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  • 1
    Electronic Resource
    Electronic Resource
    IMPLEMENTING MULTIPLE BOUNDARY CONDITIONS IN THE DQ SOLUTION OF HIGHER-ORDER PDEs: APPLICATION TO FREE VIBRATION OF PLATES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1237-1258 
    Details
    ISSN: 0029-5981
    Keywords: differential quadrature method ; numerical solution methods ; higher-order partial differential equations ; multiple boundary conditions ; free vibration ; rectangular plates ; thin plate theory ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the context of the free vibration problem of rectangular plates, this paper develops a detailed methodology for implementing multiple boundary conditions in the differential quadrature solutions of higher-order differential equations. It is explained that a certain type of boundary conditions can be built into the differential quadrature weighting coefficients themselves. This simplifies the programming of the differential quadrature solution algorithms. More importantly, however, as shown by the results of fundamental frequencies of a wide spectrum of rectangular plate configurations, the methodology results in strikingly accurate differential quadrature solutions.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Improved approximate methods for analysising steady heat conduction (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 587-592 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved version of the Rayleigh techinique used by Rayleigh and Schmidt for solid mechanics problems is extended to one- and two-dimensional problems of steady heat conduction. Here the technique is applied to the heat-balance integral (HBI) method, the variational method and the square-error method. To determine the most appropriate value of the non-integer exponent, either one of two different criteria is used: the variational or the square-error integral. Thus, four new methods are considered. A comparison with a closed-form solution is made for a one-dimensional fin. It is demonstrated that the error for a one-term trial function is much less for an improved HBI method with the variational integral criterion. Thus, additional terms should not be needed in most instances. Excellent results are also achieved by using one of the new methods in a two-dimensional problem with internal heat generation.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020606
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