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  • Polymer and Materials Science  (3,144)
  • Biochemistry and Biotechnology  (524)
  • Engineering  (448)
  • 1985-1989  (4,116)
  • 1965-1969
  • 1950-1954
  • 1987  (4,116)
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  • 1985-1989  (4,116)
  • 1965-1969
  • 1950-1954
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  • 201
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 188 (1987), S. 2857-2863 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: During the reaction of 1-phenoxy-2,3-epoxypropane (1) with catalytic amounts of Mg(ClO4)2 a variety of reaction products are formed which do not correpond to a normally distributed oligomer range. Essentially, three reaction paths can be distinguished which lead to oligo-(hydroxyether)s of similar structure (6 and 8) and to cyclic, isomeric dimers (9 and 10) of very low reactivity. During the reaction of bifunctional 2,3-epoxypropyl ethers, cyclic products act as nonreactive diluents decreasing the network density of the final crosslinked product.
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  • 202
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Quaternization reactions of poly(2-dimethylaminoethyl methacrylate) using methyl iodide were carried out up to 50% conversion in 18 chemically different solvents. Copolymers which contain moderate hydrophilic 2-dimethylaminoethoxycarbonyl groups and strongly hydrophilic 2-trimethylammoniumethoxycarbonyl iodide groups were obtained. Potentiometric titration showed that in some solvents the reaction proceeds by the zip mechanism, i.e. copolymers with a predominantly block structure are formed, while in other solvents the reaction proceeds along the macromolecular chain randomly, that is, giving rise to statistical copolymers.
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  • 203
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    Die Makromolekulare Chemie 188 (1987), S. 135-148 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Detailed 13C NMR chemical shift rules are devised for ethylene and propylene polymers and for low-molecular-weight analogs. The rules are additive and account for substituent effects as well as for configurational sequences. The agreement between the observed and the predicted shifts is excellent. A computer program has been written to obtain the predicted shifts quickly and with minimum effort.
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  • 204
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Debromination side-reactions which occur during the synthesis of poly(arylene sulfide)s from copper(I) 4-bromothiophenoxidesSystematic name: Copper(I) 4-bromobenzenethiolates. were investigated using bromobenzene as a model for the end unit in a poly(1,4-phenylene sulfide) chain. Model reactions were conducted in quinoline, pyridine, and 10:1 (v/v) quinoline/pyridine solution in the presence and absence of copper(I) bromide, the condensation product of polymerisation. Reaction liquors were subjected to GLC and MS analysis and evidence is presented which indicates that a copper(I) initiated debromination reaction occurs yielding monophenylquinolines. A mechanism is proposed for the reaction and critically discussed. The consequences of the reaction at the macromolecular level are also described.
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  • 205
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Hydroxytelechelic polybutadiene (HTPB) Arco-R45M® obtained by free-radical-initiated polymerization of butadiene was fractionated by preparative gel permeation chromatography (GPC) using styragel and silicagel as column material. The fractions separated were extensively studied by vapour pressure osmometry (VPO), GPC, and 1H NMR. Commercially available non-hydroxylated polystyrene and polybutadiene standards cannot be utilized for the proper direct determination of the molecular weight of HTPB by means of GPC. Both high and low hydroxyl functionalities were found for high- and low-molecular-weight HTPB. The analytical results are discussed in terms of the polymerization mechanism.
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  • 206
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    Die Makromolekulare Chemie 188 (1987), S. 619-627 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The method for the evaluation of spherulite growth after completed crystallization is further refined by comparison of the predicted and real shapes of the more slowly growing spherulite encompassed by the faster-growing one. The shielding effect (the effect of distorted growth of the faster-growing spherulite behind the more slowly-growing one) is theoretically described, compared with the observation, and used for the evaluation of the relative rate of spherulite growth. As an example, measurements are reported with samples of poly(vinylidene fluoride).
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  • 207
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The previously derived so called Bonart-Mulzer (BM)-equation which gives the interference effect of fully elongated A/B block copolymers depending on the length distributions of the A- and B-blocks, is specialized onto first-order Markoff chains as characterized by the transition probabilities pAA, pBB and pAB, pBA for homo- and cross-steps, respectively. The resulting interference function is illustrated by means of simple model calculations. The specilization is applicable to liquid-crystalline block copolymers in order to analyse the statistical chain character.
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  • 208
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 2-Mono- and 2,4,5-trisubstituted 1,3-dioxolan-2-ylium salts were reacted with dimethoxymethane representing the model of the polydioxolane chain. The products were identified and analysed by means of 1H NMR spectroscopy and gas chromatography. The reaction was found to proceed mainly via interchange of the C-2 carbon atom of the salt and the methylene group of dimethoxymethane yielding 1,3-dioxolane or 4,5-disubstituted dioxolane and the unstable dimethoxymethylium derivative, which decomposes into the respective methyl ester and methyl cation. The formation of some by-products follows the main reaction path. The amount and the kind of substituents as well as the configuration influence the reactivity of the salts in the processes investigated.
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  • 209
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    Die Makromolekulare Chemie 188 (1987), S. 693-702 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effect of 2,2′-azoisobutyronitrile (AIBN) on the kinetics and mechanism of emulsion polymerization of butyl methacrylate was studied in the presence of anionic emulsifier disodium dodecylphenoxybenzene disulfonate (Dowfax® 2A1) at 60°C. The ratio between the proportion of the polymerization in monomer droplets and that of the polymerization in the aqueous phase was determined for the overall initial rate of butyl methacrylate polymerization in the region of the increasing polymerization rate (interval I). Using the model of polymerization in discrete particles, the portion of the polymerization in monomer droplets with a diameter of 100 nm in the overall polymerization rate is 24,4%; the portion of the polymerization in the water phase is only 0,022% for a concentration of Dowfax® 2A1 of 5 · 10-2 mol · dm-3, and 60,4% and 0,054% for a Dowfax® 2A1 concentration of 1 · 10-2 mol · dm-3. The exponent of the emulsifier concentration in the equation for the polymerization rate is 0,56 for interval I and 0,36 for interval II; the exponent for the concentration of AIBN over the conversion range between 0 and 30% is 0,34. For the proposed reaction mechanism it is assumed that 2-cyanoisopropyl radicals, generated from AIBN in the water phase, are responsible for the initiation of polymerization in micelles swollen by monomer and in polymer/monomer particles. Polymer/monomer particles are formed also by co-precipitation of oligomer radicals, which in turn are formed by polymerization of monomer molecules present in the water phase. Polymerization within monomer droplets has no significant influence on the course of emulsion polymerization.
