A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented

Buckling and Postbuckling Structures: Experimental, Analytical and Numerical Studies

This book provides an in-depth treatment of the study of the stability of engineering structures. Contributions from internationally recognized leaders in the field ensure a wide coverage of engineering disciplines in which structural stability is of importance, in particular the analytical and numerical modelling of structural stability applied to aeronautical, civil, marine and offshore structures. The results from a number of comprehensive experimental test programs are also presented, thus enhancing our understanding of stability phenomena as well as validating the analytical and computational solution schemes presented. A variety of structural materials are investigated with special emphasis on carbon-fibre composites, which are being increasingly utilized in weight-critical structures. Instabilities at the meso- and micro-scales are also discussed. This book will be particularly relevant to professional engineers, graduate students and researchers interested in structural stability.

Analytical approximations to numerical solutions of theoretical emission measure distributions

Emission line fluxes from cool stars are widely used to establish an apparent emission measure distribution, EmdApp(Te), between temperatures characteristic of the low transition region and the low corona. The true emission measure distribution, EmdTrue(Te), is determined by the energy balance and geometry adopted and, with a numerical model, can be used to predict EmdApp(Te), to guide further modelling. The scaling laws that exist between coronal parameters arise from the dimensions of the terms in the energy balance equation. Here, analytical approximations to numerical solutions for EmdTrue(Te) are presented, which show how the constants in the coronal scaling laws are determined. The apparent emission measure distributions show a minimum value at some T0 and a maximum at the mean coronal temperature Tc (although in some stars, emission from active regions can contribute). It is shown that, for the energy balance and geometry adopted, the analytical values of the emission measure and electron pressure at T0 and Tc depend on only three parameters: the stellar surface gravity and the values of T0 and Tc. The results are tested against full numerical solutions for e Eri (K2 V) and are applied to Procyon (a CMi, F5 IV/V). The analytical approximations can be used to restrict the required range of full numerical solutions, to check the assumed geometry and to show where the adopted energy balance may not be appropriate. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

An in situ spatially resolved analytical technique to simultaneously probe gas phase reactions and temperature within the packed bed of a plug flow reactor

This paper reports the detailed description and validation of a fully automated, computer controlled analytical method to spatially probe the gas composition and thermal characteristics in packed bed systems. As an exemplar, we have examined a heterogeneously catalysed gas phase reaction within the bed of a powdered oxide supported metal catalyst. The design of the gas sampling and the temperature recording systems are disclosed. A stationary capillary with holes drilled in its wall and a moveable reactor coupled with a mass spectrometer are used to enable sampling and analysis. This method has been designed to limit the invasiveness of the probe on the reactor by using the smallest combination of thermocouple and capillary which can be employed practically. An 80 mu m (O.D.) thermocouple has been inserted in a 250 mu m (O.D.) capillary. The thermocouple is aligned with the sampling holes to enable both the gas composition and temperature profiles to be simultaneously measured at equivalent spatially resolved positions. This analysis technique has been validated by studying CO oxidation over a 1% Pt/Al2O3 catalyst and the spatial resolution profiles of chemical species concentrations and temperature as a function of the axial position within the catalyst bed are reported.

Understanding how HR systems work: the role of HR philosophy and HR processes

Despite the proliferation of studies of HR systems, there are still substantial gaps in our understanding
of how such systems actually work. This article, by focusing on the neglected areas of HR philosophy
and HR processes in the composition of HR systems, and by using a qualitative, employee-centred
approach in the collection and analysis of data, provides new insights into the working of HR systems.
Using data from interviews with 56 knowledge workers employed in the information and
communications technology sector in Ireland and the UK, we explore employee-level reactions to two
different types of HR systems. We highlight the various ways in which HR processes interact with HR
practices and the different outcomes that may result, and we identify the key role of HR philosophy in
HR system operation.