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  • Wiley-Blackwell  (133)
  • 2015-2019
  • 1995-1999  (50)
  • 1985-1989  (83)
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  • 1
    Electronic Resource
    Electronic Resource
    Ammoniakdiffusion in Polymerfilmen (1989)
    Weinheim : Wiley-Blackwell
    Angewandte Makromolekulare Chemie 173 (1989), S. 69-84 
    Details
    ISSN: 0003-3146
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: With the help of a novel test method, diffusion-coefficients of ammonia were determined in 22 transparent, filmforming polymers at room temperature. This method is based upon the UV-VIS-spectroscopically followable reversible reaction of ammonia with 4-nitro phenol to a Meisenheimer-complex.The dye-building reaction was studied and analyzed by a simple approximation of the diffusion equation. Diffusion coefficients obtained are in good agreement with the few available data in the literature.The dependence of the NH3-diffusion coefficients upon the polymer structure corresponds with the obtained diffusion coefficients, which are known for permanent gases.The described method allows the measurement of diffusion coefficients, which are distinguished up to three orders of magnitude, without any problem (ethylcellulose: 1,07 · 10-7 cm2 · s-1; poly(vinylalcohol): 0.9 · 10-10 cm2 · s-1).
    Notes: Mit Hilfe einer neuartigen Untersuchungsmethode wurden die Diffusionskoeffizienten von Ammoniak (NH3) in 22 transparenten filmbildenden Polymeren bei Raumtemperatur bestimmt. Die Methode beruht auf der UV-VIS-spektroskopisch verfolgbaren reversiblen Reaktion von Ammoniak mit 4-Nitrophenol zu einem 4-Nitrophenolat-Ammoniak-Meisenheimer-Komplex.Die Farbbildungsreaktion im Polymerfilm wurde untersucht und anhand einer einfachen Näherung der Diffusionsgleichung ausgewertet. Die erhaltenen Diffusionskoeffizienten stimmen sehr gut mit den wenigen verfügbaren Literaturwerten überein.Die Abhängigkeit der NH3-Diffusionskoeffizienten von der Polymerstruktur ist weitgehend der für permanente Gase bekannten analog.Die beschriebene Methode erlaubt problemlos, Diffusionskoeffizienten zu messen, die sich bis zu drei Größenordnungen unterscheiden (Ethylcellulose: 1,07 · 10-7 cm2 · s-1; Polyvinylalkohol: 0,9 · 10-10 cm2 · s-1).
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/apmc.1989.051730106
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  • 2
    Electronic Resource
    Electronic Resource
    Unexpected Hydroxyspirolactone Formation upon Baeyer-Villiger Oxidation of a trans-α-decalone (trans-octahydronaphthalen-1(2H)-one) and X-ray structure of the product (1995)
    New York, NY : Wiley-Blackwell
    Helvetica Chimica Acta 78 (1995), S. 887-890 
    Details
    ISSN: 0018-019X
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: trans-4,4,10-Trimethyl-9-decalone ( = trans-5,5,8a-trimethyl-octahydronaphthalen-1(2H)-one; 1), when treated with trifluoroperacetic acid, gave the unexpected hydroxyspirolactone 7-hydroxy-7,11,11-trimethyl-1-oxaspiro[5.5]undecan-2-one (6), in which the two new O-atoms were introduced in a 1,2-trans relationship. The structure of this compound was conclusively proven by X-ray crystallography. The process involves the intermediacy of 7-membered lactone 2, the expected Baeyer-Villiger product, which could also be successfully prepared under controlled conditions at 0° in a buffered medium containing Na2HPO4.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/hlca.19950780411
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  • 3
    Electronic Resource
    Electronic Resource
    Soliton defects in polyacetylene: Local-density functional results (1986)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 29 (1986), S. 793-797 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report local-density functional results for the electronic structure of neutral soliton defects in polyacetylene. The results were obtained using a modified version of the discrete variational method Xα molecular cluster model. For defect-free chains the calculated X-ray and ultraviolet photoelectron spectra are in good agreement with experiment. For chains with low concentrations of solitons, we find the forbidden gap broadens slightly, and two nearly dispersionless bands, split by several tenths of eV, are introduced into the gap. The predicted splitting is in accord with recent experimental results for this defect.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560290418
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  • 4
    Electronic Resource
    Electronic Resource
    An algorithm for exact eigenvalue calculations for rotationally periodic structures (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 609-622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An existing algorithm ensures that no eigenvalues are missed when using the stiffness matrix method of structural analysis, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The algorithm permits efficient multi-level substructuring and gives ‘exact’ results when the member equations used are those obtained by solving appropriate differential equations. The present paper extends this algorithm to cover rotationally periodic (i.e. cyclically symmetric) three-dimensional structures which are analysed by using complex arithmetic to obtain a stiffness matrix which involves only one of the rotationally repeating portions of the structure. Nodes and members are allowed to coincide with the axis of rotational periodicity and the resulting modes are classified. Rigid body freedoms are accounted for empirically, and the ‘exact’ member equations and efficient multi-level substructuring of the earlier algorithm can be used when assembling the stiffness matrix of the repeating portion.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230407
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  • 5
    Electronic Resource
    Electronic Resource
    Exact eigenvalue calculations for structures with rotationally periodic substructures (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 695-706 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory presented enables rotationally periodic (i.e. cyclically symmetric) three-dimensional substructures to be included when using existing algorithms to ensure that no eigenvalues are missed when the stiffness matrix method of structural analysis is used, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. A substructure can be connected in any required way to a parent structure which shares its rotational periodicity, or can be connected by nodes at each end of its axis of periodicity to any parent structure, i.e. the parent structure need not be periodic. The theory uses complex arithmetic, involves only one of the rotationally repeating portions of the substructure, allows nodes and members to coincide with the axis of rotational periodicity, permits efficient multi-level use of rotationally periodic substructures, and gives ‘exact’ eigenvalues if the member equations used are those obtained by solving appropriate differential equations. The competitiveness of the method is illustrated by approximate predictions of computation times and savings for two structures which contain rotationally periodic substructures.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230411
