7,476 research outputs found
Bending of a cracked plate with arbitrary stress distribution across the thickness
Bending of cracked plate with arbitrary stress distribution across plate thicknes
Long's Vortex Revisited
The conical self-similar vortex solution of Long (1961) is reconsidered, with
a view toward understanding what, if any, relationship exists between Long's
solution and the more-recent similarity solutions of Mayer and Powell (1992),
which are a rotational-flow analogue of the Falkner-Skan boundary-layer flows,
describing a self-similar axisymmetric vortex embedded in an external stream
whose axial velocity varies as a power law in the axial (z) coordinate, with
phi=r/z^n being the radial similarity coordinate and n the core growth rate
parameter. We show that, when certain ostensible differences in the
formulations and radial scalings are properly accounted for, the Long and
Mayer-Powell flows in fact satisfy the same system of coupled ordinary
differential equations, subject to different kinds of outer-boundary
conditions, and with Long's equations a special case corresponding to conical
vortex core growth, n=1 with outer axial velocity field decelerating in a 1/z
fashion, which implies a severe adverse pressure gradient. For pressure
gradients this adverse Mayer and Powell were unable to find any
leading-edge-type vortex flow solutions which satisfy a basic physicality
criterion based on monotonicity of the total-pressure profile of the flow, and
it is shown that Long's solutions also violate this criterion, in an extreme
fashion. Despite their apparent nonphysicality, the fact that Long's solutions
fit into a more general similarity framework means that nonconical analogues of
these flows should exist. The far-field asymptotics of these generalized
solutions are derived and used as the basis for a hybrid spectral-numerical
solution of the generalized similarity equations, which reveal the existence of
solutions for more modestly adverse pressure gradients than those in Long's
case, and which do satisfy the above physicality criterion.Comment: 30 pages, including 16 figure
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The Measurement of the Thermal Properties and Absorptances of Powders Near their Melting Temperatures
A new technique, using a laser as the heating source, has been adopted to measure the heat
capacities, thermal diffusivities, thermal conductivities, and absorptances of powders (especially
polymer powders) near their melting temperatures. This makes use of an unsteady state process.
The data of the thermal conductivities obtained through this technique below 100°C are in concord
with the values obtained through the other techniques, which predicts well for the use of this
technique for still higher temperatures, up to the melting temperatures of the powders to be
investigated.Mechanical Engineerin
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Measurement of the Thermal Conductivity of Powders by Two Different Methods
The thermal diffusivities and thermal conductivities of powders, especially PMMA-coated
silicon carbide, at various temperatures, have been tested by two different dynamic methods, the
water-bath method and the laser-heated method. The thermal conductivity data found by these two
techniques are found to be consistent with each other.Mechanical Engineerin
Crack-like imperfections in a spherical shell
Mathematical model for stress analysis of cracks in spherical shell
Sudden bending of cracked laminates
A dynamic approximate laminated plate theory is developed with emphasis placed on obtaining effective solution for the crack configuration where the 1/square root of r stress singularity and the condition of plane strain are preserved. The radial distance r is measured from the crack edge. The results obtained show that the crack moment intensity tends to decrease as the crack length to laminate plate thickness is increased. Hence, a laminated plate has the desirable feature of stabilizing a through crack as it increases its length at constant load. Also, the level of the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers. The present theory, although approximate, is useful for analyzing laminate failure to crack propagation under dynamic load conditions
Slow and fast motion of cracks in inelastic solids. Part 1: Slow growth of cracks in a rate sensitive tresca solid. Part 2: Dynamic crack represented by the Dugdale model
An extension is proposed of the classical theory of fracture to viscoelastic and elastic-plastic materials in which the plasticity effects are confined to a narrow band encompassing the crack front. It is suggested that the Griffith-Irwin criterion of fracture, which requires that the energy release rate computed for a given boundary value problem equals the critical threshold, ought to be replaced by a differential equation governing the slow growth of a crack prior to the onset of rapid propagation. A new term which enters the equation of motion in the dissipative media is proportional to the energy lost within the end sections of the crack, and thus reflects the extent of inelastic behavior of a solid. A concept of apparent surface energy is introduced to account for the geometry dependent and the rate dependent phenomena which influence toughness of an inelastic solid. Three hypotheses regarding the condition for fracture in the subcritical range of load are compared. These are: (1) constant fracture energy (Cherepanov), (2) constant opening displacement at instability (Morozov) and (3) final stretch criterion (Wnuk)
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