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  • 1
    Electronic Resource
    Electronic Resource
    Effective hybrid hierarchical element generator for vibration analysis of plates (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1615-1628 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Cost effective high precision hybrid elements are presented in a hierarchical form for vibration analysis of plates. The elements are constructed by introducing computer installed hierarchical element generator algorithms which take advantage of the exact analytical treatment of the energy integrals automatically. Additional benefits accrue from: (i) the careful selection of assumed stresses and displacements satisfying finite element requirements, and maintaining the correct stiffness rank and invariance; (ii) the ability to reduce computational costs associated with various operations and the independence with respect to element geometries, which serve to build up a methodology to handle the generation of finite elements in any general purpose finite element system efficiently. Extensive numerical studies are made to predict the natural frequencies and harmonic response of plates with different boundary conditions. Accuracy of the solutions is assessed by comparison with the well established results. The noteworthy aspects of the applications are that the proposed elements are faster than those cited previously, and show a more favourable comparison to the analytical solutions for a wider range of vibration modes by maintaining rapid convergence characteristics.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240902
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Oscillatory integrals by Hermite interpolatory rules (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 463-470 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the numerical construction of Hermite interpolatory product integration rules at arbitrarily prescribed nodes. The heart of the computational scheme is the efficient construction of Hermite functions of any order for any set of points. For the purpose of illustration, quadrature formulae based on the use of Basu. Clenshaw, Filippi, Filon and Polyá nodes are generated for oscillatory integrals. Of the nodes considered. Basu nodes yield the most accurate results in the interesting case of rapid oscillations, while Filippi nodes give rise to efficient common-point quadrature rules when the integrand has slight oscillations. The results also demonstrate that Hermite rules compare well with the Lagrange quadrature for the same number of function evaluations.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020503
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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