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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2012, Volume 15, Number 2, Pages 165–174 (Mi sjvm467)  
This article is cited in 13 scientific papers (total in 13 papers)

Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition

A. Burelab, S. Impérialea, P. Jolya

a POEMS, UMR 7231, CNRS-ENSTA-INRIA, INRIA, Le Chesnay, France
b Université Paris-Sud XI, Laboratoire d'Analyse Numérique, Orsay, France
Full-text PDF (568 kB) Citations (13)
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Abstract: In this article, elastic wave propagation in a homogeneous isotropic elastic medium with a rigid boundary is considered. A method based on the decoupling of pressure and shear waves via the use of scalar potentials is proposed. This method is adapted to a finite element discretization, which is discussed. A stable, energy preserving numerical scheme is presented, as well as 2D numerical results.
Key words: elastic wave propagation, vector potentials, finite elements, clamped boundary condition.
Received: 24.10.2011
English version:
Numerical Analysis and Applications, 2012, Volume 5, Issue 2, Pages 136–143
DOI: https://doi.org/10.1134/S1995423912020061
Bibliographic databases:
Document Type: Article
MSC: 35L05, 35L20,65N30
Language: Russian
Citation: A. Burel, S. Impériale, P. Joly, “Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition”, Sib. Zh. Vychisl. Mat., 15:2 (2012), 165–174; Num. Anal. Appl., 5:2 (2012), 136–143
Citation in format AMSBIB
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\by A.~Burel, S.~Imp\'eriale, P.~Joly
\paper Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
\issue 2
\pages 165--174
\mathnet{http://mi.mathnet.ru/sjvm467}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 2
\pages 136--143
\crossref{https://doi.org/10.1134/S1995423912020061}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862127600}
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  • https://www.mathnet.ru/eng/sjvm467
  • https://www.mathnet.ru/eng/sjvm/v15/i2/p165
    • This publication is cited in the following 13 articles:
    1. Silvia Falletta, Matteo Ferrari, Letizia Scuderi, “A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials”, Journal of Computational and Applied Mathematics, 441 (2024), 115625  crossref
    2. S. Falletta, G. Monegato, L. Scuderi, INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022, 3094, INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022, 2024, 220005  crossref
    3. Can Ulaş Doğruer, Can Barış Toprak, Bora Y{\i}ld{\i}r{\i}m, “Advancing Modal Analysis of Mechanical Linkages via Differential Algebraic Equations”, Politeknik Dergisi, 28:1 (2024), 159  crossref
    4. J. Albella, R. Rodríguez, P. Venegas, “Numerical approximation of a potentials formulation for the elasticity vibration problem”, Computers & Mathematics with Applications, 137 (2023), 61  crossref
    5. Silvia Falletta, Giovanni Monegato, Letizia Scuderi, “An overview on a time discrete convolution—space collocation BEM for 2D exterior wave propagation problems”, Ann Univ Ferrara, 68:2 (2022), 311  crossref
    6. S. Falletta, G. Monegato, L. Scuderi, “Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains”, Computers & Mathematics with Applications, 114 (2022), 132  crossref
    7. Akram Beni Hamad, Geoffrey Beck, Sébastien Imperiale, Patrick Joly, “An Efficient Numerical Method for Time Domain Electromagnetic Wave Propagation in Co-axial Cables”, Computational Methods in Applied Mathematics, 22:4 (2022), 861  crossref
    8. Alessandra Aimi, Giulia Di Credico, Mauro Diligenti, Chiara Guardasoni, “Highly accurate quadrature schemes for singular integrals in energetic BEM applied to elastodynamics”, Journal of Computational and Applied Mathematics, 410 (2022), 114186  crossref
    9. Albella Martinez J., Imperiale S., Joly P., Rodriguez J., “Numerical Analysis of a Method For Solving 2D Linear Isotropic Elastodynamics With Traction Free Boundary Condition Using Potentials and Finite Elements”, Math. Comput., 90:330 (2021), 1589–1636  crossref  mathscinet  isi  scopus
    10. Falletta S., Monegato G., Scuderi L., “Two Boundary Integral Equation Methods For Linear Elastodynamics Problems on Unbounded Domains”, Comput. Math. Appl., 78:12 (2019), 3841–3861  crossref  mathscinet  isi  scopus
    11. Albella Martinez J., Imperiale S., Joly P., Rodriguez J., “Solving 2D Linear Isotropic Elastodynamics By Means of Scalar Potentials: a New Challenge For Finite Elements”, J. Sci. Comput., 77:3, SI (2018), 1832–1873  crossref  mathscinet  zmath  isi  scopus
    12. R. Kolman, S. S. Cho, K. C. Park, “Efficient implementation of an explicit partitioned shear and longitudinal wave propagation algorithm”, Int. J. Numer. Methods Eng., 107:7 (2016), 543–579  crossref  isi
    13. Chabassier J., Imperiale S., “Stability and Dispersion Analysis of Improved Time Discretization for Simply Supported Prestressed Timoshenko Systems. Application to the Stiff Piano String”, Wave Motion, 50:3 (2013), 456–480  crossref  mathscinet  isi  scopus
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