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  • 6
    Electronic Resource
    Electronic Resource
    Thermal stress analysis of sintering using a moving grid (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 47-57 
    Details
    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.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240104
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  • 7
    Electronic Resource
    Electronic Resource
    Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 2289-2302 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Bernoulli-Euler theory and Bessel functions are used to obtain explicit expressions for the exact dynamic stiffnesses for axial, torsional and flexural vibrations of any beam which is tapered such that A varies as yn and GJ and I both vary as y(n + 2), where A, GJ and I have their usual meanings; y = (cx/L) + 1; c is a constant such that c 〉 - 1; L is the length of the beam; and x is the distance from one end of the beam. Numerical checks give better than seven-figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements. A procedure is given for calculating the number of natural frequencies exceeded by any trial frequency when the ends of the member are clamped. This enables an existing algorithm to be used to obtain the natural frequencies of structures which contain tapered members.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620211212
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  • 8
    Electronic Resource
    Electronic Resource
    Exact Bernoulli-Euler static stiffness matrix for a range of tapered beam-columns (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1615-1628 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Bernoulli-Euler theory and Bessel functions are used to obtain explicit expressions for the exact static stiffnesses for axial, torsional and flexural deformation of an axially loaded beam which is tapered such that A varies as yl, GJ as ym+2, and I as yn+2, where A, GJ and I have their usual meanings, y = (cx/L) + 1, c is a constant such that c 〉 - 1, L is the length of the beam, x is the distance from one end of the beam, l and m can have any value and n is 1,2 or - 1. The work complements the similar dynamic stiffness derivations of Reference 2. Numerical results for a beam with substantial taper (c = 1.0) give better than seven figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements. A procedure is given for calculating the number of critical buckling loads of a clamped/clamped member that are exceeded by any trial load so that an existing algorithm can be used to obtain the exact critical buckling loads of structures which contain tapered members.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230904
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  • 9
    Electronic Resource
    Electronic Resource
    The method of lines and exponential fitting (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 557-567 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When the method of lines is used for solving time-dependent partial differential equations, finite differences are commonly employed to obtain the semidiscrete equations. Usually, if the solution is expected to be smooth, symmetric difference formulae are chosen for approximating the spatial derivatives. These difference formulae are almost invariably based on Lagrange type differentiation formulae. However, if it is known in advance that periodic components of given frequency are dominating in the solution, more accurate difference formulae, based on exponentials with imaginary exponent, are available. This paper derives such formulae and presents numerical results which clearly indicate that the accuracy can be improved considerably by exploiting additional knowledge on the frequencies of the solution.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240307
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  • 10
    Electronic Resource
    Electronic Resource
    Reliable use of determinants to solve non-linear structural eigenvalue problems efficiently (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1825-1841 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A ‘multiple determinant parabolic interpolation method’ is described and evaluated, principally by using a plane frame test-bed program. It is intended primarily for solving the transcendental eigenvalue problems arising when the ‘exact’ member equations obtained by solving the governing differential equations of members are used to find the eigenvalues (i.e. critical buckling loads or undamped natural frequencies) of structures. The method has five stages which together ensure successful convergence on the required eigenvalues in all circumstances. Thus, whenever checks indicate its suitability, parabolic interpolation is used to obtain eigenvalues more rapidly than would the popular bisection alternative. The checks also ensure a wise choice of the determinant used by the interpolation. The determinants available are all usually zero at eigenvalues, and comprise the determinant of the overall stiffness matrix Kn and the determinants which result, with negligible extra computation, from effectively considering all except the last m (m=1, 2,…, n-1) freedoms to which Kn corresponds as internal substructure freedoms. Tests showed time savings compared to bisection of 31 per cent when finding non-coincident eigenvalues to relative accuracy ∊ = 10-4, increasing to 62 per cent when ∊ = 10-8. The tests also showed time savings of about 10 per cent compared with an earlier Newtonian approach. The method requires no derivatives and its use in the widely available space frame program BUNVIS-RG has demonstrated how easily it can replace bisection, which was used in the earlier program BUNVIS.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260810
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