8,748 research outputs found
Radial asymptotics of Lemaitre-Tolman-Bondi dust models
We examine the radial asymptotic behavior of spherically symmetric
Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along
radial rays, which are spacelike geodesics parametrized by proper length
, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing
quasi-local scalars defined as integral functions along the rays, we obtain a
complete and covariant representation of the models, leading to an initial
value parametrization in which all scalars can be given by scaling laws
depending on two metric scale factors and two basic initial value functions.
Considering regular "open" LTB models whose space slices allow for a diverging
, we provide the conditions on the radial coordinate so that its
asymptotic limit corresponds to the limit as . The "asymptotic
state" is then defined as this limit, together with asymptotic series expansion
around it, evaluated for all metric functions, covariant scalars (local and
quasi-local) and their fluctuations. By looking at different sets of initial
conditions, we examine and classify the asymptotic states of parabolic,
hyperbolic and open elliptic models admitting a symmetry center. We show that
in the radial direction the models can be asymptotic to any one of the
following spacetimes: FLRW dust cosmologies with zero or negative spatial
curvature, sections of Minkowski flat space (including Milne's space), sections
of the Schwarzschild--Kruskal manifold or self--similar dust solutions.Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style.
Typos corrected and an important reference added. Accepted for publication in
General Relativity and Gravitatio
Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful
TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design
This paper introduces the software TiGL: TiGL is an open source high-fidelity
geometry modeler that is used in the conceptual and preliminary aircraft and
helicopter design phase. It creates full three-dimensional models of aircraft
from their parametric CPACS description. Due to its parametric nature, it is
typically used for aircraft design analysis and optimization. First, we present
the use-case and architecture of TiGL. Then, we discuss it's geometry module,
which is used to generate the B-spline based surfaces of the aircraft. The
backbone of TiGL is its surface generator for curve network interpolation,
based on Gordon surfaces. One major part of this paper explains the
mathematical foundation of Gordon surfaces on B-splines and how we achieve the
required curve network compatibility. Finally, TiGL's aircraft component module
is introduced, which is used to create the external and internal parts of
aircraft, such as wings, flaps, fuselages, engines or structural elements
On Micromechanical Parameter Identification With Integrated DIC and the Role of Accuracy in Kinematic Boundary Conditions
Integrated Digital Image Correlation (IDIC) is nowadays a well established
full-field experimental procedure for reliable and accurate identification of
material parameters. It is based on the correlation of a series of images
captured during a mechanical experiment, that are matched by displacement
fields derived from an underlying mechanical model. In recent studies, it has
been shown that when the applied boundary conditions lie outside the employed
field of view, IDIC suffers from inaccuracies. A typical example is a
micromechanical parameter identification inside a Microstructural Volume
Element (MVE), whereby images are usually obtained by electron microscopy or
other microscopy techniques but the loads are applied at a much larger scale.
For any IDIC model, MVE boundary conditions still need to be specified, and any
deviation or fluctuation in these boundary conditions may significantly
influence the quality of identification. Prescribing proper boundary conditions
is generally a challenging task, because the MVE has no free boundary, and the
boundary displacements are typically highly heterogeneous due to the underlying
microstructure. The aim of this paper is therefore first to quantify the
effects of errors in the prescribed boundary conditions on the accuracy of the
identification in a systematic way. To this end, three kinds of mechanical
tests, each for various levels of material contrast ratios and levels of image
noise, are carried out by means of virtual experiments. For simplicity, an
elastic compressible Neo-Hookean constitutive model under plane strain
assumption is adopted. It is shown that a high level of detail is required in
the applied boundary conditions. This motivates an improved boundary condition
application approach, which considers constitutive material parameters as well
as kinematic variables at the boundary of the entire MVE as degrees of freedom
in...Comment: 37 pages, 25 figures, 2 tables, 2 algorithm
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