4,122 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 Carreraās 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
Virtual Testing of Experimental Continuation
We present a critical advance in experimental testing of nonlinear
structures. Traditional quasi-static experimental methods control the
displacement or force at one or more load-introduction points on a structure.
This approach is unable to traverse limit points in the control parameter, as
the immediate equilibrium beyond these points is statically unstable, causing
the structure to snap to another equilibrium. As a result, unstable
equilibria---observed numerically---are yet to be verified experimentally.
Based on previous experimental work, and a virtual testing environment
developed herein, we propose a new experimental continuation method that can
path-follow along unstable equilibria and traverse limit points. To support
these developments, we provide insightful analogies between a fundamental
building block of our technique---shape control---and analysis concepts such as
the principle of virtual work and Galerkin's method. The proposed testing
method will enable the validation of an emerging class of nonlinear structures
that exploit instabilities for novel functionality
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
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.
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.
A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part I:Model Formulation
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.
MEAM interatomic potentials of Ni, Re, and NiāRe alloys for atomistic fracture simulations
Second nearest neighbor modified embedded atom method (2NN-MEAM) interatomic potentials are developed for the Ni, Re, and NiāReĀ binaries. To construct the potentials, density functional theory (DFT) calculations have been employed to calculate fundamental physical properties that play a dominant role in fracture. The potentials are validated to accurately reproduce material properties that correlate with materialās fracture behavior. The thus constructed potentials were applied to perform large scale simulations of mode I fracture in Ni and NiāReĀ binaries with lowĀ ReĀ content. SubstitutionalĀ ReĀ did not alter the ductile nature of crack propagation, though it resulted in a monotonous increase of the critical stress intensity factor withĀ ReĀ content
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