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  • 210
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effect of the nature of the crosslinking agents in template-imprinted polymers on the selectivity during racemic resolution was investigated. Ethylene dimethacrylate was found to be the best crosslinking agent. The highest selectivity was achieved with polymers which have been prepared with 70-95% crosslinking agent in the monomeric mixture. A new optically active crosslinking agent, 1,4;3,6-dianhydro-D-sorbitol 2,5-dimethacrylate, was synthesized and was used for the preparation of template-imprinted polymers. Interpenetrating networks consisting of two different crosslinking systems did not bring about any significant improvement in selectivity for racemic resolution. A strong temperature effect for racemic resolution was observed; an ethylene dimethacrylate-crosslinked, template-imprinted polymer showed an optimum selectivity at 75°C with a ratio of distribution coefficients of the D- and L-isomers of α = 4,56 for the separation of the racemate of the template.
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  • 211
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    Die Makromolekulare Chemie 188 (1987), S. 763-768 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A novel method was applied to improve the activity of enzymes immobilized in photocrosslinked poly(vinyl alcohol). Whereas the addition of glycerol to photosensitive poly(vinyl alcohol), bearing a styrylpyridinium group, diminishes the rate of photocrosslinking as well as the mechanical strength of the insolubilized gel, no considerable decrease in the rate of photoreaction was observed when poly(vinyl alcohol) was mixed with poly(ethylene glycol). This difference is based on the phase separation of the two water-soluble polymers, resulting in the formation of a porous structure of the photocrosslinked gel. Immobilization of invertase in the photocrosslinked gel in the presence of poly(ethylene glycol) changes the activity, because of the case of diffusion of the substrate into the porous matrix.
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  • 212
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    Die Makromolekulare Chemie 188 (1987), S. 791-797 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Star polymers with 2, 3 and 4 branches were synthesized in coupling reactions of poly(tetrahydrofuran) [poly(THF)] containing an azetidinium ring as single end group with di-, tri-, and tetrafunctional carboxylates, respectively. The coupling reaction proceeded by simple precipitation of the star polymer by addition of the polymer to an aqueous solution containing an excess of the corresponding sodium carboxylate. Model networks with 3 and 4 branches were produced by the same technique using poly(THF) with two azetidinium rings as end groups and tri- and tetrafunctional carboxylates, respectively.
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  • 213
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The syndiotactic Nα-protected poly(2-methylallyl L-histidinate) and the corresponding copolymers, poly[(2-methylallyl alcohol)-s-co-(2-methylallyl L-histidinate)], were complexed with different Cu(II) compounds and used as catalysts for the aerobic oxidation of hydroquinone to quinone. The apparent first order rate constants were one to two orders of magnitude larger for the Cu(II)-complexed homo- and copolymers than for the Cu(II) compounds or the polymers alone, or for the model compound in its complexed or uncomplexed state.
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  • 214
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    Die Makromolekulare Chemie 188 (1987), S. 855-860 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In aqueous KSCN solutions the salt is preferentially desorbed from the domain of gelatin molecules, similarly to synthetic polyelectrolytes. Light-scattering measurements in gelatin solutions in 0,5 M KSCN and in a single solvent (formamide) show that both solvents are suited for the molecular characterization of gelatin at room temperature. Neglecting the effect of selective sorption in salt solutions does not cause any considerable error in the molar mass determination of gelatin.
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  • 215
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    Die Makromolekulare Chemie 188 (1987), S. 887-898 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Derivatives of silicic acid of the type Si6O5R18 and Si8O7R18 (R = Cl, OCH3, and OC2H5) as well as bicyclic Si8O9(OC2H5)14 were isolated and characterized by 29Si NMR. The spin-lattice-relaxation and the nuclear Overhauser enhancement factor of the esters were determined between 273 and 343 K. The temperature dependency of the dipolar contribution to the longitudinal relaxation time gave an energy of activation for the segmental motion of the siloxane skeleton of about 10 kJ/mol which is independent of the kind of building unit.
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  • 216
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    Die Makromolekulare Chemie 188 (1987), S. 607-617 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A study of the rheological behaviour of poly(ethylene oxide)-poly(methyl methacrylate) and poly(ethylene oxide)-poly(vinyl acetate) compatible blends in the molten state is reported. Zero shear viscosity η0 and the activation energy for the viscous flow ΔE* were obtained as function of both composition and molar mass of the components. Positive and negative deviations from the additivity rule were observed both in the case of log η0 and ΔE*.
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  • 217
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    Die Makromolekulare Chemie 188 (1987), S. 665-674 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: X-ray measurements of stretched crosslinked liquid-crystalline side group polymers show that two types of orientation of the mesogenic groups relative to the polymer chains (parallel or perpendicular) are possible, depending on the structure of the polymer chain. For two liquid-crystalline polymethacrylates with long spacer groups (6 methylene units) the mesogenic groups orient preferably perpendicularly to the polymer chains (axis of strain). For three liquid-crystalline polyacrylates with long or short spacer groups (6 or 2 methylene units), the mesogenic groups orient preferably parallel to the polymer chains (axis of strain). The reason for this difference is not yet clear. These results are compared with earlier results of melt-drawn fibres of uncrosslinked polymers.
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  • 218
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Telomers were prepared from acrylic or methacrylic acid and CCl3Br, C12H25SH, C18H37SH or C8F17C2H4SH by initiation with 2,2'-azoisobutyronitrile. The transfer constant of CCl3Br and the thiols, which are about 0,03 and 0,5, respectively, were determined. These telomers were used as supports of photopolymerizable functions, which were introduced by grafting of 2,3-epoxypropyl methacrylate, catalysed with dodecyldimethylamine. The reactions were followed by 1H NMR, elemental analyses, tonometrie, and especially by GPC and titration of the acid functions. The grafting telomers, holding many acrylic functions which react upon UV and electron irradiation, give photoreticulated varnish coatings with very interesting properties.
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  • 219
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    Die Makromolekulare Chemie 188 (1987), S. 1075-1084 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Poly(butadiene-alt-propene) (1) was degraded by metathesis reaction using symmetric olefins (3-hexene and 4-octene) in chlorobenzene solution in the presence of WCl6/(CH3)4Sn as catalyst. Identification of the degradation products by means of a combination of gas chromatography (GC) and mass spectrometry (MS) revealed small amounts of “defects” in the almost ideally alternating copolymer 1. These were non-alternating sequences of 2-butenylene and methylethylene units, vinylethylene units and branching points. In addition, the metathesis degradation of 1 with 4-octene was investigated kinetically between 15 and 40°C. The measurements confirm that the thermodynamically stable 4-methylcyclohexene is the final product. This can be formed directly from the polymer and via oligomeric products. The formation of these intermediates is preceded by an induction period. Their concentrations pass maxima, the positions of which depend on the size of the molecules and on the temperature.
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  • 220
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: New polyamides having in-chain trans-1,2-dicarbazolylcyclobutane (DCZB) units were prepared. Fluorescence studies have shown that the fluorescence quantum yields of these polyamides are rather low in comparison with those of DCZB alone and vinyl polymers containing the DCZB units. Furthermore, time-resolved measurements have revealed that the fluorescence decay of these polyamides can, in general, be analyzed by a triple exponential decay with life times of 1-2 ns (≈20%), 5-6 ns (≈35%), and 12-14 ns (≈45%).
