Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Mathematical modeling of crystallization analysis fractionation (Crystaf) of polyethylene

Four polyethylene samples (PE) with different molecular weight distributions (MWD) were analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects, which are ignored in all previous Crystaf models. The Crystaf model we proposed can fit the experimental Crystaf profiles of the 4 polyethylene resins very well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2749–2759, 2006     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Untersuchung der thermischen Eigenschaften von Alkalibenzolsulfonaten

Zusammenfassung Der Einfluß von Atmosphäre, Aufheizungsgeschwindigkeit und Spülgasgeschwindigkeit auf die thermische Zersetzung von Alkalibenzolsulfonaten wurde untersucht. Kristallwassergehalt, Dehydratations-temperatur und -wärme, gegebenenfalls die Zusammensetzung, Art, Temperatur und Wärme der Modifikationsänderungen, Schmelzpunkte und Schmelzwärmen der Verbindungen wurden bestimmt. Die Zersetzung verläuft in zwei Abschnitten. In dem ersten Hauptteil entstehen in Inertgasatmosphäre Diphenyloxid, Diphenyl, Diphenylsulfon, Benzol, Phenol, Thiophenol, Diphenylsulfid, Thiantren, Diphenylenoxid und wahrscheinlich Diphenylensulfid, weiterhin Koks, Schwefeldioxid, Natriumsulfit und wenig Natriumsulfat, Natriumsulfid, Acetylen und Wasser. Im zweiten Hauptzersetzungsvorgang entstehen Natriumsulfid und Kohlenoxid. Die Produkte wurden isoliert und analysiert. Dazu wurden Derivatographie, Differentialthermoanalyse, Gaschromatographie, Infrarotspektroskopie, kontinuierliche thermische Titration und chemische Methoden gemeinsam angewandt.

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Summary An investigation was made of the influence of the atmosphere, rate of temperature rise, and velocity of the purging gas on the thermal decomposition of alkali benzene sulfonates. The crystal water content, the dehydration temperature and heat, and if need be the composition, the kind, temperature, and heat of the modification changes, melting points and heats of fusion of the compounds, were determined. The decomposition proceeds in two stages. In the first main stage (in an inert atmosphere) the resulting compounds include diphenyl oxide, diphenyl, diphenylsulfone, benzene, phenol, thiophenol, diphenyl sulfide, thianthrene, diphenylene oxide and probably diphenylene sulfide; also coke, sulfur dioxide, sodium sulfite and a little sodium sulfate, sodium sulfide, acetylene, water. Sodium sulfide and carbon monoxide are formed in the second main decomposition. The products were isolated and analyzed. Furthermore, use was made of derivatography, differential thermal analysis, gas chromatography, infra red spectroscopy, continuous thermal titration, and chemical methods.

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Résumé On a étudié l'influence de l'atmosphère, de la vitesse d'échauffement et de balayage du gaz, sur la décomposition thermique des benzène-sulfonates alcalins. On a déterminé la teneur en eau de cristallisation, la température et la chaleur de déshydratation, éventuellement la composition, la nature, la température et la chaleur des changements d'état, les points de fusion et les chaleurs de fusion des composés. La décomposition s'effectue en deux temps. Tout d'abord, en atmosphère inerte, il se forme de l'oxyde de diphényle, du diphényle, de la diphénylsulfone, du benzène, du phénol, du thiophénol, du sulfure de diphényle, du thianthrène, de l'oxyde de diphénylène et probablement du sulfure de diphénylène, et aussi du coke, de l'anhydride sulfureux, du sulfite de sodium et, en moins grande quantité, du sulfate de sodium, du sulfure de sodium, de l'acétylène et de l'eau. Dans une deuxième étape de la décomposition principale, du sulfure de sodium et de l'oxyde de carbone prennent naissance. On a isolé et analysé ces produits. Pour cela, on a utilisé simultanément la dérivatographie, l'analyse thermique différentielle, la chromatographie en phase gazeuse, la spectroscopie infrarouge, le titrage thermique en continu et les méthodes chimiques.

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Vorgetragen beim Symposium für analytische Chemie in Graz, 29. September bis 1. Oktober 1965.     

Zur Kenntnis von Natrium-hexafluoromanganat(III)

Sodium hexafluoromanganate(III) has been synthesized by heating equimolecular quantities of Na₂MnF₅ and NaF in argon atmosphere. The compound is monoclinic witha=5.56 (1) Å,b=5.84 (1) Å,c=8.10 (2) Å, =90.7 (2) andZ=2. It is a high spin complex with _eff and the deformation of the octahedra is evident from its IR-spectra. Two enantiotropic transitions (at 562 and 653°C) and the melting point at 800°C have been observed.

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8. Mitt.: Mh. Chem.106, 483 (1975).