3,535 research outputs found
Static inconsistencies in certain axiomatic higher-order shear deformation theories for beams, plates and shells
AbstractStatic inconsistencies that arise when modelling the flexural behaviour of beams, plates and shells with clamped boundary conditions using a certain class of axiomatic, higher-order shear deformation theory are discussed. The inconsistencies pertain to displacement-based theories that enforce conditions of vanishing shear strain at the top and bottom surfaces a priori. First it is shown that the essential boundary condition of vanishing Kirchhoff rotation perpendicular to an edge (w,x=0 or w,y=0) is physically inaccurate, as the rotation at a clamped edge may in fact be non-zero due to the presence of transverse shear rotation. As a result, the shear force derived from constitutive equations erroneously vanishes at a clamped edge. In effect, this boundary condition overconstrains the structure leading to underpredictions in transverse bending deflection and overpredictions of axial stresses compared to high-fidelity 3D finite element solutions for thick and highly orthotropic plates. Generalised higher-order theories written in the form of a power series, as in Carrera’s Unified Formulation, do not produce this inconsistency. It is shown that the condition of vanishing shear tractions at the top and bottom surfaces need not be applied a priori, as the transverse shear strains inherently vanish if the order of the theory is sufficient to capture all higher-order effects. Finally, the transverse deflection of the generalised higher-order theories is expanded in a power series of a non-dimensional parameter and used to derive a material and geometry dependent shear correction factor that provides more accurate solutions of bending deflection than the classical value of 5/6
Shape Control for Experimental Continuation
An experimental method has been developed to locate unstable equilibria of
nonlinear structures quasi-statically. The technique involves loading a
structure by application of either a force or a displacement at a main
actuation point, while simultaneously controlling the overall shape using
additional probe points. The method is applied to a shallow arch, and unstable
segments of its equilibrium path are identified experimentally for the first
time. Shape control is a fundamental building block for the experimental---as
opposed to numerical---continuation of nonlinear structures, which will
significantly expand our ability to measure their mechanical response.Comment: Updated Figure 6 experimental results with correct calibration factor
for linear transducer. Updated Figure 6 finite element results with correct
load multiplier for half-model. Updated paper text to reflect these changes.
5 pages, 6 figure
Crystal structures and freezing of dipolar fluids
We investigate the crystal structure of classical systems of spherical
particles with an embedded point dipole at T=0. The ferroelectric ground state
energy is calculated using generalizations of the Ewald summation technique.
Due to the reduced symmetry compared to the nonpolar case the crystals are
never strictly cubic. For the Stockmayer (i.e., Lennard-Jones plus dipolar)
interaction three phases are found upon increasing the dipole moment:
hexagonal, body-centered orthorhombic, and body-centered tetragonal. An even
richer phase diagram arises for dipolar soft spheres with a purely repulsive
inverse power law potential . A crossover between qualitatively
different sequences of phases occurs near the exponent . The results are
applicable to electro- and magnetorheological fluids. In addition to the exact
ground state analysis we study freezing of the Stockmayer fluid by
density-functional theory.Comment: submitted to Phys. Rev.
Magnetization of ferrofluids with dipolar interactions - a Born--Mayer expansion
For ferrofluids that are described by a system of hard spheres interacting
via dipolar forces we evaluate the magnetization as a function of the internal
magnetic field with a Born--Mayer technique and an expansion in the dipolar
coupling strength. Two different approximations are presented for the
magnetization considering different contributions to a series expansion in
terms of the volume fraction of the particles and the dipolar coupling
strength.Comment: 19 pages, 11 figures submitted to PR
A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part I:Model Formulation
Inhomogeneous magnetization in dipolar ferromagnetic liquids
At high densities fluids of strongly dipolar spherical particles exhibit
spontaneous long-ranged orientational order. Typically, due to demagnetization
effects induced by the long range of the dipolar interactions, the
magnetization structure is spatially inhomogeneous and depends on the shape of
the sample. We determine this structure for a cubic sample by the free
minimization of an appropriate microscopic density functional using simulated
annealing. We find a vortex structure resembling four domains separated by four
domain walls whose thickness increases proportional to the system size L. There
are indications that for large L the whole configuration scales with the system
size. Near the axis of the mainly planar vortex structure the direction of the
magnetization escapes into the third dimension or, at higher temperatures, the
absolute value of the magnetization is strongly reduced. Thus the orientational
order is characterized by two point defects at the top and the bottom of the
sample, respectively. The equilibrium structure in an external field and the
transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.