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  • 221
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A study of the copolymerization behaviour of 2-naphthyl methacrylate (M1), with styrene (M2) was carried out at 60°C in solution with 2,2′-azoisobutyronitrile as initiator and in different solvents. The following values for the monomer reactivity ratios were obtained by means of the Joshi-Joshi method: Chloroform: r1 = 0,16 ± 0,14, r2 = 0,81 ± 0,461,4-Dioxane: r1 = 0,34 ± 0,09, r2 = 0,49 ± 0,39Acetone: r1 = 0,54 ± 0,11, r2 = 0,63 ± 0,30Acetonitrile: r1 = 0,24 ± 0,09, r2 = 0,39 ± 0,33 These results are in good agreement with those obtained by means of the Fineman-Ross and Kelen-Tüdős methods. The solvent effect is discussed in terms of charge-transfer complexation between monomer and solvent molecules.
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  • 222
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    Die Makromolekulare Chemie 188 (1987), S. 1163-1175 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 4-Methylstyrene (S) was copolymerized with methyl methacrylate (M) or acrylonitrile (A) in benzene or N,N-dimethylformamide solution, respectively. The reactions were carried out at 50°C, using 2,2′-azoisobutyronitrile as free-radical initiator. The copolymer compositions were determined from oxygen (SM) or nitrogen (SA) analysis, 100 MHz 1H NMR, and 25 MHz 13C NMR spectra. These methods lead to the same results. Data plotted according to the Kelen-Tüdős (K-T) procedure indicate that the copolymerization of S with M can be adequately described by the terminal-unit model. The corresponding reactivity ratios (rS = 0,46 ± 0,02 and rM = 0,35 ± 0,02) were in good agreement with literature values and conform with the Q, e-scheme. On the other hand, the K-T plot for copolymerization of the SA system indicates deviations from the terminal model (rS = 0,27 ± 0,02 and rA = 0,10 ± 0,01) in the S- and A-rich regions. This departure was interpreted in terms of penultimate effects on the reactivity of the S- and A-ended radicals. The values of the corresponding reactivity ratios were as follows: rSS = 0,18 ± 0,03, rAS = 0,34 ± 0,04, rAA = 0,06 ± 0,01, and rSA = 0,13 ± 0,01. The theoretical curve of copolymer composition versus monomer feed, calculated with these parameters, is in excellent agreement with the experimental data. This finding shows that, on the basis of the composition data alone, the penultimate model provides an appropriate description of the copolymerization of S and A.
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  • 223
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    Die Makromolekulare Chemie 188 (1987), S. 1187-1194 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The interference function of liquid-crystalline A/B-block-copolymers is given. The function is restricted to a one-chain calculation, i.e. packing effects of neighbouring chains are neglected. It refers to fully elongated first-order Markoff-chains with A- and B-sequences, the lengths of which are controlled by the transition probabilities pAA and pBB for A-A and B-B steps. Combinations of an A- and a B-sequence each are considered as formal super-comonomers which follow randomly after each other. Thus, a statistical super-copolymer not of A- and B-monomers but of A- and B-sequences comes into existence, obeying the interference function as given by Blackwell, Biswas, and Bonart in an earlier paper. Whereas only the reference points of the A- and B-comonomers were considered in the first part of the paper, also the atomistic structures of the comonomers are now taken into account. The result renders the possibility to analyse the chain statistics of liquid-crystalline copolymers as will be shown in following papers.
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  • 224
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    Die Makromolekulare Chemie 188 (1987), S. 1217-1232 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The structure and synthesis of some poly(vinylsaccharide)s is described. Five different monomers, N-saccharide-substituted acryl-and methacrylamides, were prepared and polymerized to high molecular weight products using different initiator systems. The influence of the chemical structure of the saccharide moiety on the solution properties was studied by viscosity and light scattering measurements, and a comparative discussion of the solution behaviour of poly(2-deoxy-2-methacrylamido-D-glucose), poly(1-deoxy-1-methacrylamido-D-glucitol), poly(1-acrylamido-1-deoxy-D-glucitol) and polyacrylamide is made. The effects of hydrogenation on the intrinsic viscosity of poly(2-deoxy-2-methacrylamido-D-glucose) is shown. The crosslinking of poly(1-acrylamido-1-deoxy-D-glucitol) as a side reaction was examined by 13C NMR spectroscopy.
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  • 225
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Analytical and kinetic aspects of the photooxidation and photolysis in the solid state of various ethylene-vinyl acetate (EVA) copolymers (0 〈 VA (in mol-%) 〈 26) are described. At long wavelengths (λ 〉 300 nm), the photooxidation is independent of the vinyl acetate content. The acetate groups, which are not preferential sites for the photo-induced hydroperoxidation, are photoconverted into chain ketones similar to those formed in the photooxidation of low density polyethylene (LDPE). As the content of monomeric units of vinyl acetate increases, associations between alcohols formed and the acetate groups are observed, based on the appearance of the 3530 cm-1 absorption band. The rate of the formation of vinyl-type insaturations is a decreasing function of the content of monomeric units of vinyl acetate. At short wavelength (λ = 254 nm) direct photolysis of the acetate groups is observed through the formation of alcohols and ketones again similar to those found in LDPE photooxidation. The rate of the EVA photolysis varies linearly with the vinyl acetate content. Oxygen reacts with the primary radicals formed at 254 nm. Alcohols and ketones are formed faster than through photolysis, although no stoichiometry change is observed.
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  • 226
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Dimethyl 1,4-cyclohexanedicarboxylate was treated with various potential isomerization catalysts under reflux (ca. 280°C). Lithium cloride and sulfonic acids caused rapid isomerization. Also the diphenyl ester and 1,4-cyclohexandicarbonyl dichloride were isomerized, and in all cases a thermodynamically controlled equilibrium with 66 ± 2% trans-isomer was obtained. The same cis/trans ratio was found for the molten polyesters prepared from 1,4-butanediole, 1,6-hexanediole or phenylhydroquinone and 1,4-cyclohexanedicarboxylic acid. The polyester, prepared at 20°C from phenylhydroquinone and trans-1,4-cyclohexanedicarbonyl dichlorid, exhibits a mesogenic phase above 250°C; yet, this LC-phase is thermodynamically unstable and isomerizes to an isotropic melt containing 66 ± 2% trans-isomer. However, when the free diacid or the crystalline polyester from hydroquinone and 1,4-cyclohexanedicarboxylic acid are heated or synthesized at ca. 300°C, a content of 100% trans-isomer is the thermodynamical optimum. This is also true for the LC-phase of polyesters prepared from methyl- or chlorophydroquinone. The trans content of LC-copolyesters, containing variable mole ratios of monomeric units of hydroquinone and phenylhydroquinone, varies with these mole ratios between 66 and 100%. Obviously, the coexistence of LC-domains containing 100% trans-isomer and isotropic domains containing 66% trans-isomer are responsible for this result.
