Tikhonov regularization with Incremental Hole-Drilling and the Integral Method in Cross-Ply Composite Laminates

Background: Incremental hole-drilling with the integral method has been extensively used in composite laminates but is sensitive to small measurement errors. Error sensitivity can be reduced by limiting the number of depth increments used in the calculation procedure. This approach is limited if a rapidly varying residual stress distribution exists since the calculated stress in each incremental depth is considered constant. Distortion of stress results can consequently occur due to averaging effects if the depth increments become too large. Tikhonov regularization is usually applied in isotropic materials to smooth the resulting residual stress distribution and reduce stress uncertainties, but has only been applied to composite laminates using the slitting technique. Objective: The intention of this work is to extend the use of Tikhonov regularization to incremental hole-drilling of composite laminates using the integral method. Methods: Finite element modelling is used to calculate the necessary calibration coefficients for unit pulses of uniform stress. Monte Carlo simulation is used to the determine uncertainties in the calculated residual stress distributions. Tikhonov regularization is optimised to reduce the stress uncertainty, while ensuring that the stress solution is not distorted. Results: The method is demonstrated on a GFRP (Glass fibre reinforced plastic) laminate of [0₂/90₂]_s construction and the calculated residual stress field is compared with those obtained by the standard integral method and series expansion. Conclusions: It is found that Tikhonov regularization significantly improves the accuracy of the standard integral method in composite laminates and shows good agreement with the series expansion method.

     

Molecular simulation of loading dependent slow diffusion in confined systems

An extension to transition state theory is presented that is capable of computing quantitatively the diffusivity of adsorbed molecules in confined systems at nonzero loading. This extension to traditional transition state theory yields a diffusivity in excellent agreement with that obtained by conventional molecular dynamics simulations. While molecular dynamics calculations are limited to relatively fast diffusing molecules or small rigid molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. It is applicable in any system containing free energy barriers and for any type of guest molecule.     

Isotope ratio monitoring gas chromatography/Mass spectrometry of D/H by high temperature conversion isotope ratio mass spectrometry

Of all the elements, hydrogen has the largest naturally occurring variations in the ratio of its stable isotopes (D/H). It is for this reason that there has been a strong desire to add hydrogen to the list of elements amenable to isotope ratio monitoring gas chromatography/mass spectrometry (irm-GC/MS). In irm-GC/MS the sample is entrained in helium as the carrier gas, which is also ionized and separated in the isotope ratio mass spectrometer (IRMS). Because of the low abundance of deuterium in nature, precise and accurate on-line monitoring of D/H ratios with an IRMS requires that low energy helium ions be kept out of the m/z 3 collector, which requires the use of an energy filter. A clean mass 3 (HD(+.)) signal which is independent of a large helium load in the electron impact ion source is essential in order to reach the sensitivity required for D/H analysis of capillary GC peaks. A new IRMS system, the DELTA(plus)XL(trade mark), has been designed for high precision, high accuracy measurements of transient signals of hydrogen gas. It incorporates a retardation lens integrated into the m/z 3 Faraday cup collector. Following GC separation, the hydrogen bound in organic compounds must be quantitatively converted into H(2) gas prior to analysis in the IRMS. Quantitative conversion is achieved by high temperature conversion (TC) at temperatures >1400 degrees C. Measurements of D/H ratios of individual organic compounds in complicated natural mixtures can now be made to a precision of 2 per thousand (delta notation) or, better, with typical sample amounts of approximately 200 ng per compound. Initial applications have focused on compounds of interest to petroleum research (biomarkers and natural gas components), food and flavor control (vanillin and ethanol), and metabolic studies (fatty acids and steroids). Copyright 1999 John Wiley & Sons, Ltd.     

Mass spectral characterization of 3,4,6-tri-O-benzyl-β-C-glucopyranosides containing XC6H4S substituents of C(2)

Electron impact mass spectra (70 eV) were generated for tri-O-benzyl-D -glucal and six XC₆H₅S substituted 3,4,6-tri-O-benzyl-β-C-glucosides which had been modified at C(2) by the introduction of an XC₆H₄S fragment (where X = CH₃ or CI) in an effort to understand better fragmentation processes for the structural characterization of this important class of compounds. The model compounds which were synthesized were glucoside derivatives of CH₂CHO, C(CH₃)₂CHO, , C₆H₅ and CN. For all O-benzylated compounds, the benzyl moiety was the base ion; however, the molecule ion of each modified glucoside was significantly abundant. A characteristic feature of S-containing C-glucosides was an abundant CH₃C₆H₅S?CHCH?CH₂ ion at m/z 163. Fragmentation of these C-glucosides was interpreted in terms of positive charge localization on the molecule ion according to rules for normal carbohydrates. Knowledge of the fragmentation on the S-containing C-glucosides should be useful for the characterization of additional new analogues.     

Simultaneous correlation chromatography,a new technique applied to calibration in high-performance liquid chromatography

Simultaneous correlation chromatography (SCC) is introduced as a technique capable of analyzing several different samples simultaneously on the same chromatographic column. The theoretical basis of the technique is outlined and a computer simulation demonstrates the feasibility of the method. The advantages and potential of the technique are discussed. The technique is applied experimentally in a calibration procedure for high-performance liquid chromatography. During the calibration, unknown sample and calibration standards are processed under the same conditions, resulting in very accurate calibration. Other applications are outlined.     

Correlation chromatography

In correlation chromatography the usual chromatographic procedure is modified, utilizing the capabilities of microcomputers. The most striking property is the semicontinuous character of the method, leading to a very efficient use of the column and a rapid decrease in the detection limit in a relatively short time.     

Molecular simulations of surface forces and film rupture in oil/water/surfactant systems

We use dissipative particle dynamics (DPD) and molecular models to simulate interacting oil/water/surfactant interfaces. The system comprises sections of two emulsion droplets separated by a film. The film is in equilibrium with a continuous phase, in analogy with the surface force apparatus. This is achieved by combining DPD with a Monte Carlo scheme to simulate a muVT ensemble. The setup enables the computation of surface forces as a function of the distance between the two interfaces, as well as the detection of film rupture. We studied monolayers of nonionic model surfactants at different densities and compared oil-water-oil and water-oil-water emulsion films. Between surfactant monolayers facing each other tails-on (water-oil-water films), we observed repulsive forces due to the steric interaction between overlapping hydrophobic tails. The repulsion increases with surfactant density. Conversely, no such repulsion is observed between surfactant monolayers facing each other heads-on. Instead, the film ruptures, the monolayers merge, and a channel forms between the two droplet phases. Film rupture can also be induced in the water-oil-water films by forcing the interfaces together. The separation at rupture increases for oil-water-oil films and decreases for water-oil-water films when the surfactant density increases. The results are in qualitative agreement with existing theories of emulsion stability in creams, in particular with the channel nucleation theory based on the natural curvature of surfactants.     

The effects of errors in measuring the independent variable in least-squares regression analysis

It is well known that linear regression analysis gives unbiased estimates of the slope and intercept of a straight line if the dependent variable y is subject to random errors of measurement while the independent variable x is not. It is much less well known that, if x is also subject to random errors of measurement, linear regression analysis yields an underestimate of the slope and a correspondingly biased estimate of the intercept. These errors cannot be removed by weighted regression. Similar errors arise in non-linear regression when the independent variable is afflicted by random errors of measurement.