept is also tested in a commercial finite element package, where a number of parametric studies are performed. Both the demonstrator and the FE model confirm the validity of the design while a series of parametric studies helps establish the limits of this behaviour with respect to local and global geometry of grid shell and honeycomb structures. BibTeX: @article{seffen2015c, author = {E. G. Loukaides and K. A. Seffen}, title = {Multistable Grid and Honeycomb Shells}, journal = {International Journal of Solids and Structures}, year = {2015}, volume = {59}, pages = {46-57}, doi = {10.1016/j.ijsolstr/2015.01.002} }  Audoly B and Seffen K A (2015), "Buckling of Naturally Curved Elastic Strips: the Ribbon Model Makes a Difference", Journal of Elasticity, Special Edition: Mobius Project, Vol. 119, pp. 293-320 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We analyze the stability of naturally curved, inextensible elastic ribbons. In experiments,we first show that a loop formed using a metallic strip can become unstable if its radius is larger than its natural radius of curvature (undercurved case): the loop then folds onto itself into a smaller, multiply-covered loop. Conversely, a multi-covered, overcurved metallic strip can unfold dynamically into a circular configuration having a lower covering index. We analyze these instabilities using a one-dimensional mechanical model for an elastic ribbon introduced recently (Dias and Audoly in J. Elast., 2014), which extends Sadowsky's developable elastic ribbon model in the presence of natural curvature. Combining linear stability analyses and numerical computations of the post-buckled configurations, we classify the equilibria of the ribbon as a function of the ratio of its natural curvature to its actual curvature. Our ribbon model is formulated in close analogy with classical rod models; this allows us to adapt classical stability methods for rods to the case of a ribbon. The stability of a ribbon is found to differ significantly from that of an anisotropic rod: we attribute this difference to the fact that the tangent twisting modulus of a ribbon can be negative, in contrast to what is possible in the well-studied case of linearly elastic rods. The specific stability properties predicted by the curved ribbon model are confirmed by a finite element analysis of cylindrical shells having a small height-to-radius ratio. BibTeX: @article{seffen2015a, author = {B. Audoly and K. A. Seffen}, title = {Buckling of Naturally Curved Elastic Strips: the Ribbon Model Makes a Difference}, journal = {Journal of Elasticity}, year = {2015}, volume = {119}, pages = {293-320}, doi = {10.1007/s10659-015-9520-y} }  2014 Loukaides E G, Smoukov S K and Seffen K A (2014), "Magnetic Actuation and Transition Shapes of a Bistable Spherical Cap", Internation Journal of Smart and Nano Materials, Vol. 5(4), pp. 270-282 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Multistable shells have been proposed for a variety of applications; however, their actuation is almost exclusively addressed through embedded piezoelectric patches. Additional actuation techniques are needed for applications requiring high strains or where remote actuation is desirable. Part of the reason for the lack of research in this area is the absence of appropriate models describing the detailed deformation and energetics of such shells. This work presents a bistable spherical cap made of iron carbonyl-infused polydimethylsiloxane. The magnetizable structure can be actuated remotely through permanent magnets while the transition is recorded with a high-speed camera. Moreover, the experiment is reproduced in a finite element (FE) dynamic model for comparison with the physical observations. High-speed footage of the physical cap inversion together with the FE modeling gives valuable insight on preferable intermediate geometries. Both methods return similar values for the magnetic field strength required for the snap-through. High-strain multistable spherical cap transformation is demonstrated, based on informed material selection. We discover that non-axisymmetric transition shapes are preferred in intermediate geometries by bistable spherical caps. We develop the methods for design and analysis of such actuators, including the feasibility of remote actuation methods for multistable shells. BibTeX: @article{seffen2015b, author = {E. G. Loukadies, S. K. Smoukov, and K. A. Seffen}, title = {Magnetic Acturation and Transition Shapes of a Bistable Spherical Cap}, journal = {International Journal of Smart and Nano Materials}, year = {2014}, volume = {5}, pages = {270-282}, doi = {10.1080/19475411.2014.997322} }  Fischer S C, Blanchard G B, Duque J, Adams R J, Arias A M, Guest, S D, and Gorfinkiel, N (2014), "Contractile and Mechanical Properties of Epithelia with Perturbed Actomyosin Dynamics", PLoS One, Vol. 9(4), paper e95695 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Mechanics has an important role during morphogenesis, both in the generation of forces driving cell shape changes and in determining the effective material properties of cells and tissues. Drosophila dorsal closure has emerged as a reference model system for investigating the interplay between tissue mechanics and cellular activity. During dorsal closure, the amnioserosa generates one of the major forces that drive closure through the apical contraction of its constituent cells. We combined quantitation of live data, genetic and mechanical perturbation and cell biology, to investigate how mechanical properties and contraction rate emerge from cytoskeletal activity. We found that a decrease in Myosin phosphorylation induces a fluidization of amnioserosa cells which become more compliant. Conversely, an increase in Myosin phosphorylation and an increase in actin linear polymerization induce a solidification of cells. Contrary to expectation, these two perturbations have an opposite effect on the strain rate of cells during DC. While an increase in actin polymerization increases the contraction rate of amnioserosa cells, an increase in Myosin phosphorylation gives rise to cells that contract very slowly. The quantification of how the perturbation induced by laser ablation decays throughout the tissue revealed that the tissue in these two mutant backgrounds reacts very differently. We suggest that the differences in the strain rate of cells in situations where Myosin activity or actin polymerization is increased arise from changes in how the contractile forces are transmitted and coordinated across the tissue through ECadherin-mediated adhesion. Altogether, our results show that there is an optimal level of Myosin activity to generate efficient contraction and suggest that the architecture of the actin cytoskeleton and the dynamics of adhesion complexes are important parameters for the emergence of coordinated activity throughout the tissue. BibTeX: @article{guest2014g, author = {S. C. Fischer, G. B. Blanchard, J. Duque, R. J. Adams, A. M. Arias, S. D. Guest, and N. Gorfinkiel}, title = {Contractile and Mechanical Properties of Epithelia with Perturbed Actomyosin Dynamics}, journal = {PLoS ONE}, year = {2014}, volume = {9}, pages = {e95695}, doi = {10.1371/journal.pone.0095695} }  Schenk M, and Guest S D (2014), "On Zero Stiffness", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 228(10), pp. 1701-1714 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings. BibTeX: @article{guest2014f, author = {M. Schenk, and S. D. Guest}, title = {On Zero Stiffness}, journal = {Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science}, year = {2014}, volume = {228}, pages = {1701-1710}, doi = {10.1177/0954406213511903} }  Schenk M, Guest S D, and McShane G J (2014), "Novel Stacked Folded Cores for Blast-Resistant Sandwich Beams", Internation Journal of Soilds and Structures, Vol. 51, pp. 4196-4214 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Recent research has established the effectiveness of sandwich structures with metallic cellular cores for blast mitigation. The choice of core architecture can enhance sandwich performance, dissipating energy through plastic core compression and exploiting fluidstructure interaction effects to reduce the momentum imparted to the structure by the blast. In this paper we describe the first analysis of a novel sandwich core concept for blast mitigation: the stacked folded core. The core consists of an alternating stacked sequence of folded sheets in the Miura (double-corrugated) pattern, with the stack oriented such that the folding kinematics define the out-of plane compressive strength of the core. It offers a number of distinct characteristics compared to existing cellular cores. (i) The kinematics of collapse of the core by a distinctive folding mechanism give it unique mechanical properties, including strong anisotropy. (ii) The fold pattern and stacking arrangement is extremely versatile, offering exceptional freedom to tailor the mechanical properties of the core. This includes freedom to grade the core properties through progressive changes in the fold pattern. (iii) Continuous manufacturing processes have been established for the Miura folded sheets which make up the core. The design is therefore potentially more straightforward and economical to manufacture than other metallic cellular materials. In this first investigation of the stacked folded core, finite element analysis is used to investigate its characteristics under both quasistatic and dynamic loading. A dynamic analysis of an impulsively loaded sandwich beam with a stacked folded core reveals the versatility of the concept for blast mitigation. By altering the fold pattern alone, the durations of key phases of the dynamic sandwich response (core compression, beam bending) can be controlled. By altering both fold pattern and sheet thickness in the core, the same is achieved without altering the density of the core or the mass distribution of the sandwich beam. BibTeX: @article{guest2014e, author = {M. Schenk, S. D. Guest, and G. J. McShane}, title = {Novel Stacked Folded Cores for Blast-Resistant Sandwich Beams}, journal = {International Journal of Solids and Structures}, year = {2014}, volume = {51}, pages = {4196-4214}, doi = {10.1016/j.ijsolstr.2014.07.027} }  Seereeram V R and Seffen K A (2014), "Confirming Inextensional Theory", International Journal of Solids and Structures, Vol 51, pp. 3439-3448 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Thin, initially-flat plates can deform