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  • 227
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The polymerization of β-propiolactone (βPL) with crowned K+ counterion has been shown previously to be a living process. This behaviour was used to prepare macromonomers of poly(βPL) with the methacryloyl reactive group. Poly(βPL) is known to be a crystalline polymer; thus, copolymers of poly(βPL) macromonomers with butyl acrylate gave graft copolymers with properties stemming from this ability. Selected mechanical properties of the copolymers are close to those of acrylic rubbers reinforced with fillers.
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  • 228
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    Keywords: Chemistry ; Polymer and Materials Science
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    Notes: Unsaturated oligoesters with carboxylic acid end groups were prepared from maleic and/or fumaric acid and 1,6-hexanediol. The oligomers with molar masses between 700 and 1 100 were synthesized from smaller ester units via the corresponding isoureas, applying the carbodiimide method. Three oligoesters with uniform molar masses and chemical structures were obtained in excellent yields. They were characterized by gel permeation chromatography, infrared spectroscopic analysis, elemental analysis and by determination of their acid numbers.
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  • 229
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    Die Makromolekulare Chemie 188 (1987), S. 1403-1414 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Three samples of poly(1,2-cyclohexene oxide) were prepared with ZnEt2, (EtZnOMe)4, and [{MeOCH2CH(Me)OZnO(Me)CHCH2OMe}2 · {EtZnO(Me)CHCH2OMe}2] ([Zn-MP]2,2), respectively, as initiator. Each polymer sample was treated with butyllithium to form various decomposition products having double bonds or hydroxyl groups as end groups. Two dimeric diols, were obtained from the decomposition products and were found to have isotactic (SS—SS or RR—RR) and syndiotactic (RR—SS) structure, respectively. By comparison of the relative yield of the two dimeric diols from each sample with the relative intensity of the three major signals in their 1H NMR spectra, the latter were assigned to methine protons of isotactic, syndiotactic, and heterotactic triads (from downfield to upfield). It was found that most parts of the main chain of the polymer prepared with [Zn-MP]2,2 were composed of syndiotactic triads, SS—RR—SS (or RR—SS—RR), while the polymer prepared with ZnEt2 or (EtZnOMe)4 contained syndiotactic and heterotactic triads in comparable amounts.
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  • 230
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Aromatic polyesters and polyamides with disc-like mesogens in the main chain were prepared from tetra-substituted hydroquinones and derivatives of 1,4-phenylenediamine. Depending on the atomatic acids (terephthalic acid, 2,5-dialkoxyterephthalic acid) used in the condensation reaction, the repeating units of these polymers carried 4 or 6 lateral substitutents. All polymers are highly soluble in several organic solvents, e.g. CHCl3, toluene, acetone. The phase behaviour of the polymers was studied by means of differential scanning calorimetry and optical polarizing microscopy. Depending on the number of lateral substitutents the polyesters and polyamides show crystalline and thermotropic liquid-crystalline phases. X-ray investigations showed a board-like Packing of the rigid-rod polymers which we have termed as a “sanidic” (meaning board-like) phase.
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  • 231
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    Die Makromolekulare Chemie 188 (1987), S. 1465-1475 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Thin polypyrrole (PP) films with octanesulfonate, dodecylsulfate and polystyrenesulfonate counterions were electrochemically switched between the conducting oxidized and the insulating neutral state in various electrolytes. In propionitrile under rigorous exclusion of oxygen and water PP can be cycled more than a thousand times without an appreciable decrease in electrochemical capacity. In an aqueous medium this process becomes irreversible after less than a hundred scans, the effect being strongly influenced by the pH of the electrolyte. Furthermore a pronounced dependence of the available charge upon the time (t5) between subsequent scans is found. It is known that treatment of PP films by a base leads to a remarkable decrease in conductivity. A mechanism which explains the loss of conductivity is proposed, in addition the possible occurrences of irreversible chemical changes as side reactions during electrochemical cycling is discussed.
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  • 232
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    Keywords: Chemistry ; Polymer and Materials Science
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    Topics: Chemistry and Pharmacology , Physics
    Notes: The paper presents an X-ray study of the isomers 4,4′-bis(2-hydroxyphenoxy)-, 4,4′-bis(3-hydroxyphenoxy)-, and 4,4′-bis(4-hydroxyphenoxy)octafluorobiphenyl, which are used as monomers in the synthesis of polyarylates. The molecular packing in crystals is characterized by intermolecular H-bonds, donor-acceptor and stacking interactions between the benzene rings of adjacent molecules, which results in considerable distortion of the molecular geometry. Notably, bending of biphenyl fragments accompanied by distortion of benzene ring planarity was observed, along with unusual conformations of oxydiphenylene fragments and distortions of bond angles at ipso-carbon atoms bonded to ether oxygen atoms.
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  • 233
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    Die Makromolekulare Chemie 188 (1987), S. 1537-1549 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Novel ABA block copolymers of poly(1,4-phenylene sulfide) (PPS(A)) and poly-(2-methyl-1,4-phenylene sulfide) (PMPS(B)) were synthesised from bis(4-bromophenyl) sulfone (BBS) by sequential reaction with copper(I) 4-bromo-2-methylbenzenethiolate (CBMT) and copper(I) 4-bromobenzenethiolate (CBT). PPS, PMPS and PPS/PMPS random copolymers were also prepared to aid block copolymer characterisation. Polymer fractions were studied by hot-stage microscopy to evaluate melting ranges, and molar masses were computed from bromine end-group concentrations and from gel permeation chromatography studies. Compositional analyses were made by IR and 1H NMR spectroscopy leading to confirmation of the block copolymer structure and to evaluation of the degrees of polymerisation of the individual blocks.
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    Die Makromolekulare Chemie 188 (1987), S. 1613-1619 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Block copolymers containing a rigid [oxy(2,6-dimethyl-1,4-phenylene)] block and thermotropic poly[oxyterephthaloyloxy-1,4-phenylene-hexamethylene (or/and decamethylene)-1,4-phenylene] blocks were synthesized. Their structures were examined by means of 1H and 13C NMR and X-ray diffraction, and their liquid crystalline properties investigated by polarizing microscopy.
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  • 235
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    Topics: Chemistry and Pharmacology , Physics
    Notes: The addition reaction of methacrylic acid (6) to the telomer 3, resulting from 2,3-epoxypropyl methacrylate (1) and dodecanethiol (2), (DPn = 6) was studied. The percentage of addition at 60°C was found to be 32 after 24 h. When using an epoxide/methacrylic acid mole ratio of 2:1 Products were obtained which can easily be crosslinked by UV irradiation and which stick to aluminium to give water-resistant products.
