48,432 research outputs found
Elastic strips
Motivated by the problem of finding an explicit description of a developable
narrow Moebius strip of minimal bending energy, which was first formulated by
M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently
E.L. Starostin and G.H.M. van der Heijden found a numerical description for an
elastic Moebius strip, but did not give an integrable solution. We derive two
conservation laws, which describe the equilibrium equations of elastic strips.
In applying these laws we find two new classes of integrable elastic strips
which correspond to spherical elastic curves. We establish a connection between
Hopf tori and force--free strips, which are defined by one of the integrable
strips, we have found. We introduce the P--functional and relate it to elastic
strips.Comment: 21 pages, 2 figure
Multistability of free spontaneously-curved anisotropic strips
Multistable structures are objects with more than one stable conformation,
exemplified by the simple switch. Continuum versions are often elastic
composite plates or shells, such as the common measuring tape or the slap
bracelet, both of which exhibit two stable configurations: rolled and unrolled.
Here we consider the energy landscape of a general class of multistable
anisotropic strips with spontaneous Gaussian curvature. We show that while
strips with non-zero Gaussian curvature can be bistable, strips with positive
spontaneous curvature are always bistable, independent of the elastic moduli,
strips of spontaneous negative curvature are bistable only in the presence of
spontaneous twist and when certain conditions on the relative stiffness of the
strip in tension and shear are satisfied. Furthermore, anisotropic strips can
become tristable when their bending rigidity is small. Our study complements
and extends the theory of multistability in anisotropic shells and suggests new
design criteria for these structures.Comment: 20 pages, 10 figure
Triangular buckling patterns of twisted inextensible strips
When twisting a strip of paper or acetate under high longitudinal tension,
one observes, at some critical load, a buckling of the strip into a regular
triangular pattern. Very similar triangular facets have recently been observed
in solutions to a new set of geometrically-exact equations describing the
equilibrium shape of thin inextensible elastic strips. Here we formulate a
modified boundary-value problem for these equations and construct post-buckling
solutions in good agreement with the observed pattern in twisted strips. We
also study the force-extension and moment-twist behaviour of these strips by
varying the mode number n of triangular facets
Equilibrium Shapes with Stress Localisation for Inextensible Elastic Mobius and Other Strips
We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order one-dimensional problem posed on the centreline of the strip. We derive EulerâLagrange equations for this problem in EulerâPoincarĂ© form and formulate boundary-value problems for closed symmetric one- and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami
Minimal resonances in annular non-Euclidean strips
Differential growth processes play a prominent role in shaping leaves and
biological tissues. Using both analytical and numerical calculations, we
consider the shapes of closed, elastic strips which have been subjected to an
inhomogeneous pattern of swelling. The stretching and bending energies of a
closed strip are frustrated by compatibility constraints between the curvatures
and metric of the strip. To analyze this frustration, we study the class of
"conical" closed strips with a prescribed metric tensor on their center line.
The resulting strip shapes can be classified according to their number of
wrinkles and the prescribed pattern of swelling. We use this class of strips as
a variational ansatz to obtain the minimal energy shapes of closed strips and
find excellent agreement with the results of a numerical bead-spring model.
Within this class of strips, we derive a condition under which a strip can have
vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added
2 figure
Hemihelical local minimizers in prestrained elastic bi-strips
We consider a double layered prestrained elastic rod in the limit of
vanishing cross section. For the resulting limit Kirchoff-rod model with
intrinsic curvature we prove a supercritical bifurcation result, rigorously
showing the emergence of a branch of hemihelical local minimizers from the
straight configuration, at a critical force and under clamping at both ends. As
a consequence we obtain the existence of nontrivial local minimizers of the
-d system.Comment: 16 pages, 2 figure
Revisiting the Higgs Mass and Dark Matter in the CMSSM
Taking into account the available accelerator and astrophysical constraints,
the mass of the lightest neutral Higgs boson h in the minimal supersymmetric
extension of the Standard Model with universal soft supersymmetry-breaking
masses (CMSSM) has been estimated to lie between 114 and ~ 130 GeV. Recent data
from ATLAS and CMS hint that m_h ~ 125 GeV, though m_h ~ 119 GeV may still be a
possibility. Here we study the consequences for the parameters of the CMSSM and
direct dark matter detection if the Higgs hint is confirmed, focusing on the
strips in the (m_1/2, m_0) planes for different tan beta and A_0 where the
relic density of the lightest neutralino chi falls within the range of the
cosmological cold dark matter density allowed by WMAP and other experiments. We
find that if m_h ~ 125 GeV focus-point strips would be disfavoured, as would
the low-tan beta stau-chi and stop -chi coannihilation strips, whereas the
stau-chi coannihilation strip at large tan beta and A_0 > 0 would be favoured,
together with its extension to a funnel where rapid annihilation via
direct-channel H/A poles dominates. On the other hand, if m_h ~ 119 GeV more
options would be open. We give parametrizations of WMAP strips with large tan
beta and fixed A_0/m_0 > 0 that include portions compatible with m_h = 125 GeV,
and present predictions for spin-independent elastic dark matter scattering
along these strips. These are generally low for models compatible with m_h =
125 GeV, whereas the XENON100 experiment already excludes some portions of
strips where m_h is smaller.Comment: 24 pages, 9 figure
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