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

Space shuttle: Supersonic aerodynamic characteristics of the MSC 040A orbiter (M equals 2.0 to 4.0)

A wind tunnel test of the space shuttle orbiter configuration 040A was run in a 20 in. supersonic wind tunnel. Basic aerodynamic data for this vehicle were determined at Mach 2.0, 2.4, 3.0 and 4.0

The minimum free-stream wind speed for initiating motion of surface material on Mars

Estimates of the minimum free-stream wind speed that is required for initiating the motion of surficial material on Mars have ranged from 30 to about 200 meters per second. Thus the best value for this quantity is not well established. Graphical comparison of much of the pertinent data taken in the laboratory and in the field on Earth provides a minimum value for the Bagnold coefficient of 0.08 and this in turn provides a minimum value for the threshold friction velocity of 1.3 meters per second for initiating motion of particulate matter on Mars at low elevations where the pressure is 7 millibars. The most appropriate value of the ratio of friction velocity to free-stream velocity for putative unstable condition appears to be 0.026. Thus the minimum free-stream wind speed for initiating motion is obtained as 50 meters per second. If the surface material on Mars, however, is less cohesive than that on earth, the minimum value may be smaller

Energy Spectrum Evolution of a Diffuse Field in Elastic Body Caused by Weak Nonlinearity

We study the evolution of diffuse elastodynamic spectral energy density under the influence of weak nonlinearity. It is shown that the rate of change of this quantity is given by a convolution of the linear energy at two frequencies. Quantitative estimates are given for sample aluminum and fused silica blocks of experimental interest.Comment: 9 pages, 3 figures; revised for better presentatio

On the area of the symmetry orbits in T2T^2 symmetric spacetimes

We obtain a global existence result for the Einstein equations. We show that in the maximal Cauchy development of vacuum $T^2$ symmetric initial data with nonvanishing twist constant, except for the special case of flat Kasner initial data, the area of the $T^2$ group orbits takes on all positive values. This result shows that the areal time coordinate $R$ which covers these spacetimes runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the inequality appearing as the first stage of (52) is not necessarily true), and since the appendix is unnecessary for the proof of our results, we leave it out. version 2 -- clarifications added, version 3 -- reference correcte

Pilot study and evaluation of a SMMR-derived sea ice data base

Data derived from the Nimbus 7 scanning multichannel microwave radiometer (SMMR) are discussed and the types of problems users have with satellite data are documented. The development of software for assessing the SMMR data is mentioned. Two case studies were conducted to verify the SMMR-derived sea ice concentrations and multi-year ice fractions. The results of a survey of potential users of SMMR data are presented, along with SMMR-derived sea ice concentration and multiyear ice fraction maps. The interaction of the Arctic atmosphere with the ice was studied using the Nimbus 7 SMMR. In addition, the characteristics of ice in the Arctic ocean were determined from SMMR data

Scattering fidelity in elastodynamics

The recent introduction of the concept of scattering fidelity, causes us to revisit the experiment by Lobkis and Weaver [Phys. Rev. Lett. 90, 254302 (2003)]. There, the ``distortion'' of the coda of an acoustic signal is measured under temperature changes. This quantity is in fact the negative logarithm of scattering fidelity. We re-analyse their experimental data for two samples, and we find good agreement with random matrix predictions for the standard fidelity. Usually, one may expect such an agreement for chaotic systems only. While the first sample, may indeed be assumed chaotic, for the second sample, a perfect cuboid, such an agreement is more surprising. For the first sample, the random matrix analysis yields a perturbation strength compatible with semiclassical predictions. For the cuboid the measured perturbation strength is much larger than expected, but with the fitted values for this strength, the experimental data are well reproduced.Comment: 4 page

Effect of time of thinning on berry size of girdled, gibberellin-treated 'Thompson Seedless' grapes

Gibberellin-treated 'Thompson Seedless' grapes were thinned at initiation of berry shatter following bloom or at 1 to 6 weeks thereafter. The results indicate that for maximum increase in berry size, thinning should be done during fruit-set or as soon after as possible.Der Einfluß des Ausdünnungstermins auf die Beerengröße von geringelten, gibberellinbehandelten „Thompson Seedless"-TraubenGibberellin-behandelte „Thompson-Seedless"-Trauben wurden bei Beginn des Durchrieselns oder 1-6 Wo chen danach ausgedünnt. Die Ergebnisse zeigen, daß für einen maximalen Zuwachs der Beerengröße das Ausdünnen während des Fruchtansatzes oder sobald wie möglich danach erfolgen sollte

Chemical thinning of grape clusters (Vitis vinifera L.)

Twelve thinning compounds were tested at 0.1 to 4,000 ppm on 'Carignane' and 'Thompson Seedless' clusters at 4 developmental stages (prebloom, bloom, fruit-set, and 2 weeks after fruit-set). Clusters were usually least sensitive to the compounds ut post fruit-set and, in general, 'Thompson Seedless' was more sensitive than 'Carignane'. On 'Thompson Seedless' the morphactin IT 5733 had a wider activity range than IT 5732 or IT 4433. Potassium iodide reduced set when applied at prebloom or bloom. Ethephon was usually effective at some concentration at all growth stages. Ascorbic acid, iso-ascorbic acid, and Pennthin usually were not significantly effective in thinning either cultivar.The 3-CPA had a wide range of activity on both cultivars at most stages of growth, and this compound at 10 ppm reduced number of berries at bloom and fruit set for 'Carignane' and 'Thompson Seedless', respectively. Iodoacetic acid at 1,000 ppm was effective in reducing number of berries in both cultivars at all growth stages. The 4-CPA at 100 ppm was effective at prebloom stage en 'Carignane', and .'.lt bloom on 'Thompson Seedless'. Salicylic acid at 1,000 ppm effectively reduced number of berries of each cultivar when applied at fruit-set stage