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  • 236
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    Die Makromolekulare Chemie 188 (1987), S. 1795-1808 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 1,4-Polybutadiene was partially phenylated in allyl position by bromination with N-bromosuccinimide and subsequent Grignard-Wurtz reaction with phenylmagnesium bromide. Substitution was to a certain degree coupled with double bond shift. The polymer structure was investigated via metathesis degradation with (E)-4-octene. The degradation products were identified by means of a GC/MS system and determined by GC. Cases of isomerism of products with one phenyl group were investigated. A metathesis product with two phenyl groups in one constitutional unit was found. A distribution function, based on a statistical scission of the macromolecules, was used for evaluations at different metathesis reaction times. Proofs of the reduced reactivity of CC double bonds in the neighbourhood of substituents were received. The yields of the different constitutional units in metathesis products were determined. These were compared with the results of computer simulations in a simplified model. The validity of computer simulations was thereby confirmed.
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    Die Makromolekulare Chemie 188 (1987), S. 1825-1831 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The polymerization of N-phenylmaleimide (N-PMI) was carried out with organozinc compounds as initiators. Within the initiators examined [Zn(OCH3)2·(C2H5ZnOCH3)6] gave the highest yield of poly(N-PMI). The polymer yield increased rapidly at the early stage of the polymerization reaction. The poly(N-PMI) produced shows a unimodal molecular weight distribution in the high-molecular-weight region and two components in the oligomeric region in GPC. 1H NMR and 13C NMR spectra suggest an addition polymerization without any remarkable side reactions. The results of the copolymerization with styrene and of the polymerization in nitrobenzene suggest an ionic polymerization mechanism.
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  • 238
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    Notes: The complex series of reactions that takes place between WCl6 and cyclopentene was studied spectroscopically. The products of reaction remain soluble when chlorobenzene is used as solvent. A number of intermediates was observed and the kinetics of formation and removal of these was studied in detail. A complex series of reactions was postulated to account for these changes and the significance of each reaction to the overall scheme was determined by computer simulation of the changes that occur. One of the products has particular significance in the scheme of reactions since it is believed that this species is eventually responsible for the monometallic initiation of the polymerization of cyclopentene. The reaction was also studied gas chromatographically when it was shown that the reaction is accompanied by the formation of a complex mixture of products. One of these products was shown to have the mass spectrum that would be expected of 3-chlorocyclopentene and a reaction scheme that would account for its formation is postulated. The reactions involved in the generation of centres active towards the formation of polypentenamer were considered for both monometallic and bimetallic (WCl6/AlR3) catalyst.
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  • 239
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    Die Makromolekulare Chemie 188 (1987), S. 2151-2161 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ESR spectroscopic analyses of the deep-green solutions of living poly(2-isopropenylnaphthalene) [poly(2-IPN)] in THF at -80°C provided no evidence of the presence of radical anions as long as butyllithium (BuLi) was used as initiator. In contrast to this finding, radicals could indeed be detected if the polymerization was performed with metallic potassium in THF. These radicals were found to be only stable at low temperatures. UV/VIS spectra of solutions of 2-IPN in THF or toluene and of catalytic quantities of BuLi were recorded at temperatures between -45 and +20°C. On heating to 〉0°C, the colour of the deep-green solution changes irreversibly to reddish-brown, and this colour change is associated with a spontaneous deactivation of the living poly(2-IPN). End-capping reactions with anthracene derivatives and the block copolymerization with hexamethylcyclotrisiloxane gave a first idea of the reactivity and structure of the species present in the reddish-brown solution. A suggestion is made for the deactivation mechanism.
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    Die Makromolekulare Chemie 188 (1987), S. 2177-2183 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Composition data for the copolymerization of styrene with maleic anhyride in ethyl methyl ketone at 50°C were obtained using a non-aqueous potentiometric direct titration method, and were analysed using a non-linear least squares optimization routine. Three variants of the penultimate model were fitted to the data: the four variable model (completely general), the three variable model (rmm = 0,0) and the more usual two variable model (rmm = rsm = 0,0). Of these, the two variable model was adequate to describe the data. Best estimates of the reactivity ratios for data previously reported in the literature were calculated, and in one case the best values were markedly different to those originally given.
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    Die Makromolekulare Chemie 188 (1987), S. 2193-2201 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: It has been shown that it is possible to use pressure dilatometry (also known as pressure-volume-temperature (PVT) techniques) to follow the phase separation of a polymer blend. PVT data have been obtained for polyether sulfone, poly(ethylene oxide) and blends of the two over a range of compositions. For the pure polymers one can observe the glass transition and melting transitions, respectively. In the case of the blends the volume expansion accompanying phase separation on heating can be seen along with the different thermal expansion coefficients of the generated two phase structures. One can also observe the effect of pressure in elevating the temperature of phase separation.
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    Die Makromolekulare Chemie 188 (1987), S. 2213-2221 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Dynamic viscoelasticity and differential scanning calorimetry (DSC) measurements were carried out in order to examine the effect of sulfate content on the gelling mechanism of concentrated kappa- and iota-carrageenan solutions. Alkaline pre-treatment was very effective to enhance the gelling ability of kappa-carrageenan. The melting temperature of the gels and the temperature at which elastic modulus begins to decrease rapidly were shifted to higher temperatures with increasing concentration of gels. Elastic modulus increased with increasing concentration, while endothermic enthalpy showed a maximum at a certain concentration. The effect of thermal history on DSC behavior was also examined.
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  • 243
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    Notes: A method is discussed for Monte-Carlo-simulation of copolymer molecules with chemical inhomogeneity of the second type. The copolymer molecules are formed by a polyreaction with monomer addition without chain termination, e.g. in case of an anionic “living” polymerization. The reliability of the method was statistically tested with examples. The method allows a clear presentation of the copolymer molecules mentioned in the paper.