inextensionally and elastically during large out-of-plane deformations. This paper revisits an analytical method for describing the developable shapes of displaced plate, in order to quantify and validate its effectiveness. Results from practical experiments and finite element analysis are compared to theoretical predictions from well-known examples, and excellent correlations are obtained. BibTeX: @article{seffen2014d, author = {V. R. Seereeram and K. A. Seffen}, title = {Confirming Inextensional Theory}, journal = {International Journal of Solids and Structures}, year = {2014}, volume = {51}, pages = {3439-3448}, doi = {10.1016/j.ijsolstr.2014.06.001} }  Bonin A S and Seffen K A (2014), "De-wrinkling of Pre-tensioned Membranes", International Journal of Solids and Structures, Vol. 51 pp. 3303-3313 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Thin membranes are used in the spacecraft industry as extremely lightweight structural components. They need to be stiffened, usually by applying discrete forces, and this increases their susceptibility to wrinkling in regions where high tensile stresses develop. We consider a regular polygonal membrane uniformly loaded at its corners by equal forces and we prevent wrinkle formation by trimming the edges of the polygon into very gentle curves. We confirm this performance through simple physical experiments using Kapton, a typical membrane material and, using computational analysis, we show how the distribution of compressive stresses, responsible for causing wrinkles, dissipates following trimming. Finally, we accurately predict the required level of trimming for any number of sides of polygon using a simple, linear model, which invokes a plate-bending analogy. BibTeX: @article{seffen2014c, author = {A.S. Bonin and K.A. Seffen}, title = {De-wrinkling of Pre-tensioned Membranes}, journal = {International Journal of Solids and Structures}, year = {2014}, volume = {51}, pages = {3303-3313}, doi = {10.1016/j.ijsolstr.2014.05.001} }  Schulze B, Guest S D, and Fowler P W (2014), "When is a Symmetric Body-Hinge Structure Isostatic", International Journal of Solids and Structures, Vol. 51(11-12), pp. 2157-2166 [Abstract] [BibTeX] [DOI] [PDF] Abstract: A symmetry-extended mobility rule is formulated for body-hinge frameworks and used to derive necessary symmetry conditions for isostatic (statically and kinematically indeterminate) frameworks. Constructions for symmetric body-hinge frameworks with an isostatic scalar count are reported, and symmetry counts are used to examine these structures for hidden, symmetry-detectable mechanisms. Frameworks of this type may serve as examples for exploration of a symmetry extension of the (now proven) 'molecular conjecture' BibTeX: @article{guest2014c, author = {B. Schulz, S. D. Guest and P. W. Fowler}, title = {When is a Symmetric Body-Hinge Structure Isostatic?}, journal = {International Journal of Solids and Structures}, year = {2014}, volume = {51}, number = {11-12} pages = {2157-2166}, doi = {10.1016/j.ijsolstr.2014.02.018} }  Fowler P W, Guest S D, and Tarnai T (2014), "Symmetry Perspectives on Auxetic Body-Bar Networks", Symmetry, Vol. 6(2), pp. 368-382 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode. BibTeX: @article{guest2014d, author = {P. W. Fowler, S. D. Guest and T. Tarnai}, title = {Symmetry Persepctives on Some Auxetic Body-Bar Networks}, journal = {Symmetry}, year = {2014}, volume = {6}, number = {2} pages = {368-382}, doi = {10.3390/sym6020368} }  Schenk M, Viquerat A D, Seffen K A and Guest S D (2014), "Review of Inflatable Booms for Deployable Structures: Packing and Rigidization", Journal of Spacecraft and Rockets, Vol 51(3), pp.762-778. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Inflatable structures offer the potential of compactly stowing lightweight structures, which assume a fully deployed state in space. An important category of space inflatables are cylindrical booms, which may form the structural members of trusses or the support structure for solar sails. Two critical and interdependent aspects of designing inflatable cylindrical booms for space applications are i) packaging methods that enable compact stowage and ensure reliable deployment, and ii) rigidization techniques that provide long-term structural ridigity after deployment. The vast literature in these two fields is summarized to establish the state of the art. BibTeX: @article{seffen2014b, author = {M. Schenk, A. D. Viquerat, K.A. Seffen and S. D. Guest}, title = {Review of Inflatable Booms for Deployable Structures: Packing and Rigidization}, journal = {Journal of Spacecraft and Rockets}, year = {2014}, volume = {}, pages = {}, doi = {10.2514/1.A32598} }  Seffen K A and Stott S V (2014), "Surface Texturing Through Cylinder Buckling", ASME Journal of Applied Mechanics, Vol 81(1), paper 061001. [Abstract] [BibTeX] [DOI] [PDF] Abstract: We consider the axial buckling of a thin-walled cylinder fitted onto a mandrel core with a prescribed annular gap. The buckling pattern develops fully and uniformly to yield a surface texture of regular diamond-shaped buckles, which we propose for novel morphing structures. We describe experiments that operate well into the post-buckling regime, where a classical analysis does not apply; we show that the size of buckles depends on the cylinder radius and the gap width, but not on its thickness, and we formulate simple relationships from kinematics alone for estimating the buckle proportions during loading. BibTeX: @article{seffen2014a, author = {K. A. Seffen and S. V. Stott}, title = {Surface Texturing Through Cylinder Buckling}, journal = {ASME Journal of Applied Mechanics}, year = {2014}, volume = {}, pages = {}, doi = {10.1115/1.4026331} }  Guest S D and Fowler P W (2014), "Symmetry-Extended Counting Rules for Periodic Frameworks", Philosophical Transactions of the Royal Society A, Vol. 372, paper 20120029 [Abstract] [BibTeX] [DOI] [PDF] Abstract: A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry. BibTeX: @article{guest2014a, author = {S. D. Guest and P. W. Fowler}, title = {Symmetry-Extended Counting Rules for Periodic Frameworks}, journal = {Philosophical Transactions of the Royal Society A}, year = {2014}, volume = {372}, notes = {paper 20120029}, doi = {10.1098/rsta.2012.0029} }  Guest S D, Fowler P W and Power S C (2014), "Rigidity of Periodic and Symmetric Structures in Nature and Engineering", Philosophical Transactions of the Royal Society A, Vol. 372, paper 20130358 [Abstract] [BibTeX] [DOI] [PDF] Abstract: This issue contains papers presented at the Theo Murphy Discussion Meeting, ‘Rigidity of periodic and symmetric structures in nature and engineering’, held at the Kavli Royal Society International Centre, Chicheley Hall, 2324 February 2012. In 1864, James Clerk Maxwell identified a simple counting condition that must hold if an idealized bar-joint structure is to be rigid to first order. Together with Laman's sufficiency condition, revealed only in 1970, this provided the seeds for modern combinatorial rigidity theory, with its matroidal, algebraic and algorithmic tools and perspectives. Symmetry-based methods for finite systems gave added understanding and useful tools and methods. Not surprisingly, in view of its economy and universality, rigidity theory has been taken up in very diverse areas of application. Ideas of rigidity percolation in physics date to the 1980s; the use of rigidity in understanding crystalline solids in Earth sciences was explored in the 1990s; and the relevance to micro-architectured materials has emerged over the past decade. There is a striking convergence in research themes originating in these apparently disparate topics, where workers in many of these fields are asking similar questions about the influence of periodicity and symmetry. This meeting brought together researchers from many disciplines, interested both in the mathematical methods and their physical applications. The papers contained in this Theo Murphy Meeting Issue cover many aspects of the rigidity of periodic and symmetric structures, including the identification and categorization of periodic nets, frameworks and materials, methods for determining the implications of symmetry for rigidity, and the development of methodologies for flexibility analysis of periodic structures. They will be of interest to diverse constituencies, including materials scientists, chemists and physicists working on framework materials, especially zeolites and metalorganic frameworks; Earth scientists working on crystalline minerals and phase transitions; industrial chemists working on zeolite design, for use as novel catalysts and filters; engineers involved in micro-architectured materials, in particular new smart ‘morphing’ materials; engineers and architects interested in large repetitive structures used in the built environment; and biophysicists and bioengineers interested in the implications of periodicity on the biomechanics of bones and shells. As the papers show, there is a rich mathematical vein to be worked in this area, both in the setting of proper definitions and their translation for different areas of application. The beautiful microgeometry present in nature, as illustrated by the cover image for the issue, may also inspire new pure mathematics. BibTeX: @article{guest2014b, author = {S. D. Guest, P. W. Fowler and S. C. Power}, title = {Symmetry-Extended Counting Rules for Periodic Frameworks}, journal = {Philosophical Transactions of the Royal Society A}, year = {2014}, volume = {372}, notes = {paper 20130358}, doi = {10.1098/rsta.2013.0358} }  2013 Seffen K A and Borner N (2013), "The Shape of Helically Creased Cylinders", ASME Journal of Applied Mechanics. Vol. 80(5), paper 054501. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Creasing in thin shells admits large deformation by concentrating curvatures while relieving stretching strains over the bulk of the shell: after unloading, the creases remain as narrow ridges and the rest of the shell is flat or simply curved. We present a helically creased unloaded shell that is doubly curved everywhere, which is formed by cylindrically wrapping a flat sheet with embedded foldlines not axially aligned. The finished shell is in a state of uniform self-stress and this is responsible for maintaining the Gaussian curvature outside of the creases in a controllable and persistent manner. We describe the overall shape of the shell using the familiar geometrical concept of a Mohr’s circle applied to each of its constituent featuresthe creases, the regions between the creases, and the overall cylindrical form. These Mohr’s circles can be combined in view of geometrical compatibility, which enables the observed shape to be accurately and completely described in terms of the helical pitch angle alone. BibTeX: @article{seffen2013a, author = {K.A. Seffen and N. Borner}, title = {The Shape of Helically Creased Cylinders}, journal = {ASME Journal of Applied Mechanics}, year = {2013}, volume = {61}, pages = {054501-1 --- 054501-4}, doi = {10.1115/1.4023624} }  Viquerat A D and Guest S D (2013), "Designing Folding Rings Using Polynomial Continuation", Journal of Mechanisms and Robotics, Vol 6(1), paper 011005. