2,513 research outputs found
Origami constraints on the initial-conditions arrangement of dark-matter caustics and streams
In a cold-dark-matter universe, cosmological structure formation proceeds in
rough analogy to origami folding. Dark matter occupies a three-dimensional
'sheet' of free- fall observers, non-intersecting in six-dimensional
velocity-position phase space. At early times, the sheet was flat like an
origami sheet, i.e. velocities were essentially zero, but as time passes, the
sheet folds up to form cosmic structure. The present paper further illustrates
this analogy, and clarifies a Lagrangian definition of caustics and streams:
caustics are two-dimensional surfaces in this initial sheet along which it
folds, tessellating Lagrangian space into a set of three-dimensional regions,
i.e. streams. The main scientific result of the paper is that streams may be
colored by only two colors, with no two neighbouring streams (i.e. streams on
either side of a caustic surface) colored the same. The two colors correspond
to positive and negative parities of local Lagrangian volumes. This is a severe
restriction on the connectivity and therefore arrangement of streams in
Lagrangian space, since arbitrarily many colors can be necessary to color a
general arrangement of three-dimensional regions. This stream two-colorability
has consequences from graph theory, which we explain. Then, using N-body
simulations, we test how these caustics correspond in Lagrangian space to the
boundaries of haloes, filaments and walls. We also test how well outer caustics
correspond to a Zel'dovich-approximation prediction.Comment: Clarifications and slight changes to match version accepted to MNRAS.
9 pages, 5 figure
Compliant morphing structures from twisted bulk metallic glass ribbons
In this work, we investigate the use of pre-twisted metallic ribbons as
building blocks for shape-changing structures. We manufacture these elements by
twisting initially flat ribbons about their (lengthwise) centroidal axis into a
helicoidal geometry, then thermoforming them to make this configuration a
stress-free reference state. The helicoidal shape allows the ribbon to have
preferred bending directions that vary throughout its length. These bending
directions serve as compliant joints and enable several deployed and stowed
configurations that are unachievable without pre-twist, provided that
compaction does not induce material failure. We fabricate these ribbons using a
bulk metallic glass (BMG), for its exceptional elasticity and thermoforming
attributes. Combining numerical simulations, an analytical model based on shell
theory and torsional experiments, we analyze the finite-twisting mechanics of
various ribbon geometries. We find that, in ribbons with undulated edges, the
twisting deformations can be better localized onto desired regions prior to
thermoforming. Finally, we join together multiple ribbons to create deployable
systems. Our work proposes a framework for creating fully metallic, yet
compliant structures that may find application as elements for space structures
and compliant robots
Autonomous Deployment of a Solar Panel Using an Elastic Origami and Distributed Shape Memory Polymer Actuators
Deployable mechanical systems such as space solar panels rely on the
intricate stowage of passive modules, and sophisticated deployment using a
network of motorized actuators. As a result, a significant portion of the
stowed mass and volume are occupied by these support systems. An autonomous
solar panel array deployed using the inherent material behavior remains
elusive. In this work, we develop an autonomous self-deploying solar panel
array that is programmed to activate in response to changes in the surrounding
temperature. We study an elastic "flasher" origami sheet embedded in a circle
of scissor mechanisms, both printed with shape memory polymers. The scissor
mechanisms are optimized to provide the maximum expansion ratio while
delivering the necessary force for deployment. The origami sheet is also
optimized to carry the maximum number of solar panels given space constraints.
We show how the folding of the "flasher" origami exhibits a bifurcation
behavior resulting in either a cone or disk shape both numerically and in
experiments. A folding strategy is devised to avoid the undesired cone shape.
The resulting design is entirely 3D printed, achieves an expansion ratio of
1000% in under 40 seconds, and shows excellent agreement with simulation
prediction both in the stowed and deployed configurations.Comment: 12 pages, 12 figure
Topological mechanics of origami and kirigami
Origami and kirigami have emerged as potential tools for the design of
mechanical metamaterials whose properties such as curvature, Poisson ratio, and
existence of metastable states can be tuned using purely geometric criteria. A
major obstacle to exploiting this property is the scarcity of tools to identify
and program the flexibility of fold patterns. We exploit a recent connection
between spring networks and quantum topological states to design origami with
localized folding motions at boundaries and study them both experimentally and
theoretically. These folding motions exist due to an underlying topological
invariant rather than a local imbalance between constraints and degrees of
freedom. We give a simple example of a quasi-1D folding pattern that realizes
such topological states. We also demonstrate how to generalize these
topological design principles to two dimensions. A striking consequence is that
a domain wall between two topologically distinct, mechanically rigid structures
is deformable even when constraints locally match the degrees of freedom.Comment: 5 pages, 3 figures + ~5 pages S
Patterning nonisometric origami in nematic elastomer sheets
Nematic elastomers dramatically change their shape in response to diverse
stimuli including light and heat. In this paper, we provide a systematic
framework for the design of complex three dimensional shapes through the
actuation of heterogeneously patterned nematic elastomer sheets. These sheets
are composed of \textit{nonisometric origami} building blocks which, when
appropriately linked together, can actuate into a diverse array of three
dimensional faceted shapes. We demonstrate both theoretically and
experimentally that: 1) the nonisometric origami building blocks actuate in the
predicted manner, 2) the integration of multiple building blocks leads to
complex multi-stable, yet predictable, shapes, 3) we can bias the actuation
experimentally to obtain a desired complex shape amongst the multi-stable
shapes. We then show that this experimentally realized functionality enables a
rich possible design landscape for actuation using nematic elastomers. We
highlight this landscape through theoretical examples, which utilize large
arrays of these building blocks to realize a desired three dimensional origami
shape. In combination, these results amount to an engineering design principle,
which we hope will provide a template for the application of nematic elastomers
to emerging technologies
Origami Multistabilty: From Single Vertices to Metasheets
We explore the surprisingly rich energy landscape of origami-like folding
planar structures. We show that the configuration space of rigid-paneled
degree-4 vertices, the simplest building blocks of such systems, consists of at
least two distinct branches meeting at the flat state. This suggests that
generic vertices are at least bistable, but we find that the nonlinear nature
of these branches allows for vertices with as many as five distinct stable
states. In vertices with collinear folds and/or symmetry, more branches emerge
leading to up to six stable states. Finally, we introduce a procedure to tile
arbitrary 4-vertices while preserving their stable states, thus allowing the
design and creation of multistable origami metasheets.Comment: For supplemental movies please visit
http://www.lorentz.leidenuniv.nl/~chen/multisheet
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