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    Die Makromolekulare Chemie 188 (1987), S. 2489-2494 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: It is found that the expected maximum strength of polymers is not proportional to the number of polymer chains per unit area. Under uniaxial stressing only part of polymer chains, i.e., overstressed chains, contribute to the strength of the polymer. The number of overstressed chains obtained here for some polymers is consistent with the results of electron paramagnetic resonance and stress-Fourier-transform IR measurements: (a) Polymers with all-trans conformation of their chains have more overstressed chains than those with helix conformation; (b) in the case of polymers with helix conformation, those with smaller side groups have more overstressed chains. Under uniaxial stress, the polymer chains change their conformation from gauche to trans which results in a relief of stress. Polymer with helix conformation thus have less overstressed chains and, hence, lower strength than polymers with all-trans conformation.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 219-229 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Microporosities often appear during the solidification of foundry pieces. They result from the volume contraction of the alloy during its solidification. Thermal transfers between alloy and mould check the solidification. They are estimated by a finite volume method, including specific calculation of the mould filling-up, the alloy solidification and the resulting feeding of the mould.The calculation uses a geometrical enmeshment of the whole mould, generating numerous elements of different sizes. From the experimental fluid flow measurement, the mould filling-up may be described step by step by the computer, as can the initial thermal transfer. Thermal transfers are related to the solidification enthalpic release obtained from quantitative differential thermal analysis. They are also related to the fluid flow induced by solidification shrinkage.Such a calculation leads to the location of the microporosities, from which pressure drops can be estimated during solidification.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 263-270 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The die-swell occurring during the extrusion of a visco-elastic fluid has been extensively examined in recent years, both experimentally and numerically. These investigations have been mainly confined to isothermal flows. If the material is initially relatively cool, however, viscous heating may lead to proportionally large changes in temperature and material properties, with significant effects on die-swell. An iterative computational model is presented which describes the flow of Maxwell and Oldroyed fluids subject to the effect of temperature gradients induced by viscous heating and thermal boundary conditions. Predictions are presented for extrusion from both slit and axisymmetric dies.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 289-300 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The presented solver uses the Crout L-U decomposition method. Disk memory space requirements are reduced to an absolute minimum and disk input-output is spectacularly limited. Very extensive pivoting improves numerical accuracy and stability. Experimental test runs prove the overall efficiency of the solver.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 337-357 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials.When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable.Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 393-417 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider finite element analysis of problems with discontinuous material coefficients. For applications in which the material interface crosses an element, we develop special elements with an embedded flux constraint at the interface. This new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by Steven.1 Supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined. Some local superconvergence behaviour is observed.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 471-473 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 24 (1987) 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 25-45 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The proposed method is the direct boundary integral equation (BIE) method applied to three-dimensional transient heat transfer analyses and to corresponding elastostatic analyses under thermal loading. The mechanical and thermal problems are decoupled. For those not familiar with the BIE method, a short survey of the basic principles is given to help them understand the mathematical treatment, which is performed in the frame of distribution theory. The tempered elementary solution of the transient heat transfer problem contains time and space variables. The numerical treatment of the thermal equation is performed analytically with respect to time and numerically with respect to space in the same way as for steady state equations. Great care is paid to space integration in order to compute the values of the kernels precisely enough on the surface and inside the volume. The computational treatments of both problems are realized in such a way as to minimize computing time. Differences between transient and steady state analyses, on the one hand, and between elastostatic analyses with and without thermal loading, on the other, are emphasized. Finally, an analytical example shows the good behaviour of the proposed method to solve singular thermal problems and an industrial example shows the accuracy of the results obtained by using the BIE method to solve three-dimensional thermo-elastic problems.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 47-57 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A moving finite element method that calculates the transient temperature distribution, the density distribution and the stress distribution during the sintering cycle has been developed. Coupled two-dimensional axisymmetric energy, continuity and stress equilibrium equations along with a constraint, specifying the direction of the initial material velocity, are solved in a Lagrangian co-ordinate system. The nodes move at the same speed as the material and therefore the convective terms in the differential equations drop out. At every time step, the energy equation is solved, and the computed temperatures are then used to find the densification rate. In two-dimensional problems, the continuity equation is not sufficient to calculate the two components of material velocity. Here, it is assumed that the diffusion caused by the density gradient is the driving force. This implies that the velocity vector of the material is perpendicular to the lines of constant density. Therefore, the combination of the diffusion and continuity equations will generate the initial sintering strains. The elastic stress equilibrium equations are then solved using the thermal and initial sintering strains as the driving forces. As a result, the final shape of the material and the stresses are determined.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 89-99 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper some numerical predictions are presented for the buoyancy-driven turbulent flow and heat transfer in a large cavity using both a prescribed eddy viscosity model and a k-∊ model. The results from these models are in good agreement, although the calculations with the prescribed eddy viscosity model are considerably cheaper. The results also show the correct qualitative behaviour, but there are some differences between the predictions and the available experimental data. Possible reasons for these are discussed.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 159-175 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper proposes a generalized least-squares time finite element procedure for analysis of transient field problems. It leads to a very general four parameter and two time level family of schemes. The free parameters are optimized in terms of accuracy, stability and oscillatory behaviour of the computational algorithm. In the case of linear problems an unconditionally stable scheme of fourth-order accuracy is obtained. Special choices of the free parameters also give a number of well-known time-integration schemes, such as the Zienkiewicz-Lewis third-order algorithm, the Goodrich scheme and standard schemes such as the Crank-Nicolson and backward fully implicit schemes. The main disadvantage of the higher order algorithm is a large bandwidth of the system matrix owing to the matrix terms of the form KTK. This drawback is reduced for special choices of the parameters by forming a product formula. Somewhat more computation is required than for popular schemes such as the generalized midpoint rule, depending on the prescribed variables. Numerical comparisons are made between the proposed higher order schemes and standard schemes.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 231-249 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical model has been developed to quantify the effects of process conditions during turbulent solidification and mixing of a liquid metal jet in a confined co-flowing molten metal stream.The modelling has been split into three parts. First, a single phase model with no latent heat effects to consider the solidification potential. Secondly, a two phase model where the second phase is comprised of solid particles which solidify during mixing of the two streams. Thirdly, a two phase model where the second phase consists of the inner jet, which is assumed to break up into droplets of given size, and solid particles are allowed to form by solidification within the droplets.The results show that the thermal history (solidification path) of the solid phase formed is affected by latent heat and particle size, which implies that solidification, nucleation and jet fragmentation events should be included dynamically to ensure realistic predictions.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 285-287 
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    International Journal for Numerical Methods in Engineering 24 (1987) 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 271-284 
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    Notes: An enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 859-869 
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    Keywords: Engineering ; Engineering General
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    Notes: The one-dimensional freezing problem can be solved numerically for the temperature distribution accompanied by explicit reference to the position of the freezing front at each time interval. A new front-tracking scheme provides accurate determination of the phase front, which is an essential requirement for the temperature distribution in the different phases of such problems. The front is made to coincide with a grid-node throughout the analysis. The scheme uses a combination of the finite difference and the finite element methods for obtaining the solution of the freezing problems.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 913-926 