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Two types of foldable rings are designed using polynomial continuation. The first type of ring, when deployed, forms regular polygons with an even number of sides and is designed by specifying a sequence of orientations which each bar must attain at various stages throughout deployment. A design criterion is that these foldable rings must fold with all bars parallel in the stowed position. At first, all three Euler angles are used to specify bar orientations, but elimination is also used to reduce the number of specified Euler angles to two, allowing greater freedom in the design process. The second type of ring, when deployed, forms doubly plane-symmetric (irregular) polygons. The doubly symmetric rings are designed using polynomial continuation, but in this example a series of bar end locations (in the stowed position) is used as the design criterion with focus restricted to those rings possessing eight bars. BibTeX: @article{guest2013e, author = {A. D. Viquerat and S. D. Guest}, title = {Designing Folding rings Using Polynomial Continuation}, journal = {Journal of Mechanisms and Robotics}, year = {2013}, volume = {6}, number = {1} pages = {paper 011005}, doi = {10.1115/1.4025857} }  Seffen K A and Maurini C (2013), "Growth and Shape Control of Disks by Bending and Extension", Journal of the Mechanics and Physics of Solids. Vol. 61, pp. 190-204. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Differential growth of thin elastic bodies furnishes a surprisingly simple explanation of the complex and intriguing shapes of many biological systems, such as plant leaves and organs. Similarly, inelastic strains induced by thermal effects or active materials in layered plates are extensively used to control the curvature of thin engineering structures. Such behaviour inspires us to distinguish and to compare two possible modes of differential growth not normally compared to each other, in order to reveal the full range of out-of-plane shapes of an initially flat disk. The first growth mode, frequently employed by engineers, is characterized by direct bending strains through the thickness, and the second mode, mainly apparent in biological systems, is driven by extensional strains of the middle surface. When each mode is considered separately, it is shown that buckling is common to both modes, leading to bistable shapes: growth from bending strains results in a double-curvature limit at buckling, followed by almost developable deformation in which the Gaussian curvature at buckling is conserved; during extensional growth, out-of-plane distortions occur only when the buckling condition is reached, and the Gaussian curvature continues to increase. When both growth modes are present, it is shown that, generally, larger displacements are obtained under in-plane growth when the disk is relatively thick and growth strains are small, and {\em vice versa}. It is also shown that shapes can be mono-, bi-, tri- or neutrally stable, depending on the growth strain levels and the material properties: furthermore, it is shown that certain combinations of growth modes result in a free, or natural, response in which the doubly-curved shape of disk exactly matches the imposed strains. Such diverse behaviour, in general, may help to realise more effective actuation schemes for engineering structures. BibTeX: @article{seffen2013, author = {K.A. Seffen and C. Maurini}, title = {Growth and Shape Control of Disks by Bending and Extension}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2013}, volume = {61}, pages = {190-204}, doi = {10.1016/j.jmps.2012.08.003} }  Mitschke H, Schroder-Turk GE, Mecke K, Fowler PW and Guest SD (2013), "Symmetry Detection of Auxetic Behaviour in 2D Frameworks", EPL Journal, Vol. 102, paper 66005 [Abstract] [BibTeX] [DOI] [PDF] Abstract: A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry has Poisson's ratio −1, with equal expansion/contraction in all directions, and is here termed equiauxetic. A framework may have a symmetry-detectable equiauxetic mechanism if it belongs to a plane group that includes rotational axes of order n = 6, 4, or 3. If the reducible representation for the net mobility contains mechanisms that preserve full rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6, mechanisms that halve rotational symmetry (B modes) are also equiauxetic. BibTeX: @article{guest2013a, author = {H. Mitschke, G. E. Schroder-Turk, K. Mecke, P. W. Fowler and S. D. Guest}, title = {Symmetry Detection of Auxetic Behaviour in 2D Frameworks}, journal = {EPL Journal}, year = {2013}, volume = {102}, notes = {paper 66005}, doi = {10.1209/0295-5075/102/66005} }  Koohestani K and Guest SD (2013), "A New Approach to the Analytical and Numerical Form-Finding of Tensegrity Structures", International Journal of Solids and Structures, Vol. 50, pp. 2995-3007 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We develop a new formulation for the form-finding of tensegrity structures in which the primary variables are the Cartesian components of element lengths. Both an analytical and a numerical implementation of the formulation are described; each require a description of the connectivity of the tensegrity, with the iterative numerical method also requiring a random starting vector of member force densities. The analytical and numerical form-finding of tensegrity structures is demonstrated through six examples, and the results obtained are compared and contrasted with those available in the literature to verify the accuracy and viability of the suggested methods. BibTeX: @article{guest2013b, author = {K. Koohestani and S. D. Guest}, title = {A New Approach to the Analytical and Numerical Form-Finding of Tensegrity Structures}, journal = {International Journal of Solids and Structures}, year = {2013}, volume = {50}, pages = {2995--3007}, doi = {10.1016/j.ijsolstr.2013.05.014} }  Viquerat AD, Hutt T and Guest SD (2013), "A Plane Symmetric 6R Foldable Ring", Mechanism and Machine Theory, Vol. 63, pp. 73-88 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The design of a deployable structure which deploys from a compact bundle of six parallel bars to a rectangular ring is considered. The structure is a plane symmetric Bricard linkage. The internal mechanism is described in terms of its DenavitHartenberg parameters; the nature of its single degree of freedom is examined in detail by determining the exact structure of the system of equations governing its movement; a range of design parameters for building feasible mechanisms is determined numerically; and polynomial continuation is used to design rings with certain specified desirable properties. BibTeX: @article{guest2013c, author = {A. D. Viquerat, T. Hutt and S. D. Guest}, title = {A Plane Symmetric 6R Foldable Ring}, journal = {Mechanism and Machine Theory}, year = {2013}, volume = {63}, pages = {73--88}, doi = {10.1016/j.mechmachtheory.2012.12.004} }  Schenk M and Guest SD (2013), "Geometry of Miura-Folded Metamaterials", Proceedings of the National Academy of Sciences USA, Vol. 110(9), pp. 3276-3281 [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson’s ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer. BibTeX: @article{guest2013d, author = {M. Schenk and S. D. Guest}, title = {Geometry of Miura-Folded Metamaterials}, journal = {Proceedings of the National Academy of Sciences USA}, year = {2013}, volume = {110}, number = {9}, pages = {3276--3281}, doi = {10.1073/pnas.1217998110} }  2012 Loukaides EG, Maurini C and Seffen KA (2012), "Elementary Morphing Shells: Their Complete Behaviour", In Proceedings of IASS Symposium. Seoul, South Korea, 21-24 May, 2012. [Abstract] [BibTeX] [PDF] Abstract: In this paper, we present a complete overview of possible stable geometries for multistable shells under the uniform curvature assumption. Based on previous work, and using some aspects of Catastrophe Theory we formally identify the boundaries between monostable, bistable and tristable regions and isolate the relevant material and geometrical parameters. The boundaries themselves represent regions of neutral stability, which in turn allow for an infinity of shapes, and we believe these exhaust the possibilities for multistable shells, putting a practical ceiling at a maximum of three states with absolute stability. BibTeX: @conference{seffen2012a, author = {E. G. Loukaides, C. Maurini and K. A. Seffen}, title = {Elementary Morphing Shells: Their Complete Behaviour}, booktitle = {Proceedings of IASS Symposium}, year = {2012},  Seffen K A (2012), "Compliant Shell Mechanisms", Philosophical Transactions of the Royal Society A. Vol. 370, pp. 2010-2026. [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper describes a class of lightweight structures known as compliant shell mechanisms. These are novel reconfigurable solutions for advanced structures, such as morphing shells and deployable membranes. They have local, discrete corrugations, which articulate and deform to achieve dramatic changes in the overall shape of the shell. The unique kinematics are considered by highlighting examples and by performing analysis using established and novel concepts, and favourable predictions of shape compared with laboratory models are demonstrated. BibTeX: @article{seffen2012, author = {K.A. Seffen}, title = {Compliant Shell Mechanisms}, journal = {Philospophical Transactions of the Royal Society A}, year = {2012}, volume = {370}, pages = {2010-2026}, doi = {10.1098/rsta.2011.0347} }  Chen Y, Guest SD, Fowler PW and Feng J (2012), "Two-Orbit Switch-Pitch Structures", Journal of the International Association for Shell and Spatial Structures, Vol. 53(3), pp. 157-162 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The Hoberman ‘switch-pitch’ ball is a