Abstract
The paper describes the extension of existing mapped infinite wave theory, (or unconjugated infinite element theory) to deal with non-circular meshes of infinite elements. The method is illustrated by results for the diffraction of waves by an elliptical cylinder. The waves are governed by Helmholtz equation, and the Sommerfeld radiation condition. The two main aspects are:
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(i)
The extension of the existing theory of infinite wave elements (which should also be applicable to wave envelope, or conjugated elements) to the case when the elements are not placed strictly radially. This involves modifications to the element theory, which are given below.
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(ii)
An example of the results for an elliptical cylinder diffraction problem, and comparison with analytical solution.
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References
Bettess, P., 1992, Infinite Elements,Penshaw Press, Sunderland, U.K., ISBN 0–9518806–0–8.
Astley, R.J., Bettess, P. and Clark, P.J., 1991, Letter to the editor concerning Zienkiewicz et al. (1985), Int. Journ. Num. Meth. Engng., Vol. 32, pp 207–209.
Astley, R. J. Macaulay G. J. and Coyette J. P., 1994, `Mapped Wave Envelope Elements for Acoustical Radiation and Scattering’, Journal of Sound and Vibration, 170 (1), pp 97–118.
Cremers, L. Fyfe K. R. and Coyette J. P., 1994, `A Variable Order Infinite Acoustic Wave Envelope Element’, Journal of Sound and Vibration, 171 (4), pp 483–508.
Bettess, P. and Zienkiewicz, O.C., 1977, “Diffraction and refraction of surface waves using finite and infinite elements”, Int. J. Num. Meth. Eng., Vol. 11, pp. 1271–1290.
Bettess, P., Emson, C.R.I. and Chiam, T.C., 1984, “A New Mapped Infinite Element for Exterior Wave Problems”, Chapter 17 of Numerical Methods in Coupled Systems, eds R. W. Lewis, P. Bettess and E. Hinton, John Wiley, Chichester.
Zienkiewicz, O.C. and Bettess, P., 1975, “Infinite elements in the study of fluid structure interaction problems”, Proc. 2nd Int. Symp. on Comp. Methods Appl. Sci.,Versailles, also published in Lecture Notes in Physics, Vol. 58, Eds. J.Ehlers et al.,Springer-Verlag, Berlin, 1976.
Zienkiewicz, O.C., Bettess, P. and Kelly, D.W., 1978, “The Finite Element Method for Determining Fluid Loadings on Rigid Structures: Two-and Three- Dimensional Formulations”, Chapter 4 of Numerical Methods in Offshore Engineering, Eds. O. C. Zienkiewicz, R. W. Lewis and K. G. Stagg, pp 141–183, John Wiley.
Zienkiewicz, O.C. and Bettess, P., 1978, “Fluid Structure Interaction ”, Chapter 5 of Numerical Methods in Offshore Engineering, Eds. O. C. Zienkiewicz, R. W. Lewis and K. G. Stagg, John Wiley.
Zienkiewicz, O.C., Bettess, P., Chiam, T.C. and Emson, C.R.I., 1981, “Numerical methods for unbounded field problems and a new infinite element formulation”, ASME, AMD, Vol. 46, pp. 115–148, New York.
Zienkiewicz, O.C., Emson, C.R.I. and Bettess, P., 1983, “A novel boundary infinite element”, Int.J. Num. Meth. Eng., Vol. 19, pp. 393–404.
Zienkiewicz, O.C., Bando, K., Bettess, P., Emson, C.R.I. and Chiam, T.C., 1985, “Mapped Infinite Elements for Exterior Wave Problems”, Int. J. Num. Meth. Eng., Vol. 21, pp. 1229–1251.
Burnett, D.S., 1994, “A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion”, Journal of the Acoustical Society of America, Vol. 95(5), pp. 2798–2816.
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Bettess, J.A., Bettess, P. (1998). New Mapped Wave Infinite Element and Diffraction of Waves by Elliptical Cylinders of Varying Aspect Ratio. In: Geers, T.L. (eds) IUTAM Symposium on Computational Methods for Unbounded Domains. Fluid Mechanics and Its Applications, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9095-2_4
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DOI: https://doi.org/10.1007/978-94-015-9095-2_4
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