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    Notes: A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (a) restructuring the governing finite element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (b) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique.A tracing parameter is introduced which identifies all the contributions to the antisymmetric response. The global approximation vectors are selected to be the solution corresponding to a zero value of the tracing parameter and the various-order derivatives of the solution with respect to this parameter, evaluated at zero value of the parameter. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions.The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving non-linear problems is discussed.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 959-973 
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    Notes: Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two-dimensional, axisymmetric and three-dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near-singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self-adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self-adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 993-1014 
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    Notes: New algorithms which improve the finite element solution on a fixed mesh of the domain are developed. For this, objective functions which depend on a positive parameter to be determined are proposed. These functions lead to criteria which combine in several ways the residual of the solution, the approximation in the Euclidean norm of the value of the solution at the nodes, and the approximations in the energy and Hk norms. Some aspects of optimality are studied and, finally, numerical results are given.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1015-1025 
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    Notes: The hybrid stress method is very successful for stress concentration problems.1-7 Especially for problems of fracture mechanics, procedures can be found that work efficiently for two- and three-dimensional problems. The rate of convergence with this method, evidently, is higher than that with conventional FE models. The BEM procedure, too, works more efficiently, but shows some essential disadvantages against the FEM, such as that for the direct method no symmetric positive definite matrix can be found and that there occur numerical problems at corners.8,9 This happens also when BEM and FEM are even coupled commonly.10-12. In the following, a hybrid BEM model will be described which combines the advantages of both the FEM and the BEM. It will be shown in this paper that BEM is very successful in formulating finite element functions for the hybrid assumed stress method.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1027-1029 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1029-1029 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1030-1030 
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    International Journal for Numerical Methods in Engineering 24 (1987) 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1031-1042 
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    Notes: This paper develops an arbitrarily quadrilateral element to analyse bending problems of plates with non-orthogonal boundaries. A second-order Jacobian matrix for the co-ordinate transformation and an explicit form of its inverse matrix are described in detail. A shape function matrix [N] for the plate element of arbitrarily quadrilateral configuration, an equivalent load vector {R}, a strain matrix [B] and element stiffness matrix are given. Finally, four illustrated examples are given and the results of computation are compared with those from other analytical methods.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1043-1078 
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    Notes: A technical description of the algorithms employed in the modified quadtree mesh generator is given. Although the basis of the mesh generator is the same as the original version developed by Yerry and Shephard,1,2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique. As demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach, but introduce additional algorithmic difficulties, the solutions of which are also presented. In addition to examples showing the capability of the mesh generator, the linear computational growth rate of the mesh generator is demonstrated.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1093-1100 
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    Notes: Numerical solution of a given non-linear algebraic system of equations by a quasi-Newton type method requires updating the approximation to the Jacobian at each step. Two methods for large sparse systems are described. The approximation for the Jacobian is factored into an LDU form at the first step, then all the subsequent updates are made to L, D and U. Computational evidence is given exhibiting the relative efficiency of these methods over those currently available in the published literature.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1079-1091 
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    Notes: This paper is concerned with a method for obtaining stresses in a rod of arbitrary cross-section subjected to combined loads of bending, shearing and torsion which are the complicated functions of time. In the first step, the analysis derives the bending moment, shearing force and torsional moment by use of a combination method of the Laplace transformation and Fourier series expansion. The transient stresses are obtained based on the two-dimensional theory of elasticity, but in which the Fourier expansion collocation procedure is applied to deal with the complex boundary shape of the cross-section. To affirm the validity of this analysis, experimental tests are also carried out for an oval rod subjected to the three combined transient loads.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1101-1121 
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    Notes: Methods for generating Pareto optimal solutions to a multicriterion optimization problem are considered. The norm methods based on the scalarization of the original multicriterion problem by using the lp-norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested. In addition, an alternative approach which, instead of scalarization, reduces the dimension of the multicriterion problem is proposed. This is called the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted sum of the criteria is used as the objective function. The first of these two approaches (norm method) is very flexible from a designer's point of view and it can be applied also in non-convex cases to the determination of the Pareto optimal set whereas the latter (partial weighting method) is especially suitable for problems where the number of criteria is large. Throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 605-620 
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    Keywords: Engineering ; Engineering General
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    Notes: This paper describes the proper external potential formulation of a cathodic protection system employed for corrosion prevention of structures in infinite electrolytes. The boundary condition associated with the mathematical formulation is not of the standard type encountered in hydrodynamic, electrostatic or heat transfer applications. The developed mathematical model is discretized by the boundary element technique, which is then solved iteratively by the Newton-Raphson method.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 621-634 
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    Notes: In the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store ‘large’ blocks of spatial information. With the advent of ‘super computers’ the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition of a domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff's equation. The elements used are triangular and compatible.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1771-1792 
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    Notes: A new computer program architecture for the solution of finite elemet systems using concurrent processing is presented. The basic approach involves the automatic splitting of an arbitrary spatial domain. Processors are dynamically re-assigned during the several phases of an analysis. Direct and iterative solution strategies are considered. Computational algorithms for finite element dynamic analysis of large-scale structural problems that exploit concurrent features of MIMD computers are implemented in modules around the basic architecture. Also, problems with localized non-linearities are treated. A first implementation on a 32-processor hypercube achieves efficiency rates of up to 90 per cent.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1823-1824 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1187-1202 
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    Notes: This paper explores the concept of moving singularities in the boundary element analysis. The singularities are placed on an auxiliary boundary which is located outside the domain of the problem and are allowed to move as part of the solution process. This results in a highly adaptive but non-linear method. Examples involving the two- and three-dimensional Laplace's equations are solved. Excellent agreement with exact solutions is obtained using a minimal number of singularities. Also, the trajectories of the singularity motion are plotted. The behaviour seen here is that, as the solution approaches convergence, the singularities exhibit a general trend of moving away from the domain of the problem.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1225-1225 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1226-1226 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1203-1224 
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    Notes: The development of a general triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates. The element formulation assumes transverse inextensibility and layerwise constant shear-angle. Convergence of transverse displacement, moments and stresses, the effects of two different Gauss quadrature schemes and comparison of the present solutions with the available analytical/finite-element results also form a part of the investigation. Furthermore, numerical results indicate close agreement between the LCST (layerwise constant shear-angle theory) and the three-dimensional elasticity theory with the length (or width) to thickness ratio as low as 4. Detailed comparison of the LCST-based finite-element solutions with those based on the CST (constant shear-angle theory) and the CLT (classical lamination theory) clearly demonstrates the superiority of the former over the latter two, especially in the prediction of the distribution of the in-plane displacements and stresses through the laminate thickness. This paper also introduces a new non-dimensionalized parameter, Δθ*, which is shown to be a very useful measure for classification of the laminated plates and the suitability of different plate theories over various ranges of length-to-thickness ratio.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1993-2015 
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    Notes: The granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour.We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom-near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non-linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non-dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two-point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins-Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 945-958 
