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  • 1
    Electronic Resource
    Electronic Resource
    Control of spurious modes in the nine-node quadrilateral element (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1576-1580 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nine-node quadrilateral is much more accurate than its eight-node relative if elements are non-rectangular. However, the nine-node element may display spurious low-energy modes under 2 × 2 Gauss quadrature. These modes can be controlled by using the 3 × 3 quadrature rule, but at added cost. This paper investigates two inexpensive control devices that can be used with 2 × 2 Gauss quadrature.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181012
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  • 2
    Electronic Resource
    Electronic Resource
    Remarks about diagonal mass matrices (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1427-1429 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170910
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  • 3
    Electronic Resource
    Electronic Resource
    Loubignac's iterative method in finite element elastostatics (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 67-75 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element models provide only approximate results under most loadings. A beam modelled by constant-strain triangles and loaded by pure moment is a case in point. Yet if the iterative method advanced by Loubignac et al.1 is applied to this model, the exact stress field will be generated. The iterative method derives from a parent formulation that can be solved without iteration.2 As shown in this paper, the parent formulation contains the sum of two stiffness matrices. One is produced by the customary finite element shape functions. The other is produced by finite difference expressions for strain gradients that are not contained in the shape functions.Loubignac's method produces a stress field that is continous across interelement boundaries. Other methods that seek to impose interelement continuity are noted in the concluding section.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180106
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical methods for partial differential equations based on power series (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 739-755 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Stable difference schemes that approximate partial differential equations to any desired order are generated by means of power series. The method is demonstrated on the one-dimensional heat equation and the stability is studied in detail. Stability analyses are then presented for parabolic linear equations with constant coefficients. A nonlinear example is presented which indicates the efficiency of the higher ordered schemes.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190508
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