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Nonlinear Spectral Finite Element Model for Analysis of Wave Propagation in Solid with Internal Friction and Dissipation

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Book cover Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2668))

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Abstract

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, INDIA

    D. Roy Mahapatra & S. Gopalakrishnan

Authors
  1. D. Roy Mahapatra
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  2. S. Gopalakrishnan
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  3. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  4. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  5. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

  6. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Mahapatra, D.R., Gopalakrishnan, S. (2003). Nonlinear Spectral Finite Element Model for Analysis of Wave Propagation in Solid with Internal Friction and Dissipation. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44843-8_81

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  • DOI: https://doi.org/10.1007/3-540-44843-8_81

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40161-2

  • Online ISBN: 978-3-540-44843-3

  • eBook Packages: Springer Book Archive

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