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    Notes: A damper technique is proposed to model the effects of radiation damping in the finite element analysis of hydrodynamic pressures generated due to the vibration of a structure submerged in a compressible fluid. The proposed damper is suitable for a time-domain analysis. It is assumed that the fluid is inviscid and its vibration is of small amplitude. The structure-fluid system is assumed to be two-dimensional, and the fluid domain is considered to be unbounded along the direction of structural vibration. In the finite element analysis, pressure is assumed to be the nodal unknown, and the discretized equations of motion are solved by using a direct integration procedure. As a result of the analysis of several cases, the proposed damper is found to be very effective and efficient for a wide range of the period of excitation. The only exception is the case when the period of excitation is near the natural period of vibration of the fluid domain. For this case, the pressure becomes infinitely large and there is no requirement for any damper. The implementation of the proposed damper in the finite element analysis requires practically no extra computational effort. With the use of the suggested technique, an unbounded fluid domain may be truncated at a relatively very short distance from the structure, as compared to the distance required when the Sommerfeld damper is used. As a result of these advantages of the proposed technique, the cost of computation is greatly reduced.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1283-1296 
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    Notes: A least-squares variational procedure for first-order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1711-1720 
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    Notes: This paper presents a new method for the direct computation of strongly singular integrals existing in the Cauchy principal value sense. It can be usefully applied in the solution by the direct boundary element method of many different problems. Initially, some considerations are provided in order to summarize the state-of-the-art on this issue. Then the features of the proposed method are reported. The procedure allows the direct calculation of Cauchy principal value integrals with first-order singularity and it is applicable even in advanced boundary element methods employing high-order elements. It requires only the use of standard Gaussian quadrature formulae plus the computation of a logarithmic term. Some examples show the effectiveness and efficiency of the procedure.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1825-1826 
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1849-1863 
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    Notes: Galerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first- and second-moment properties of the solution to be calculated. An equivalent energy-based approach similar to the Rayleigh-Ritz method is developed, from which a stochastic finite element technique is derived. Several one- and two-dimensional example problems are solved and the results discussed.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1921-1939 
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    Notes: A theory is described which guarantees an upper and lower bound estimate of the discretization error in numerical solutions of elliptic boundary value problems. This method gives bounded global estimates of the error in the energy norm. Pointwise estimates of the error in the solution variable or its derivatives can then be obtained if the numerical solution is exhibiting pointwise monotonic convergence.The versatility of this method is illustrated by its application to numerical solutions from finite element, finite difference and boundary element methods.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1941-1950 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix is derived for a finite element representing a beam column with rectangular cross section and a single edge crack. The element has zero length, and the standard nodal degrees of freedom associated with beam-column elements. To illustrate its capabilities, the element is used to model propagation of multiple cracks in a self-loaded fixed beam.
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  • 291
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 2017-2033 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fact that finite element models can give rise to violent stress oscillations and that there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations has been known for some time. However, it is less well known that these oscillations arise in a specific class of problems - where there are multiple strainfields arising from one or more field-variables and where one or more of these strain-fields must be constrained in particular physical limits. In this paper, we show that unless the interpolations for these constrained strain-fields are ‘field-consistent’, violent oscillations would set in. These oscillations represent spurious self-equilibrating stress-fields generating spurious energy terms that lead to ‘locking’.The field-consistency interpretation offers a conceptual scheme to delineate these problems and an operational procedure called the functional reconstitution technique allows the errors resulting from field-inconsistency to be anticipated a priori. We demonstrate the power of this approach through an interesting example of a multi-strain-field problem - the inextensional/nearly inextensional deformation of a shear flexible curved beam.
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  • 292
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 2037-2038 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 293
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 2036-2036 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 294
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 1865-1877 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sensitivity analysis is presented as a natural addition to interactive multiobjective optimization methods based on compromise programming. It is shown that useful information regarding trade-offs in the objectives can be generated effectively by means of an analysis of the sensitivity of solutions to variations in preference structures. An implementation based on sequential quadrative programming is provided and examples are given for illustration.
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  • 295
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1951-1971 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element model suitable for the analysis of column-supported shells of revolution is presented. This model combines in a single analysis axisymmetric shell elements with nodal circles and column elements with nodal points. Thus, it takes advantage of the axisymmetry of the shell, while the non-axisymmetric nature of individual columns is fully accounted for. The compatibility between the two different types of elements is achieved through the use of a co-ordinate transformation. The accuracy of the solutions is demonstrated through numerical examples. When a shell of revolution supported on equispaced columns of the same stiffness is subjected to a harmonically varying load in the circumferential angle, it is found that the resulting displacements are associated with selective harmonic terms. An equation which precisely defines this coupling mechanism is also derived.
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    International Journal for Numerical Methods in Engineering 24 (1987), S. 2035-2035 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 297
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    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 188 (1987), S. 149-154 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 2-Ethyl-2-oxazoline (ETOX) as nucleophilic monomer and β-butyrolactone (BUL) as electrophilic monomer were copolymerized in bulk in the absence of initiator at 45°C. Copolymers were characterized by elemental analysis, IR, 1H NMR, and 13C NMR spectroscopy. The copolymer composition was determined by elemental analysis and by 1H NMR spectroscopy. All copolymers contain a BUL:ETOX mole ratio greater than one.
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  • 298
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    Die Makromolekulare Chemie 188 (1987), S. 171-187 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of the free radical terpolymerization of diethyl maleate (DEM) (M1) with methyl methacrylate (MMA) (M2) and styrene (M3) was investigated at 60°C with AIBN as initiator. The analysis of the dependence of the terpolymer composition on the feed composition was difficult due to the similar chemical and physical properties of diethyl maleate and methyl methacrylate and also by the low content of the former monomer in the terpolymers. Finally, the terpolymer composition could be determined by means of microanalyses of carbon and hydrogen content. The results of these determinations were confirmed by 13C NMR spectroscopy. The initiation rate constant of AIBN was studied at different feed compositions by means of the inhibition method. For the study of the over-all polymerization kinetics of this ternary system it was necessary to take into account the dependence of the termination rate on the feed composition. It was found that not only the viscosity of the solution, but also the properties of the polymer segment next to the radical site have to be considered. Containing only parameters and constants measured independently from terpolymerization, the kinetic equation obtained described satisfactorily the initial over-all rates.
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    Die Makromolekulare Chemie 188 (1987), S. 201-215 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The ternary system solvent (1)/polydimethylsiloxane (2)/poly(methyl methacrylate) (3) was investigated by light scattering. First the measurements were realized on mixtures containing low-molecular-weight polydimethylsiloxane: M2 ≪ M3. In a second step, high and comparable molecular weights of both polymers were chosen for the measurements. The thermodynamic interaction parameter χ23 was determined from light scattering data (spinodal) and demixtion curves as a function of concentration and molecular weight of the polymers. Also the variation of the angular repartition of the scattered light was studied and the results were compared with calculated values.
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    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of the nonactivated anionic polymerization of 2-pyrrolidone (PD) initiated with the potassium salt of 2-pyrrolidone (KPD) and anionic polymerizations of PD accelerated with CO2 and 1-(1-pyrrolin-2-yl)-2-pyrrolidone or activated with 1-benzoyl-2-pyrrolidone and 1-acetyl-2-pyrrolidone were followed near the ceiling temperature (limit temp. T1) and discussed. The values of T1 were extrapolated from the data obtained for the given initiation systems. The dependence of T1 on the concentration of the initiation system was also investigated.
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