An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

Rhodathiaboranes with `anomalous' electron counts: synthesis, structure and reactivity

Analysis of the structures of 8,8-(PPh₃)₂-8,7-nido-RhSB₉H₁₀ and 9,9-(PPh₃)₂-9,7,8-nido-RhC₂B₈H₁₁ by RMS misfit calculations has confirmed that these rhodaheteroboranes possess nido 11-vertex cluster geometries in apparent contravention of Wade's rules. However, examination of the molecular structures of both species shows that the {RhP₂} planes are inclined by ca. 66° with respect to the metal-bonded SB₃ or CB₃ faces, and that two weak ortho-CHRh agostic interactions occupy the vacant co-ordination position thereby created. As a consequence of these agostic bonds the Rh atom, and hence the overall cluster, is provided with an additional electron pair, meaning that their nido structures are now fully consistent with Wade's rules. The chelated diphosphine compound 8,8-(dppe)-8,7-nido-RhSB₉H₁₀ is similar to the PPh₃ compound in showing the same agostic bonding. Attempts to prepare a bis-P(OMe)₃ analogue result in ligand scavenging and the formation of 8,8,8-{P(OMe)₃}₃-8,7-nido-RhSB₉H₁₀. Similarly, reaction between Cs[6-arachno-SB₉H₁₂] and RhCl(dmpe)CO does not result in CO loss but in formation of 8,8-(dmpe)-8-(CO)-8,7-nido-RhSB₉H₁₀, shown to exist as a mixture of two of three possible rotamers. Deprotonation of 8,8-(PPh₃)₂-8,7-nido-RhSB₉H₁₀ and 8,8-(dppe)-8,7-nido-RhSB₉H₁₀ with MeLi yields the anions [1,1-(PPh₃)₂-1,2-closo-RhSB₉H₉]⁻ and [1,1-dppe-1,2-closo-RhSB₉H₉]⁻, respectively, with octadecahedral cage structures. It is argued that anion formation causes the agostic bonding to be `switched-off' and results in the cluster adopting the closo architecture predicted by Wade's rules. This structural change is fully reversible on reprotonation, and if reprotonation of [1,1-(dppe)-1,2-closo-RhSB₉H₉]⁻ is carried out in MeCN, the product 8,8-(dppe)-8-(MeCN)-8,7-nido-RhSB₉H₁₀ forms. Interestingly, 8,8-(dppe)-8-(MeCN)-8,7-nido-RhSB₉H₁₀ reconverts to 8,8-(dppe)-8,7-nido-RhSB₉H₁₀ on standing in CDCl₃, suggesting that the agostic bonding is sufficiently strong to displace co-ordinated MeCN. All new compounds are fully characterised by multinuclear NMR spectroscopy and, in many cases, by single crystal X-ray diffraction.     

Evaluation of the accuracy of the determination of lead isotope ratios in wine by ICP MS using quadrupole, multicollector magnetic sector and time-of-flight analyzers

Different mass analysers [(quadrupole (Q), time-of-flight (TOF) and multicollector (MC) sector-field (SF)] of ions produced in an inductively coupled plasma were evaluated for the determination of lead isotope ratios in wine samples. A population of 20 wines of different origin including two reference wines from the EC Standards, Measurement and Testing Programme with concentrations varying between 7-140 mug Pb l(-1) was investigated. Wines were analyzed directly by Q ICP MS and MC ICP MS. The poor sensitivity of the TOF instrument, further aggravated by matrix signal suppression, did not allow the acquisition of data for wine samples that contained less than 50 mug l(-1) in the direct sample introduction mode. The separation and preconcentration of lead were therefore required. The precision obtained for the (206)Pb/(207)Pb and (208)Pb/(206)Pb were similar and equal to 0.14-2.7% for Q ICP MS, 0.04-0.17% for TOF ICP MS and 0.01-0.12% for MC ICP MS. The precision for (206)Pb/(204)Pb was 0.44-5.29, 0.15-1.7, 0.08-1.6%, respectively. On the level of accuracy, the data from TOF ICP MS and MC ICP MS were in good agreement. The accuracy of Q ICP MS data was judged satisfactory in comparison with the other techniques but their poor precision was a significant obstacle on the way of using these data for the determination of the geographic origin of wine.     

Speciation of organotin in environmental sediment samples

An optimized sample preparation procedure for organotin speciation in sediment samples has been applied to the analysis of sediments collected in the environment. The method is based on tropolone complexation of the ionic organotins, followed by extraction into a hexane-ethylacetate mixture and derivatization by NaBEt(4). The method was applied to the determination of organotin in various harbour, shipyard and dry-dock sediments in Belgium. Butyltin compounds were detected in all samples analyzed, often at high mg kg(-1) levels. A limited number of samples showed the presence of phenyltin compounds. Further, the method was adapted to the analysis of river sediments sampled from the vicinity of shipyards. Butyltin concentrations were detected at the microg kg(-1) level in the majority of samples.     

Evaluation of a purge-and-trap injection system for capillary gas chromatography-microwave induced plasma-atomic emission spectrometry for the determination of volatile selenium compounds in water

A method is presented for the selective determination of the volatile selenium species dimethylselenide and dimethyldiselenide, using a commercially available purge-and-trap injection system coupled to capillary gas chromatography-microwave induced plasma-atomic emission spectrometry. The efficiency of the purging step was evaluated and the parameters affecting the purge and trap processes were optimized. The method was applied to the determination of volatile selenium compounds in lake water. Relative detection limits of 2ng/l for dimethylselenide and dimethyldiselenide, corresponding to an absolute detection limit of 10 pg, were achieved.     

Tube-excited energy-dispersive X-ray fluorescence analysis. II. Energy-dispersive X-ray fluorescence analysis of air particulate material.

The use of monoenergetic exciting radiation of molybdenum obtained with a secondary target set-up, a conventional water-cooled tungsten anode x-ray tube and a Si(Li) semiconductor detector permits many trace and minor constituents from chlorine to strontium to be determined in particulate material collected on cellulose filters. The method is rapid and economical compared to other multielement techniques. The use of one or more single-element thin-film standards to calibrate for the analysis of many elements appears to be possible, but some systematic errors must be prevented. Absorption of the fluorescent radiation is remedied by a simple correction method. The precision and the accuracy of the method were critically examined by independent analysis of a number of samples with instrumental neutron activation analysis and by interlaboratory comparisons on the same samples.     

Preparation of polysiloxane stationary phases for capillary column chromatography: A New methoxyphenyl phase

Contemporary methods for the synthesis of alkyl- and arylsubstituted polysiloxane stationary phases are reviewed. A new, moderately polar phase containing the 3-(4-methoxyphenyl)-propyl group is reported.