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

Crucial cross-talk of interleukin-1β and progesterone in human choriocarcinoma

Copyright @ 2012 Spandidos Publications Ltd. This article can be accessed from the links below.This article has been made available through the Brunel Open Access Publishing Fund.Choriocarcinoma is a highly malignant epithelial tumour that is most often associated with hydatidiform mole and presents the most common emergency medical problem in the management of trophoblast disease. We hypothesise that the hormones/cytokines present within the tumour microenvironment play key roles in the development of choriocarcinoma. In this study we assessed the effects of interleukin-1β (IL-1β) on cell death in the presence or absence of the sex hormone progesterone using two choriocarcinoma cell lines (BeWo and JEG-3) as in vitro experimental models. Although IL-1β induced cell death in both cell lines, the effect was more pronounced in JEG-3 cells, where cell death reached 40% compared to 15% in BeWo cells. Cell death of JEG-3 cells in response to IL-1β was significantly decreased by co-treatment with 100 nM and 1000 nM progesterone and completely abolished at a progesterone concentration of 1000 nM. Progesterone was also able to induce phosphorylation of ERK1/2 in these cells. Pretreatment of JEG-3 cells with a specific MAPK inhibitor (UO126) inhibited progesterone's inhibitory effect on cell death. Collectively, these data provide evidence of cross-talk between progesterone and IL-1β in this aggressive and poorly understood tumour that involves activation of a MAPK pathway and involvement of numerous progesterone receptors.This research was funded by a National Institutes of Health Grant ESO12961. This article is made available through the Brunel Open Access Publishing Fund

Water production models for Comet Bradfield (1979 l)

The IUE observations of Comet Bradfield (1979 l) made 10 January 1980 to 3 March 1980 permit a detailed study of water production for this comet. Brightness measurements are presented for all three water dissociation products, H, O, and OH, and comparisons are made with model predictions. The heliocentric variation of the water production rate was derived

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

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

Sensitivity of cross-sectional compliance to manufacturing tolerances for wind turbine blades

Wind-turbine blades are complex structures and, despite advancements in analysis techniques, differences persist between predictions of their elastic response and experimental results. This undermines confidence in the ability to reliably design and certify novel blade designs that include self-regulating features like bend-twist coupling To address these discrepancies, this study investigates the influence of manufacturing tolerances on the compliance properties of blade cross-sections, focusing specifically on a previously disregarded feature: the trailing edge bond-line. To conduct this investigation, the validated cross-sectional modelling tools BECAS and VABS are used to demonstrate that even small geometric variations can have significant influence on cross-sectional stiffness properties. The results are further examined and substantiated through the utilisation of 3D finite element models, adopting both shell and solid elements. We conclude that an accurate geometric representation of the cross-section is necessary to adequately capture the shear flow within it and assure accurate predictions on cross-sectional stiffness properties.</p

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

This paper treats the global existence question for a collection of general relativistic collisionless particles, all having the same mass. The spacetimes considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore, the spacetimes considered are isometrically invariant under a two-dimensional group action, the orbits of which are spacelike 2-tori. It is known from previous work that the area of the group orbits serves as a global time coordinate. In the present work it is shown that the area takes on all positive values in the maximal Cauchy development.Comment: 27 pages, version 2 minor changes and correction

Expression of membrane and nuclear progesterone receptors in two human placental choriocarcinoma cell lines (JEG-3 and BeWo): Effects of syncytialization

This article has been made available through the Brunel Open Access Publishing Fund and is available from the specified link - Copyright @ 2011 Spandidos Publications Ltd.A vital function of the human placenta is to produce steroid hormones such as progesterone, which are essential for the maintenance of pregnancy and the onset of parturition. Although choriocarcinoma cell lines are valuable placental models for investigations of steroid hormone actions, little is known about the expression of progesterone receptors (PRs) in these cell lines. Therefore, in this study, the expression of membrane and nuclear PRs was investigated in cultures of fusigenic (BeWo) and non-fusigenic (JEG-3) human choriocarcinoma cell lines. In addition, the effects of an inducer of syncytialization (forskolin) on the PR expression in BeWo cells were assessed. Quantitative RT-PCR revealed that in fully syncytialized BeWo cells (treated with 50 mu M forskolin for 72 h) there was a significant down-regulation of mPR alpha and up-regulation of mPR beta and of the progesterone membrane component-1 (PGRMC1) when compared with non-syncytialized BeWo cells. Expression of all the mPR and PGRMC1 mRNAs was significantly lower in JEG-3 cells compared to non-syncytialized BeWo cells. Interestingly, expression of PR-B was unaltered between the two BeWo states but was significantly higher in JEG-3 cells. Immunofluorescence analysis revealed that mPR proteins are differentially expressed in these choriocarcinoma cell lines as well as in the human placenta. The data demonstrate that human choriocarcinoma cell lines have a complex system of progesterone signalling involving multiple classes of PRs. The finding that syncytialization is accompanied by changes in the expression of these receptors may suggest that this process influences progesterone signalling