2,383 research outputs found
Singular limiting induced from continuum solutions and the problem of dynamic cavitation
In the works of
K.A. Pericak-Spector and S. Spector [Pericak-Spector, Spector 1988, 1997] a class of self-similar
solutions are constructed for the equations of radial isotropic elastodynamics
that describe cavitating solutions. Cavitating solutions decrease the total
mechanical energy and provide a striking example of non-uniqueness of entropy weak solutions
(for polyconvex energies) due to point-singularities at the cavity. To resolve
this paradox, we introduce the concept of singular limiting induced from continuum solution (or slic-solution),
according to which a discontinuous motion is a slic-solution if its averages
form a family of smooth approximate solutions to the problem. It turns out that there is an energetic cost for
creating the cavity, which is captured by the notion of slic-solution but neglected by the
usual entropic weak solutions. Once this cost is accounted for, the total mechanical energy of the
cavitating solution is in fact larger than that of the homogeneously deformed state.
We also apply the notion of slic-solutions to a one-dimensional example describing the onset of fracture,
and to gas dynamics in Langrangean coordinates with Riemann data inducing vacuum in the wave fan
The problem of dynamic cavitation in nonlinear elasticity
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to
the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of
entropic weak solutions (with polyconvex energy) due to a forming cavity
On the construction and properties of weak solutions describing dynamic cavitation
We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations
of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation.
For dimensions d =2, 3 we show that cavity formation is necessarily associated with a unique precursor shock.
We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation
as a function of the cavity speed of the self-similar profiles. We show that
for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents
Models for Flow Rate Simulation in Gear Pumps: A Review
Gear pumps represent the majority of the fixed displacement machines used for flow generation in fluid power systems. In this context, the paper presents a review of the different methodologies used in the last years for the simulation of the flow rates generated by gerotor, external gear and crescent pumps. As far as the lumped parameter models are concerned, different ways of selecting the control volumes into which the pump is split are analyzed and the main governing equations are presented. The principles and the applications of distributed models from 1D to 3D are reported. A specific section is dedicated to the methods for the evaluation of the necessary geometric quantities: analytic, numerical and Computer-Aided Design (CAD)-based. The more recent studies taking into account the influence on leakages of the interactions between the fluid and the mechanical parts are explained. Finally the models for the simulation of the fluid aeration are described. The review brings to evidence the increasing effort for improving the simulation models used for the design and the optimization of the gear machines
Study of fluid transients in closed conduits annual report no. 1
Atmospheric density effect on computation of earth satellite orbit
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