transformable structure with a single folding and unfolding path. The underlying cubic structure has a novel mechanism that retains tetrahedral symmetry during folding. Here, we propose a generalized class of structures of a similar type that retain their full symmetry during folding. The key idea is that we require two orbits of nodes for the structure: within each orbit, any node can be copied to any other node by a symmetry operation. Each member is connected to two nodes, which may be in different orbits, by revolute joints. We will describe the symmetry analysis that reveals the symmetry of the internal mechanism modes for a switch-pitch structure. To follow the complete folding path of the structure, a nonlinear iterative predictor-corrector algorithm based on the Newton method is adopted. First, a simple tetrahedral example of the class of two-orbit structures is presented. Typical configurations along the folding path are shown. Larger members of the class of structures are also presented, all with cubic symmetry. These switch-pitch structures could have useful applications as deployable structures. BibTeX: @article{guest2012a, author = {Y. Chen, S. D. Guest, P. W. Fowler and J. Feng}, title = {Two-Orbit Switch-Pitch Structures}, journal = {Journal of International Association for Shell and Spatial Structures}, year = {2012}, volume = {53}, number = {3}, pages = {157--162}, doi = {} }  Tarnai T, Kovacs F, Fowler PW and Guest SD (2012), "Wrapping the Cube and Other Polyhedra", Proceedings of the Royal Society A, Vol. 468, pp. 2652-2666 [Abstract] [BibTeX] [DOI] [PDF] Abstract: An infinite series of twofold, two-way weavings of the cube, corresponding to ‘wrappings’, or double covers of the cube, is described with the aid of the two-parameter GoldbergCoxeter construction. The strands of all such wrappings correspond to the central circuits (CCs) of octahedrites (four-regular polyhedral graphs with square and triangular faces), which for the cube necessarily have octahedral symmetry. Removing the symmetry constraint leads to wrappings of other eight-vertex convex polyhedra. Moreover, wrappings of convex polyhedra with fewer vertices can be generated by generalizing from octahedrites to i-hedrites, which additionally include digonal faces. When the strands of a wrapping correspond to the CCs of a four-regular graph that includes faces of size greater than 4, non-convex ‘crinkled’ wrappings are generated. The various generalizations have implications for activities as diverse as the construction of woven-closed baskets and the manufacture of advanced composite components of complex geometry. BibTeX: @article{guest2012b author = {T. Tarnai, F. Kovacs, P. W. Fowler and S. D. Guest}, title = {Wrapping the Cube and Other Polyhedra}, journal = {Proceedings of the Royal Society A}, year = {2012}, volume = {468}, pages = {2652--2666}, doi = {10.1098/rspa.2012.0116} }  2011 Guest S, Kebadze E and Pellegrino S (2011), "A Zero-Stiffness Elastic Shell Structure", Journal of the Mechanics of Materials and Structures. Vol. 6(1-4), pp. 203-212. [Abstract] [BibTeX] [DOI] [PDF] Abstract: A remarkable shell structure is described that, due to a particular combination of geometry and initial stress, has zero stiffness for any finite deformation along a twisting path; the shell is in a neutrally stable state of equilibrium. Initially the shell is straight in a longitudinal direction, but has a constant, non-zero curvature in the transverse direction. If residual stresses are induced in the shell by, e.g., plastic deformation, to leave a particular resultant bending moment, then an analytical inextensional model of the shell shows it to have no change in energy along a path of twisted configurations. Real shells become closer to the inextensional idealization as their thickness is decreased; experimental thin-shell models have confirmed the neutrally stable configurations predicted by the inextensional theory. A simple model is described that shows that the resultant bending moment that leads to zero stiffness gives the shell a hidden symmetry, which explains this remarkable property. BibTeX: @article{guest2011, author = {S.D. Guest and E. Kebadze and S. Pellegrino}, title = {A Zero-Stiffness Elastic Shell Structure}, journal = {Journal of the Mechanics of Materials and Structures}, year = {2011}, volume = {6}, number = {1-4}, pages = {203-212}, doi = {10.2140/jomms.2011.6.203} }  Schenk M and Guest SD (2011), "Origami Folding: A Structural Engineering Approach", In Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (5OSME). , pp. 293-305. CRC Press. [Abstract] [BibTeX] [PDF] Abstract: In this paper we present a novel engineering application of Origami, using it for both the flexibility and the rigidity the folding patterns provide. The proposed Folded Textured Sheets have several interesting mechanical properties. The folding patterns are modelled as a pin-jointed framework, which allows the use of established structural engineering methods to gain insight into the kinematics of the folded sheet. The kinematic analysis can be naturally developed into a stiffness matrix approach; by studying its softest eigenmodes, important deformations of a partially folded sheet can be found, which aids in the understanding of Origami sheets for engineering applications. BibTeX: @incollection{schenk2010, author = {Mark Schenk and Simon D. Guest}, editor = {Patsy Wang-Iverson and Robert J. Lang and Mark YIM}, title = {Origami Folding: A Structural Engineering Approach}, booktitle = {Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (5OSME)}, publisher = {CRC Press}, year = {2011}, pages = {293-305} }  Schenk M, Allwood JM and Guest SD (2011), "Cold Gas-Pressure Folding of Miura-ori Sheets" Aachen, Germany, September 25-30th, 2011. [Abstract] [BibTeX] [PDF] Abstract: Folding sheets from flat sheet materials into 3D surfaces provides a way to form textured sheets with a deep relief, without stretching the base material. Manufacturing can therefore be done using only low-energy bending operations along the fold lines. An important challenge to be overcome in the manufacturing process is the significant in-plane biaxial contraction during the folding process. A novel manufacturing process is herein introduced, which uses cold gas-pressure to fold the sheets and requires a minimum of initial tooling. Calculations were done to determine the required forming pressure to fold an example folded sheet, a Miura-ori sheet, and were compared with trials. BibTeX: @unpublished{schenk2011, author = {M. Schenk and Julian M. Allwood and Simon D. Guest}, title = {Cold Gas-Pressure Folding of Miura-ori Sheets}, year = {2011}, note = {Accepted for presentation at the International Conference on Technology of Plasticity (ICTP 2011); selected for publication in Steel Research International.} }  Seffen KA and Guest SD (2011), "Pre-stressed Morphing Bistable and Neutrally Stable Shells", ASME Journal of Applied Mechanics. Vol. 78(1), pp. 011002-1 - 011002-6. [Abstract] [BibTeX] [DOI] [PDF] Abstract: This study deals with prestressed shells, which are capable of “morphing” under large deflexions between very different load-free configurations. Prestressing involves plastically curving a flat, thin shell in orthogonal directions either in the opposite or same sense, resulting in two unique types of behavior for isotropic shells. Opposite-sense prestressing produces a bistable, cylindrically curved shell provided the prestress levels are large enough and similar in size: This effect forms the basis of a child's “flick” bracelet and is well known. On the other hand, same-sense prestressing results in a novel, neutrally stable shell provided the levels are also sufficiently large but identical: The shell has to be made precisely, otherwise, it is monostable and is demonstrated here by means of a thin, helically curved strip. The equilibrium states associated with both effects are quantified theoretically and new expressions are determined for the requisite prestress levels. Furthermore, each stability response is revealed in closed form where it is shown that the neutrally stable case occurs only for isotropic materials, otherwise, bistability follows for orthotropic materials, specifically, those, which have a shear modulus different from the isotropic value. Finally, prestressing and initial shape are considered together and, promisingly, it is predicted that some shells can be neutrally stable and bistable simultaneously. BibTeX: @article{seffen2011, author = {K. A. Seffen and S. D. Guest}, title = {Pre-stressed Morphing Bistable and Neutrally Stable Shells}, journal = {ASME Journal of Applied Mechanics}, year = {2011}, volume = {78}, number = {1}, pages = {011002-1 -- 011002-6}, doi = {10.1115/1.4002117} }  2010 Guest SD (2010), "The stiffness of tensegrity structures", IMA Journal of Applied Mathematics. Vol. 76(1), pp. 57-66. [Abstract] [BibTeX] [DOI] [PDF] Abstract: The stiffness of tensegrity structures comes from two sources: the change of force carried by members as their length is changed, and the reorientation of forces as already stressed members are rotated. For any particular tensegrity, both sources of stiffness may have a critical role to play. This paper explores how the stiffness of two example tensegrity structures changes as the level of prestress in a member varies. It is shown that, for high levels of prestress, an originally stable tensegrity can be made to have zero stiffness, or indeed be made unstable. BibTeX: @article{guest2011b, author = {S. D. Guest}, title = {The stiffness of tensegrity structures}, journal = {IMA Journal of Applied Mathematics}, year = {2010}, volume = {76}, number = {1}, pages = {57-66}, doi = {10.1093/imamat/hxq065} }  Guest SD, Schulze B and Whiteley WJ (2010), "When is a Body-Bar Structure Isostatic?", International Journal of Solids and Structures, Vol. 47, pp. 2745-2754 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Body-bar frameworks provide a special class of frameworks which are well understood generically, with a full combinatorial theory for rigidity. Given a symmetric body-bar framework, this paper exploits group representation theory to provide necessary conditions for rigidity in the form of very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. We give some initial results, and conjectures, for when these conditions are also sufficient for rigidity. BibTeX: @article{guest2010a author = {S. D. Guest, B. Schulze and W. J. Whiteley}, title = {When is a Body-Bar Structure Isostatic?