Computational Science and Its Applications — ICCSA 2003
Volume 2668 of the series Lecture Notes in Computer Science pp 745754
Nonlinear Spectral Finite Element Model for Analysis of Wave Propagation in Solid with Internal Friction and Dissipation
 D. Roy MahapatraAffiliated withDepartment of Aerospace Engineering, Indian Institute of Science
 , S. GopalakrishnanAffiliated withDepartment of Aerospace Engineering, Indian Institute of Science
Abstract
A geometrically nonlinear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study nonlinear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to nonlinear 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.
 Title
 Nonlinear Spectral Finite Element Model for Analysis of Wave Propagation in Solid with Internal Friction and Dissipation
 Book Title
 Computational Science and Its Applications — ICCSA 2003
 Book Subtitle
 International Conference Montreal, Canada, May 18–21, 2003 Proceedings, Part II
 Pages
 pp 745754
 Copyright
 2003
 DOI
 10.1007/3540448438_81
 Print ISBN
 9783540401612
 Online ISBN
 9783540448433
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2668
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Vipin Kumar ^{(4)} ^{(5)}
 Marina L. Gavrilova ^{(6)}
 Chih Jeng Kenneth Tan ^{(7)} ^{(8)}
 Pierre L’Ecuyer ^{(9)}
 Editor Affiliations

 4. Army High Performance Computing Research Center
 5. Department of Computer Science and Engineering, University of Minessota
 6. Department of Computer Science, University of Calgary
 7. Heuchera Technologies Inc.
 8. School of Computer Science, The Queen’s University of Belfast
 9. Département d’informatique et de recherche opérationelle, Université de Montréal
 Authors

 D. Roy Mahapatra ^{(10)}
 S. Gopalakrishnan ^{(10)}
 Author Affiliations

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