Ferromagnetic Liquid Thin Films Under Applied Field
Theoretical calculations, computer simulations and experiments indicate the
possible existence of a ferromagnetic liquid state, although definitive
experimental evidence is lacking. Should such a state exist, demagnetization
effects would force a nontrivial magnetization texture. Since liquid droplets
are deformable, the droplet shape is coupled with the magnetization texture. In
a thin-film geometry in zero applied field, the droplet has a circular shape
and a rotating magnetization texture with a point vortex at the center. We
calculate the elongation and magnetization texture of such ferromagnetic thin
film liquid droplet confined between two parallel plates under a weak applied
magnetic field. The vortex stretches into a domain wall and exchange forces
break the reflection symmetry. This behavior contrasts qualitatively and
quantitatively with the elongation of paramagnetic thin films.Comment: 10 pages, 4 figures, Submitted to Phys. Rev.
The three-dimensional structure of the Eta Carinae Homunculus
We investigate, using the modeling code SHAPE, the three-dimensional
structure of the bipolar Homunculus nebula surrounding Eta Carinae, as mapped
by new ESO VLT/X-Shooter observations of the H2 micron
emission line. Our results reveal for the first time important deviations from
the axisymmetric bipolar morphology: 1) circumpolar trenches in each lobe
positioned point-symmetrically from the center and 2) off-planar protrusions in
the equatorial region from each lobe at longitudinal (~55 degrees) and
latitudinal (10-20 degrees) distances from the projected apastron direction of
the binary orbit. The angular distance between the protrusions (~110 degrees)
is similar to the angular extent of each polar trench (~130 degrees) and nearly
equal to the opening angle of the wind-wind collision cavity (~110 degrees). As
in previous studies, we confirm a hole near the centre of each polar lobe and
no detectable near-IR H2 emission from the thin optical skirt seen prominently
in visible imagery. We conclude that the interaction between the outflows
and/or radiation from the central binary stars and their orientation in space
has had, and possibly still has, a strong influence on the Homunculus. This
implies that prevailing theoretical models of the Homunculus are incomplete as
most assume a single star origin that produces an axisymmetric nebula. We
discuss how the newly found features might be related to the Homunculus
ejection, the central binary and the interacting stellar winds. We also include
a 3D printable version of our Homunculus model.Comment: 14 pages, 7 color figures, 1 interactive 3D figure (Figure 5,
requires Adobe Reader), published in MNRAS. A 3D printable version of our
Homunculus model can be downloaded from
http://svs.gsfc.nasa.gov/vis/a010000/a011500/a011568/Eta_Car_Homunuculus_3D_model.zip
or from the 'Supporting Information' link in the electronic version of the
MNRAS articl
Phase Coexistence of a Stockmayer Fluid in an Applied Field
We examine two aspects of Stockmayer fluids which consists of point dipoles
that additionally interact via an attractive Lennard-Jones potential. We
perform Monte Carlo simulations to examine the effect of an applied field on
the liquid-gas phase coexistence and show that a magnetic fluid phase does
exist in the absence of an applied field. As part of the search for the
magnetic fluid phase, we perform Gibbs ensemble simulations to determine phase
coexistence curves at large dipole moments, . The critical temperature is
found to depend linearly on for intermediate values of beyond the
initial nonlinear behavior near and less than the where no
liquid-gas phase coexistence has been found. For phase coexistence in an
applied field, the critical temperatures as a function of the applied field for
two different are mapped onto a single curve. The critical densities
hardly change as a function of applied field. We also verify that in an applied
field the liquid droplets within the two phase coexistence region become
elongated in the direction of the field.Comment: 23 pages, ReVTeX, 7 figure
Orientational order in dipolar fluids consisting of nonspherical hard particles
We investigate fluids of dipolar hard particles by a certain variant of
density-functional theory. The proper treatment of the long range of the
dipolar interactions yields a contribution to the free energy which favors
ferromagnetic order. This corrects previous theoretical analyses. We determine
phase diagrams for dipolar ellipsoids and spherocylinders as a function of the
aspect ratio of the particles and their dipole moment. In the nonpolar limit
the results for the phase boundary between the isotropic and nematic phase
agree well with simulation data. Adding a longitudinal dipole moment favors the
nematic phase. For oblate or slightly elongated particles we find a
ferromagnetic liquid phase, which has also been detected in computer
simulations of fluids consisting of spherical dipolar particles. The detailed
structure of the phase diagram and its evolution upon changing the aspect ratio
are discussed in detail.Comment: 35 pages LaTeX with epsf style, 11 figures in eps format, submitted
to Phys. Rev.
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