}, journal = {International Journal of Solids and Structures}, year = {2010}, volume = {47}, pages = {2745--2754}, doi = {10.1016/j.ijsolstr.2010.06.001} }  Zhang JY, Guest SD, Connelly R and Ohsaki M (2010), "Dihedral 'Star' Tensegrity Structures", International Journal of Solids and Structures, Vol. 47, pp. 1-9 [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper presents conditions for self-equilibrium and super stability of dihedral ‘star’ tensegrity structures, based on their dihedral symmetry. It is demonstrated that the structures are super stable if and only if they have an odd number of struts, and the struts are as close as possible to each other. Numerical investigations show that their prestress stability is sensitive to the geometry realisation. BibTeX: @article{guest2010b author = {J. Y. Zhang, S. D. Guest, R. Connelly and M. Ohsaki}, title = {Dihedral 'Star' Tensegrity Structures}, journal = {International Journal of Solids and Structures}, year = {2010}, volume = {47}, pages = {1--9}, doi = {10.1016/j.ijsolstr.2009.05.018} }  Guest SD and Fowler PW (2010), "Mobility of N-Loops: Bodies Cyclically Connected by Intersecting Revolute Hinges", Proceedings of the Royal Society A, Vol. 466, pp. 63-77 [Abstract] [BibTeX] [DOI] [PDF] Abstract: The mobilities of many objects from toys and molecular models to large-scale deployable structures can be understood in terms of N-loops: sets of N bodies, cyclically connected by pairs of intersecting revolute hinges. A symmetry-extended version of the Grübler criterion for counting kinematic degrees of freedom is used to explain and rationalize the observed mobilities of N-loops with small N. Compared with simple counting, the symmetry-based approach gives improved detection and visualization of mechanisms and states of self-stress. It can also give a better account of the differing mobilities of conformers occupying different regions of the phase space, such as the rigid chair and flexible boat forms of cyclohexane. BibTeX: @article{guest2010c author = {S. D. Guest and P. W. Fowler}, title = {Mobility of N-Loops: Bodies Cyclically Connected by Intersecting Revolute Hinges}, journal = {Proceedings of the Royal Society A}, year = {2010}, volume = {466}, pages = {63--77}, doi = {} }  2009 Santer MJ and Seffen KA (2009), "Optical Space Telescopes Structures: the State of the Art and Future Directions", Aeronautical Journal. Vol. 113(1148), paper 3348. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Future space telescopes will be required to have significantly greater aperture and lower areal density than is currently achievable. Gossamer spacecraft structures have been proposed as a means of achieving this, but the technologies are far from mature. A state-ofthe- art review is timely and necessary as new structural paradigms are being considered for the next generation of space telescopes. There is, however, a knowledge gap between the structural engineering community and the additional fields involved in the complete telescope system, leading to the proposal of structures which are unlikely to be launched. It is hoped that, by providing a resource by which structural engineers are made aware of the wider issues in telescope design, this review will serve to overcome this knowledge gap to facilitate productive collaboration. BibTeX: @article{seffen2009A, author = {M. J. Santer and K. A. Seffen}, title = {Optical Space Telescopes Structures: the State of the Art and Future Directions}, journal = {Aeronautical Journal}, year = {2009}, volume = {113}, number = {1148}, notes = {paper 3348} }  Gentilini C, Nobile L and Seffen KA (2009), "Numerical Analysis of Morphing Corrugated Plates", Procedia Engineering. Vol. 1, pp.79-82. [Abstract] [BibTeX] [DOI] [PDF] Abstract: In this paper a numerical model for investigating the moment-rotation response of corrugated plates is presented. In particular, the effect of the geometry of the plate on the bending response is considered. Results are compared with a simplified theoretical model recently appeared in the literature. Combining geometrical effects and prestress, corrugated plates can become multistable forming the basis of new morphing structures. © 2009 Elsevier BibTeX: @article{seffen2009B, author = {C. Gentilini, L. Nobile and K. A. Seffen}, title = {Numerical Analysis of Morphing Corrugated Plates}, journal = {Procedia Engineering}, year = {2009}, volume = {1}, pages = {79-82} }  Saeed TI, Graham WR, Babinksy H, Eastwood JP, Hall CA, Jarrett JP, Lone MM and Seffen KA (2009), "Conceptual Design for a Laminar Flying Wing", In Proceedings of 27th AIAA Applied Aerodynamics Conference. San Anotnio, Texas, 22-25 June, 2009. [Abstract] [BibTeX] [PDF] Abstract: Growing air travel, with its associated environmental impact, is increasingly becoming a public concern. The laminar flying wing (LFW), which utilises boundary layer suction as a means of laminar flow control, has been proposed by Greener by Design as a potential solution, with preliminary estimates suggesting a significant reduction in fuel-burn. The purpose of this study is to investigate whether a conceptual design which supports this assertion can be produced. The starting point is to find the overall size, cruise speed and cruise altitude that satisfy constraints imposed by the LFW con guration: subcritical flow, limited by Reynolds number, efficient fliight and satisfactory passenger accommodation. By treating the aircraft as an unswept 'flying plank', we find that a maximum section thickness-to-chord ratio of 28%, a chord length of 8.9 m, a span of 80 m, along with a cruise Mach number of 0.58 at an altitude of 10900 m and a cruise weight of 69 tonnes, meet these demands. A planform and section geometries are then developed to allow an estimate of the suction required to maintain laminar flow; this is 20.7 kg/s, requiring 625 kW of power. The associated cruise thrust is 7.6 kN; the engine is designed to provide this plus the off-take to power the suction system and auxiliary components. The resulting specific fuel consumption is 18.4 g/kN.s. The structural weight is estimated via standard preliminary design methods for a metal aircraft, and is 30.5 tonnes. With the operating empty weight determined, and 32.2 tonnes allowed for fixments, passengers (120) and baggage, 6.3 tonnes is left available for cruise fuel; on the basis that 5.2 tonnes is usable, this gives a 4125 nm range at a fuel-burn of 6 g/pax.km. The longitudinal static stability of the design remains an issue: the estimated centre-of-gravity range implies that a feedback control system would be required. BibTeX: @conference{seffen2009, author = {T. I. Saeed, W. R. Graham, H. Babinksy, J. P. Eastwood, C. A. Hall, J. P. Jarrett, M. M. Lone and K. A. Seffen}, title = {Conceptual Deisgn for a Laminar Flying Wing}, booktitle = {Proceedings of 27th AIAA Applied Aerodynamics Conference}, year = {2009}, note = {Paper number AIAA-2009-3616} }  Santer MJ, Bonin A and Seffen KA (2009), "Small Diameter Membrane Reflector Structures", In Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Palm Springs, California, 4-7 May, 2009. [Abstract] [BibTeX] [PDF] Abstract: This paper proposes the use of membrane reflectors for space telescopes having apertures currently achievable using monolithic designs. It is shown, both analytically, and by numerical optimization, that membrane reflectors including necessary support structure may achieve comparable areal density to monolithic reflectors at a significantly reduced cost. Design formulae for the membrane reflector support structure are derived and validated. BibTeX: @conference{seffen2009a, author = {M. J. Santer, A. Bonin and K. A. Seffen}, title = {Small Diameter Membrane Reflector Structures}, booktitle = {Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference}, year = {2009}, note = {Paper number AIAA-2009-2150} }  Bonin A, Seffen KA and Santer MJ (2009), "Small Diameter Membrane Reflector Wrinkling", In Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Palm Springs, California, 4-7 May, 2009. [Abstract] [BibTeX] [PDF] Abstract: This study concerns the wrinkling performance of thin membranes for use as novel reflectors in space-based telescopes. We introduce small-scale experiments for inducing and interrogating wrinkling patterns in flat membranes, and we capture these details computationally by performing a range of finite element analysis. The overall aim is to assess the sophistication of modelling, to verify the feasibility of a small-diameter reflector concept proposed in accompanying work. BibTeX: @conference{seffen2009b, author = {A. Bonin, K. A. Seffen and M. J. Santer}, title = {Small Diameter Membrane Reflector Wrinkling}, booktitle = {Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference}, year = {2009}, note = {Paper number AIAA-2009-2164} }  Golabchi M and Guest SD (2009), "Morphing Multistable Textured Shells", In IASS 2009. Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures. Valencia, Spain, 28 Sep-2 Oct, 2009. [Abstract] [BibTeX] [PDF] Abstract: Forming surface features in a shell, and combining this ‘texture’ with prestress, can lead to a range of distinctive multistable properties. This paper is concerned with describing thestructural properties of shell surfaces where local indentation and corrugation are used to replace the isotropic behaviour of the shell, and studies the possibilities of using theseshells as morphing and multistable structures. By taking advantage of the anisotropic properties of the textured shell structure and further prestressing the shell, a range of interesting multistable properties can be achieved. This study investigates the properties of a particular example of a textured shell surface using experimental and computational techniques. Remarkably, these results shown that dimpled textured shells can achieve an effective Poisson’s ratio in bending of close to -1, providing interesting insights into the remarkable multistable properties that textured shell surfaces can achieve. BibTeX: @conference{golabchi2009, author = {M.R. Golabchi and S. D. Guest}, title = {Morphing Multistable Textured Shells}, booktitle = {IASS 2009. Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures}, year = {2009} }  Norman A, Seffen K and Guest S (2009), "Morphing of curved corrugated shells", International Journal of Solids and Structures. Vol. 46(7-8), pp. 1624–1633. