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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1505-1520 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
    Additional Material: 9 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Zeitschrift für anorganische Chemie 486 (1982), S. 136-146 
    ISSN: 0044-2313
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Dichlorophosphato Complexes of Tin, Titanium, and Molybdenum. Crystal Structure of (AsPh4)2[MoOCl3(PO2Cl2)]2The dichlorophosphate complexes (AsPh4)2[SnCl4(PO2Cl2)]2 (I), (AsPh4)2[TiCl4(PO2Cl2)]2 (II) and (AsPh4)2[MoOCl3(PO2Cl2)]2 (III) are prepared by the reactions of SnCl4, TiCl4, and MoCl5, respectively, with AsPh4[PO2Cl2] in dichlormethan solutions. According to their i.r. spectra, the complex anions form dimeric species via the oxygen atoms of the dichlorophosphate groups; the 119Sn Mössbauer spectra of I are reported in addition. The crystal structure of III is solved by X-ray diffraction methods and refined to R = 4.3%. (AsPh4)2[MoOCl3(PO2Cl2)]2 crystallizes in the triclinic space group P1 with one formula unit pro unit cell. The structure consists of tetraphenylarsonium cations and centrosymmetric anions [MoOCl3(PO2Cl2)]22⊖. The molybdenum atoms of the anions are linked via the O atoms of the dichlorophosphate groups forming nonplanar Mo2O4P2 eight-membered rings.
    Notes: Die Dichlorphosphato-Komplexe (AsPh4)2[SnCl4(PO2Cl2)]2 (I), (AsPh4)2[TiCl4(PO2Cl2)]2 (II) und (AsPh4)2[MoOCl3(PO2Cl2)] 2 (III) werden aus SnCl4, TiCl4 bzw. MoCl5 mit AsPh4[PO2Cl2] in Dichlormethanlösung hergestellt. Nach den Schwingungsspektren sind die komplexen Anionen über die O-Atome der Dichlorphosphatgruppen zu Dimeren assoziiert; für I wird zusätzlich das 119Sn-Mößbauer-Spektrum mitgeteilt. Die Kristallstruktur von III wurde mittels Röntgenbeugung ermittelt und bis R = 4,3% verfeinert. (AsPh4)2[MoOCl3(PO2Cl2)]2 kristallisiert triklin in der Raumgruppe P1 mit einer Formeleinheit pro Elementarzelle. Die Struktur besteht aus Tetraphenylarsoniumkationen und zentrosymmetrischen Anionen [MoOCl3(PO2Cl2)]22⊖. Die Molybdänatome der Anionen sind über die O-Atome der Dichlorphosphatgruppe zu einem gewellten Mo2O4P2 Achtring verknüpft. Die äquatorial angeordneten, terminalen Oxoliganden (r MoO = 166 pm) üben auf die Mo—O-Bindungen der Dichlorphosphatliganden einen starken trans-Effekt aus, so daß sich zwei verschiedene Mo—O-Bindungsabstände von 227 bzw. 210 pm ergeben.
    Additional Material: 2 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 115 (1982), S. 3436-3443 
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Synthese und Reaktionsfähigkeit von 2-Aroylbenzoesäuren, II. 2-(4-Hydroxy-3-isopropylbenzoyl)benzoesäureDie Friedel-Crafts-Acylierung von 2-Isopropylphenol mit Phthalsäureanhydrid liefert nur die 2-(4-Hydroxy-3-isopropylbenzoyl)benzoesäure (1) vom p-Acylphenol-Typ. Die Reaktionsfähigkeit der Säure 1 wurde untersucht, und ihre Derivate 2-10 werden beschrieben.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 99-109 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two highly accurate implicit Padé approximations to the transient heat conduction equation are investigated using the conjugate gradient method to solve, for the temperatures. The accuracy and stability of the approximations are discussed and numerical examples are presented showing the relative performance. Comparisons with the Crank-Nicolson method are also presented.
    Additional Material: 4 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 967-979 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, efficient and economical numerical technique for the analysis of shallow shells-of arbitrary shape is presented. The technique is based upon the method of constant-deflection contours combined with the well-known finite element method. In the proposed method the elemental stiffness matrix is derived from a system of two consistent partial differential equations for two scalar functions using Galerkin's method. Several representative examples are included to indicate the effectiveness of the method.
    Additional Material: 6 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1829-1854 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time-dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.
    Additional Material: 12 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 591-607 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To account for plastic deformation in plate and shell structures an elasto-viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time-dependent elasto-viscoplastic situations and by allowing steady-state conditions to be reached, elasto-plastic problems can also be considered.For the large displacement elasto-viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization.The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources where available.
    Additional Material: 13 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 675-685 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The position, size and surface temperature of circular holes inside a two-dimensional heat conductor are optimized to produce a minimum variation in surface temperature over a portion of the outer boundary. This problem, whic arises in thermal desing of moulds and dies, resembles those encountered in structural shape optimization because the internal geometry of the heat conductor depends on the design variables. In this paper, some of the traditional difficulties associated with shape optimization are overcome by analysing steady heat conduction with a special boundary integral method developed for two-dimensional regions with circular hole. This approach eliminates the need to regenerate a finite element mesh over the interior of the region each time the geometry is changed during the design process. It also increases the efficiency of the analysis by reducing the number of unknowns in the numerical discretization of the region. Since the objective function depends only on the boundary temperatures, there is no need to determine temperatures in the interior.The analysis method is applied to two problems arising in optimal thermal design of compression moulds. These examples show that the number of holes choson for the design strongly affects their resulting optimal arrangement as well as the ultimate uniformity of the cavity surface temperature.
    Additional Material: 5 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1801-1820 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Fourier series solution is presented for a system of first-order partial differential equations which describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. A central step in the method for solving the system of equations is to combine a complementary function with a particular solution of the system in order to satisfy the boundary conditions. The complementary function is the sum of two series. The terms of the first series are products of a Fourier term in one space variable with the solution of an eigenvalue problem in the other space variable. The second series is similar and comes from reversing the roles of the space variables.
    Additional Material: 9 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1587-1600 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element procedure for calculating stress intensity factors in elastic crack problems is developed. In common with a number of other approaches in the literature, the procedure combines the analytical singular fields present in a problem with a finite element treatment of the residual regular problem. What distinguishes the procedure is the use of path-independent integrals to balance the analytical and numerical contributions. A set of test problems with exact solutions is analysed and demonstrates that the procedure is readily implemented and can accurately evaluate stress intensity factors with a modest amount of computational effort. The application of two competing methods to the test problems further demonstrates that the new procedure is markedly superior in both its initial accuracy and its rate of convergence. The paper concludes with two additional illustrations of the procedure as applied to the single-edge crack and the centre crack; these also yield accurate results for little computational effort.
    Additional Material: 4 Ill.
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