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Thin sheet materials of low bending stiffness but high membrane stiffness are often corrugated in order to achieve improvements of several orders of magnitude in bending stiffness with only minimal increases in weight and cost. If these corrugated sheets are initially curved along the corrugations, much of this stiffness gain is lost. In return, the sheets are then capable of significant elastic changes in shape overall, including large changes in overall Gaussian curvature. These shape changes are described here by non-linear and coupled kinematical relationships, which are verified against experiment and finite-element simulations. It is found that gross simplifications can be made about the large displacement behaviour of such shells without a loss of accuracy. BibTeX: @article{norman2009, author = {A.D. Norman and K.A. Seffen and S.D. Guest}, title = {Morphing of curved corrugated shells}, journal = {International Journal of Solids and Structures}, year = {2009}, volume = {46}, number = {7-8}, pages = {1624–1633}, doi = {10.1016/j.ijsolstr.2008.12.009} }  Kapko V, Treacy MMJ, Thorpe MF and Guest SD (2009), "On the Collapse of Locally Isostatic Networks", Proceedings of the Royal Society A, Vol. 465, pp. 3517-3530 [Abstract] [BibTeX] [DOI] [PDF] Abstract: We examine the flexibility of periodic planar networks built from rigid corner-connected equilateral triangles. Such systems are locally isostatic, since for each triangle the total number of degrees of freedom equals the total number of constraints. These nets are two-dimensional analogues of zeolite frameworks, which are periodic assemblies of corner-sharing tetrahedra. If the corner connections are permitted to rotate, as if pin-jointed, there is always at least one collapse mechanism in two dimensions (and at least three mechanisms in three dimensions). We present a number of examples of such collapse modes for different topologies of triangular net. We show that the number of collapse mechanisms grows with the size of unit cell. The collapsible mechanisms that preserve higher symmetry of the network tend to exhibit the widest range of densities without sterical overlap. BibTeX: @article{guest2009a author = {V. Kapko, M. M. J. Treacy, M. F. Thorpe and S. D. Guest}, title = {On the Collapse of Locally Isostatic Networks}, journal = {Proceedings of the Royal Society A}, year = {2009}, volume = {465}, pages = {3517--3530}, doi = {10.1098/rspa.2009.0307} }  Connelly R, Fowler PW, Guest SD, Schulze B and Whiteley WJ (2009), "When is a Pin-Jointed Framework Isotatic", International Journal of Solids and Structures, Vol. 46, pp. 762-773 [Abstract] [BibTeX] [DOI] [PDF] Abstract: Maxwell’s rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework. BibTeX: @article{guest2009b author = {R. Connelly, P. W. Fowler, S. D. Guest, B. Schulze and W. J. Whiteley}, title = {When is a Pin-Jointed Framework Isotatic}, journal = {International Journal of Solids and Structures}, year = {2009}, volume = {46}, pages = {762--773}, doi = {10.1016/j.ijsolstr.2008.09.023} }  Zhang JY, Guest SD and Oshaki M (2009), "Symmetric Prismatic Tensegrity Structures: Part II. Symmetry-Adapted Formulations", International Journal of Solids and Structures, Vol. 46, pp. 15-30 [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper presents analytical formulations for the symmetry-adapted equilibrium, force density and geometrical stiffness matrices for prismatic tensegrity structures with dihedral symmetries. An analytical expression for the infinitesimal mechanisms is also derived. BibTeX: @article{guest2009c author = {Z. Y. Zhang, S. D. Guest and M. Oshaki}, title = {Symmetric Prismatic Tensegrity Structures: Part II. Symmetry-Adapted Formulations}, journal = {International Journal of Solids and Structures}, year = {2009}, volume = {46}, pages = {15--30}, doi = {10.1016/j.ijsolstr.2008.07.035} }  Zhang JY, Guest SD and Oshaki M (2009), "Symmetric Prismatic Tensegrity Structures: Part I. Configuration and Stability", International Journal of Solids and Structures, Vol. 46, pp. 1-14 [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper presents a simple and efficient method to determine the self-equilibrated configurations of prismatic tensegrity structures, nodes and members of which have dihedral symmetry. It is demonstrated that stability of this class of structures is not only directly related to the connectivity of members, but is also sensitive to their geometry (height/radius ratio), and is also dependent on the level of self-stress and stiffness of members. A catalogue of the structures with relatively small number of members is presented based on the stability investigations. BibTeX: @article{guest2009d author = {Z. Y. Zhang, S. D. Guest and M. Oshaki}, title = {Symmetric Prismatic Tensegrity Structures: Part I. Configuration and Stability}, journal = {International Journal of Solids and Structures}, year = {2009}, volume = {46}, pages = {1--14}, doi = {10.1016/j.ijsolstr.2008.08.032} }  2008 Norman AD, Seffen KA and Guest SD (2008), "Multistable Corrugated Shells", Proceedings of the Royal Society A, Vol. 464, pp. 1653-1672. [Abstract] [BibTeX] [DOI] [PDF] Abstract: We have been constructing and investigating multistable corrugated shell structures. The multistability arises from the interaction between internal prestresses created during forming and non-linear geometrical changes during deformation. Using a simplified analytical elastic model, we homogenise the properties of the shells through simultaneously considering the material on two scales: the ‘local’ scale of the isotropic material and the ‘global’ scale of the corrugated sheet, which is then modelled as an equivalent flat sheet with anisotropic properties. This model is applied to simulate two modes of bistability observed in prototypes: first, prestressed corrugated shells which, when buckled, can coil up into a tube repeatably and reversibly and, second, corrugated sheets with assymmetry-breaking ‘twisting’ curvature. The model gives an intuitive understanding of the behaviour, and has enabled us to understand forming processes that give the behaviour we wish, including tristable shells which combine both bistable modes. BibTeX: @article{norman2008, author = {A. D. Norman and K. A. Seffen and S. D. Guest}, title = {Multistable Corrugated Shells}, journal = {Proceedings of the Royal Society A}, year = {2008}, volume = {464}, pages = {1653-1672}, doi = {10.1098/rspa.2007.0216} }  Fowler PW, Guest SD and Tarnai T (2008), "A Symmetry Treatment of Danzerian Rigidity for Circle Packing", Proceedings of the Royal Society A, Vol. 464, pp. 3237-3254. [Abstract] [BibTeX] [DOI] [PDF] Abstract: A symmetry-extended mobility criterion that incorporates Danzer's concept of bar-and-joint assemblies is derived and applied to the spherical circle-packing problem. The known scalar counting rule for Danzerian freedoms is strengthened in an equation that predicts not only the number, but also the symmetries, of distortion modes that may be used to improve a packing. Relationships between alternative candidates for best packing are consequences of the co-kernel structure of the representation spanned by Danzerian mechanisms, and in several cases lead to new local optima. BibTeX: @article{norman2008, author = {P. W. Fowler, S. D. Guest and T. Tarnai}, title = {A Symmetry Treatment of Danzerian Rigidity for Circle Packing}, journal = {Proceedings of the Royal Society A}, year = {2008}, volume = {464}, pages = {3237--3254}, doi = {10.1098/rspa.2008.0164} }  Norman AD, Golabchi M, Seffen K and Guest SD (2008), "Multistable Textured Shell Structures", Advances in Science and Technology. Vol. 54, pp. 168-173. [Abstract] [BibTeX] [PDF] Abstract: Multistable structures are a promising basis for reconfigurable systems. A multistable structure will remain in one of its stable configurations until actuation forces it to move to another stable configuration. This paper will describe a promising method of forming structures with useful multiple stable states by using prestressed textured shell surfaces. Textured shell structures have features at a scale intermediate between the global structural scale, and the material scale, and can have some remarkable structural properties. This paper will describe two simple examples: a globally flat, but corrugated shell, and a globally curved, doubly corrugated shell. Both structures show additional stable equilibrium configurations that would not be possible without the textured surface. BibTeX: @article{norman2008b, author = {A. D. Norman and M.R. Golabchi and K.A. Seffen and S. D. Guest}, title = {Multistable Textured Shell Structures}, journal = {Advances in Science and Technology}, year = {2008}, volume = {54}, pages = {168-173} }  Gentilini C, Seffen KA, Guest SD and Nobile L (2008), "On the Behaviour of Corrugated Plates in Bending", In AES-ATEMA 2008, Second International Conference. Cesena, Italy, 2008. BibTeX: @conference{seffen2008a, author = {C. Gentilini, K. A. Seffen, S. D. Guest and L. Nobile}, title = {On the Behaviour of Corrugated Plates in Bending}, booktitle = {AES-ATEMA 2008}, year = {2008} }  Gentilini C, Seffen KA, Guest SD and Nobile L (2008), "On the Effect of Pre-stress on the Bistable Behaviour of Tape-springs", In AES-ATEMA 2008, Second International Conference. Cesena, Italy, 2008. BibTeX: @conference{seffen2008b, author = {C. Gentilini, K. A. Seffen, S. D. Guest and L. Nobile}, title = {On the Effect of Pre-stress on the Bistable Behaviour of Tape-springs}, booktitle = {AES-ATEMA 2008}, year = {2008} }  2007 Leung ACH and Guest SD (2007), "Single member actuation of kagome lattice structures", Journal of Mechanics of Materials and Structures. Vol. 2(2), pp. 303-317. [Abstract] [BibTeX] [URL] [PDF] Abstract: The two-dimensional kagome lattice has been shown to be a promising basis for active shape-changing structures, having both low actuation resistance and high passive stiffness. Activation of some members results in a global macroscopic shape change. Small deformation models show that the kagome lattice’s properties are critically dependent on its initial geometry. This paper investigates the fundamental actuation properties of a kagome lattice subject to single-member actuation, particularly when geometric nonlinearity is introduced with large actuation strains. Actuation resistance is found to be lowered with expansive actuation; a limiting peak actuation stiffness is observed when the actuator is flexible. Conversely, actuation resistance is found to increase with contractile actuation. BibTeX: @article{leung2007, author = {A. C. H. Leung and S. D. Guest}, title = {Single member actuation of kagome lattice structures}, journal = {Journal of Mechanics of Materials and Structures}, year = {2007}, volume = {2}, number = {2}, pages = {303-317}, url = {http://pjm.math.berkeley.edu/jomms/2007/2-2/p06.xhtml} }  Norman AD, Guest SD and Seffen KA (2007), "Novel Multistable Corrugated Structures", In Proceedings of 48th AIAA/ASME/ASCE/AHS/ ASC Structures, Structural Dynamics and Materials Conference. Waikiki, Hawaii, 23-26 April, 2007. [Abstract] [BibTeX] [PDF] Abstract: We have been investigating the properties, behaviour and stability of multistable open corrugated shells. This multistability arises from the interaction between internal prestresses created during forming and non-linear geometrical changes during deformation. Two modes of bistability are described here: prestressed corrugated shells which, when buckled, can coil up into a tube repeatably and reversibly, and corrugated sheets with a global cylindrical curvature, which is stable in either of two symmetric directions. Both modes can be present at the same time, creating a tristable shell. Using simplified analytical elastic models, we homogenise the properties of the shells through simultaneously considering the material on two scales: the ‘local’ scale of the isotropic material and the ‘global’ scale of the corrugated sheet, which is then modelled as a homogenised, flat, anisotropic sheet. The models produce similar behaviour to our prototypes, and have taught us how to incorporate or eradicate the various modes at will. The insights and methods developed from these simple models are paving the way to developing more complex corrugated forms with even more general and interesting shape-changing characteristics. BibTeX: @conference{norman2007, author = {A. D. Norman and S. D. Guest and K. A. Seffen}, title = {Novel Multistable Corrugated Structures}, booktitle = {Proceedings of 48th AIAA/ASME/ASCE/AHS/ ASC Structures, Structural Dynamics and Materials Conference}, year = {2007}, note = {Paper number AIAA-2007-2228} }  Schenk M, Guest SD and Herder JL (2007), "Zero Stiffness Tensegrity Structures", International Journal of Solids and Structures. Vol. 44(20), pp. 6569-6583. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Tension members with a zero rest length allow the construction of tensegrity structures that are in equilibrium along a continuous path of configurations, and thus exhibit mechanism-like properties; equivalently, they have zero stiffness. The zero-stiffness modes are not internal mechanisms, as they involve first-order changes in member length, but are a direct result of the use of the special tension members. These modes correspond to an infinitesimal affine transformation of the structure that preserves the length of conventional members, they hold over finite displacements and are present if and only if the directional vectors of those members lie on a projective conic. This geometric interpretation provides several interesting observations regarding zero stiffness tensegrity structures. BibTeX: @article{schenk2007, author = {M. Schenk and S. D. Guest and J. L. Herder}, title = {Zero Stiffness Tensegrity Structures}, journal = {International Journal of Solids and Structures}, year = {2007}, volume = {44}, number = {20}, pages = {6569-6583}, doi = {10.1016/j.ijsolstr.2007.02.041} }  Seffen KA (2007), "Hierarchical Multi-stable Shapes in Mechanical Memory Metal", Scripta Materialia. Vol. 56(5), pp. 417-420. [Abstract] [BibTeX] [DOI] Abstract: The mechanism by which novel dimpled metallic sheets adopt multi-stable cylindrical modes is determined using a straightforward homogenization scheme, which identifies highly compliant narrow regions linked to the unit cell geometry of dimple layout. The sheet prefers to bend about these regions to maximize the curving induced by residual stresses. BibTeX: @article{seffen2007a, author = {K. A. Seffen}, title = {Hierarchical Multi-stable Shapes in Mechanical Memory Metal}, journal = {Scripta Materialia}, year = {2007}, volume = {56}, number = {5}, pages = {417--420}, doi = {10.1016/j.scriptamat.2006.10.038} }  Seffen KA (2007), "Theoretical Performance of a Coiled Coil Piezoelecric Bimorph", Sensors and Actuators A. Vol. 133, pp. 486-492. [Abstract] [BibTeX] [DOI] [PDF] Abstract: The electromechanical coupling behaviour of a novel, highly coiled piezoelectric strip structure is developed in full, in order to expound its performance and efficiency. The strip is doubly coiled for compactness and, compared to a standard straight actuator of the same cross-section, it is shown that the actuator here offers better generative forces and energy conversion, and substantial actuated displacements, however, at the expense of a much lower stiffness. The device is therefore proposed for high-displacement, quasi-static applications. BibTeX: @article{seffen2007c, author = {K. A. Seffen}, title = {Theoretical Performance of a Coiled Coil Piezoelectric Bimorph}, journal = {Sensors and Actuators A}, year = {2007}, volume = {133}, pages = {486--492}, doi = {10.1016/j.sna.2006.04.016} }  Seffen KA (2007), "'Morphing' Bistable Orthotropic Elliptical Shallow Shells", Proceedings of the Royal Society A, Vol. 463(2077), pp. 67-83. [Abstract] [BibTeX] [DOI] [PDF] Abstract: This study is concerned with the equilibrium shapes of orthotropic, elliptical plates and shells deforming elastically without initial stresses. The aim is to explore potential bistable configurations and their dependencies on material parameters and initial shape for elucidating novel morphing structures. A strain energy formulation gives way to a compact set of governing equations of deformation, which can be solved in closed form for some isotropic and orthotropic conditions. It is shown that bistability depends on the change in Gaussian curvature of the shell, in particular, for initially untwisted shells, isotropy precludes bistability, where there is negative initial Gaussian curvature, but orthotropic materials yield bistability irrespective of the sign of the initial Gaussian curvature. This improved range of performance stems from increasing the independent shear modulus, which imparts sufficient torsional rigidity to stabilize against perturbations in the deformed state. It is also shown that the range of bistable configurations for initially twisted shells generally diminishes as the degree of twist increases. BibTeX: @article{seffen2007b, author = {K. A. Seffen}, title = {'Morphing' Bistable Orthotropic Elliptical Shallow Shells}, journal = {Proceedings of the Royal Society A}, year = {2007}, volume = {463}, number = {2077}, pages = { 67--83}, doi = {10.1098/rspa.2006.1750} }  Seffen KA and McMahon RA (2007), "Heating of a Uniform Wafer Disk", International Journal of Mechanical Sciences. Vol. 49, pp. 230-238. [Abstract] [BibTeX] [DOI] [PDF] Abstract: The closed-form heating response of a thin uniform circular wafer is obtained, in view of a new processing method for semiconductor materials. A strain energy formulation is obtained expeditiously using Gaussian curvature and associated structural concepts. The method is developed for generally curved wafers, which accounts for flat, spherical, cylindrical and twisted shapes. Solutions for the first two types become available in closed form, and the deformation can exhibit a sudden change in axi-symmetrical response or a snapthrough buckling, or both: for the latter two types, a numerical solution points to progressive deformation in both without buckling. All results are shown to compare rather well with finite element analysis. BibTeX: @article{seffen2007e, author = {K. A. Seffen and R. A. McMahon}, title = {Heating of a Uniform Wafer Disk}, journal = {International Journal of Mechanical Sciences}, year = {2007}, volume = {49}, pages = { 230--238}, doi = {10.1016/j.ijmecsci.2006.08.003} }  2006 Guest SD and Pellegrino S (2006), "Analytical Models for Bistable Cylindrical Shells", Proceedings of the Royal Society A, Vol. 462(2067), pp. 839-854. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Thin cylindrical shell structures can show interesting bistable behaviour. If made unstressed from isotropic materials they are only stable in the initial configuration, but if made from fibre-reinforced composites they may also have a second, stable configuration. If the layup of the composite is antisymmetric, this alternative stable configuration forms a tight coil; if the layup is symmetric the alternative stable configuration is helical. A simple two-parameter model for these structure is presented that is able to distinguish between these different behaviours. BibTeX: @article{guest2006, author = {S. D. Guest and S. Pellegrino}, title = {Analytical Models for Bistable Cylindrical Shells}, journal = {Proceedings of the Royal Society A}, year = {2006}, volume = {462}, number = {2067}, pages = {839-854}, doi = {10.1098/rspa.2005.1598} }  Leung ACH and Guest SD (2006), "Actuation-Softening in Kagome Lattice Structures", In Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Newport, RI, USA, 1-4 May, 2006. [Abstract] [BibTeX] [PDF] Abstract: The two-dimensional kagome lattice has been shown to be a promising basis for active shape-changing structures, having both low actuation resistance and high passive stiﬀness. Linear actuators replace some members of the truss: activation of the actuators results in a global macroscopic shape change. The linear behaviour of the structure, and in particular the high passive stiﬀness, depends crucially on the straight bars running across the structure; but this straightness is destroyed when bars are actuated. The current paper investigates this behaviour by imposing large actuations to create geometrically non-linearity. A column of actuators is introduced into a kagome lattice, so that for every actuator, the actuator directly above and below is also activated; the horizontal stiﬀness of the system is then measured. Numerical results show that when the actuators are extended, there is a sudden drop in passive stiﬀness at a ‘critical’ actuation strain. This critical actuation strain depends on the stockiness of the bars of the lattice, and the stiﬀness of the actuator itself. For lattices with contracting actuators, the stiﬀness degradation is gradual, and less severe. BibTeX: @conference{leung2006, author = {A. C. H. Leung and S. D. Guest}, title = {Actuation-Softening in Kagome Lattice Structures}, booktitle = {Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference}, year = {2006}, note = {Paper no. AIAA-2006-1888} }  Schenk M, Herder JL and Guest SD (2006), "Design of a Statically Balanced Tensegrity Mechanism", In Proceedings of IDETC/CIE 2006 ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Philadelphia, Pennsylvania, USA, September 10-13, 2006. [Abstract] [BibTeX] [PDF] Abstract: The combination of static balancing and tensegrity structures has resulted in a new class of mechanisms: Statically Balanced Tensegrity Mechanisms. These are prestressed structures that are in equilibrium in a wide range of positions, and thus exhibit mechanism-like properties. This paper describes the design of a prototype model of a statically balanced tensegrity mechanism based on a classic tensegrity structure. BibTeX: @conference{schenk2006, author = {M. Schenk and J. L. Herder and S. D. Guest}, title = {Design of a Statically Balanced Tensegrity Mechanism}, booktitle = {Proceedings of IDETC/CIE 2006 ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference}, year = {2006}, note = {Paper number DETC2006-99727} }  Seffen KA (2006), "Mechanical Memory Metal: a Novel Material for Developing Morphing Engineering Structures", Scripta Materialia. Vol. 55(4), pp. 411-414. [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper describes a profiled metallic sheet with discrete, self-locking modes of deformation, which can be curved, flattened or asymmetrical. This behaviour is achieved by depressing dimples on its surface, and is completely reversible. The governing mechanism depends on the interaction between residual stresses and non-linear deformation coupled to the orientation of each dimple, resulting in complex distortions; we predict these changes in shape using a straightforward computational model, which will expedite the design of novel morphing structures. BibTeX: @article{seffen2006, author = {K. A. Seffen}, title = {Mechanical Memory Metal: a Novel Material for Developing Morphing Engineering Structures}, journal = {Scripta Materialia}, year = {2006}, volume = {55}, number = {4}, pages = {411--414}, doi = {10.1016/j.scriptamat.2006.03.028} }  Seffen KA, Guest SD and Norman AD (2006), "Multistable Structural Member And Method For Forming A Multistable Structural Member", UK Patent Application 0612558.7., July, 2006. [BibTeX] BibTeX: @misc{seffen2006-patent, author = {K. A. Seffen and S. D. Guest and A. D. Norman}, title = {Multistable Structural Member And Method For Forming A Multistable Structural Member}, year = {2006} }  2004 Galletly DA and Guest SD (2004), "Bistable Composite Slit tubes. I. A Beam Model", International Journal of Solids and Structures. Vol. 41(16-17), pp. 4517-4533. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Composite slit tubes with a circular cross-section show an interesting variety in their large-deformation behaviour, that depends on the layup of the surface that is used: tubes made from many antisymmetric laminae are bistable, and have a compact coiled configuration, tubes made from similar, but symmetric, laminae do not have a compact coiled state, and indeed may not be bistable, while tubes made from an isotropic sheet are not bistable. A simple model is presented here that is able to distinguish between these behaviours; it assumes that the cross-section remains circular, but allows twist, which is shown to be the key to making the distinction between the behaviours described. BibTeX: @article{galletly2004a, author = {Diana A. Galletly and Simon D. Guest}, title = {Bistable Composite Slit Tubes. I. A Beam Model}, journal = {International Journal of Solids and Structures}, year = {2004}, volume = {41}, number = {16--17}, pages = {4517--4533}, doi = {10.1016/j.ijsolstr.2004.02.036} }  Galletly DA and Guest SD (2004), "Bistable Composite Slit Tubes. II. A Shell Model", International Journal of Solids and Structures. Vol. 41(16-17), pp. 4503-4516. [Abstract] [BibTeX] [DOI] [PDF] Abstract: The detailed shape of bistable tubes at a second stable equilibrium point is examined. The existence of a short boundary layer' at the edge of the tube is found, which is particularly significant for tubes that are initially shallow. BibTeX: @article{galletly2004b, author = {Diana A. Galletly and Simon D. Guest}, title = {Bistable Composite Slit Tubes. II. A Shell Model}, journal = {International Journal of Solids and Structures}, year = {2004}, volume = {41}, number = {16--17}, pages = {4503--4516}, doi = {10.1016/j.ijsolstr.2004.02.037} }  Kebadze E, Guest SD and Pellegrino S (2004), "Bistable Prestressed Shell Structures", International Journal of Solids and Structures. Vol. 41(11-12), pp. 2801-2820. [Abstract] [BibTeX] [DOI] [PDF] Abstract: The paper investigates a cylindrical shell which has two stable configurations, due to a particular distribution of residual stresses induced by plastic bending. The basic mechanics of the bistability are explained, along with details of the plastic forming. A comprehensive analytical model is developed which predicts the residual stress distribution and bistable configurations of the shell. Good correlation has been found between experimental results and predictions from this model. BibTeX: @article{kebadze2004, author = {E. Kebadze and S. D. Guest and S. Pellegrino}, title = {Bistable Prestressed Shell Structures}, journal = {International Journal of Solids and Structures}, year = {2004}, volume = {41}, number = {11-12}, pages = {2801-2820}, doi = {10.1016/j.ijsolstr.2004.01.028} }  Leung ACH, Symons DD and Guest SD (2004), "Actuation of Kagome Lattice Structures", In Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Palm Springs, CA, 19–22 April, 2004. [Abstract] [BibTeX] [PDF] Abstract: The kagome lattice has been shown to have promise as the basis of active structures, whose shape can be changed by linear actuators that replace some of the bars of the lattice. As a preliminary examination, this paper examines the eﬀect of the actuation of a single bar in a large two-dimensional kagome lattice. Previous work has shown that interesting properties of the kagome lattice depend on the bars that are co-linear with the actuated bar being straight, but has also shown that actuation causes these bars to bend; this paper therefore explores the geometrically non-linear response of the structure. Numerical results show that due to geometrically non-linear eﬀects, the actuation stiﬀness is reduced from that predicted by linear models, while the peak elastic strain in the structure is increased. BibTeX: @conference{leung2004, author = {A. C. H. Leung and D. D. Symons and S. D. Guest}, title = {Actuation of Kagome Lattice Structures}, booktitle = {Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference}, year = {2004}, note = {Paper no. AIAA-2004–1525} }  Seffen KA (2004), "Bi-stable Concepts for Reconfigurable Structures", In Structures TC Special Session on Concepts for Morphing and Reconfigurable Structures, 45th Structures and Structural Dynamics, and Materials Conference. Palm Springs California, 19-22 April, 2004. [BibTeX] BibTeX: @conference{seffen2004a, author = {K. A. Seffen}, title = {Bi-stable Concepts for Reconfigurable Structures}, booktitle = {Structures TC Special Session on Concepts for Morphing and Reconfigurable Structures, 45th Structures and Structural Dynamics, and Materials Conference}, year = {2004}, note = {Paper 2004-1526} }  Seffen KA and Toews E (2004), "Hyperhelical Actuators: Coils and Coiled Coils", In Proceedings of 12th AIAA/ASME/AHS Adaptive Structures Conference. Palm Springs, California, 19-22 April, 2004. [BibTeX] BibTeX: @conference{seffen2004b, author = {K. A. Seffen and E. Toews}, title = {Hyperhelical Actuators: Coils and Coiled Coils}, booktitle = {Proceedings of 12th AIAA/ASME/AHS Adaptive Structures Conference}, year = {2004}, note = {Paper 2004-1814} }  Wicks N and Guest SD (2004), "Single Member Actuation in Large Repetitive Truss Structures", International Journal of Solids and Structures. Vol. 41(3-4), pp. 965-978. [Abstract] [BibTeX] [DOI] [PDF] Abstract: Numerical results are presented for the energy required to actuate a single member in three large two-dimensional lattice structures. As expected, the actuation energy, relative to the energy required to stretch a bar, scales with bar stockiness to the power two for a hexagonal lattice, whose behaviour is bending dominated, but is not greatly affected by stockiness for a triangulated lattice, whose response is stretching dominated. For a kagome lattice, however, the relative actuation energy scales with stockiness to the power one. Simple models show that, for the kagome, the attenuation of the deformation with distance from the actuated bar itself depends on the stockiness, and this results in the unexpected energy scaling; they also show that the energy is approximately equally partitioned between bending and stretching. BibTeX: @article{wicks2004, author = {N. Wicks and S. D. Guest}, title = {Single Member Actuation in Large Repetitive Truss Structures}, journal = {International Journal of Solids and Structures}, year = {2004}, volume = {41}, number = {3-4}, pages = {965-978}, doi = {10.1016/j.ijsolstr.2003.09.029} }  2003 Guest SD and Hutchinson JW (2003), "On the Determinacy of Repetitive Structures", Journal of the Mechanics and Physics of Solids. Vol. 51(3), pp. 383-391. [Abstract] [BibTeX] [DOI] [PDF] Abstract: This paper shows that repetitive, infinite structures cannot be simultaneously statically, and kinematically, determinate. BibTeX: @article{guest2003, author = {S. D. Guest and J. W. Hutchinson}, title = {On the Determinacy of Repetitive Structures}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2003}, volume = {51}, number = {3}, pages = {383-391}, doi = {10.1016/S0022-5096(02)00107-2} }  2000 Galletly D and Guest SD (2000), "Equilibrium and Stability Analysis of Bistable Composite Slit Tubes", In Proceedings of IASS - IACM 2000, Fourth International Colloquium on Computation of Shell & Spatial Structures. Chania, Crete, 4-7 June, 2000. [BibTeX] BibTeX: @conference{galletly2000, author = {D. Galletly and S. D. Guest}, title = {Equilibrium and Stability Analysis of Bistable Composite Slit Tubes}, booktitle = {Proceedings of IASS - IACM 2000, Fourth International Colloquium on Computation of Shell & Spatial Structures}, year = {2000} } `
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