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Transient dynamic analysis of generally anisotropic materials using the boundary element method

Acta Mechanica volume 229, pages 1893–1910 (2018)Cite this article

Abstract

This work presents the use of an explicit-form Green’s function for 3D general anisotropy in conjunction with the dual reciprocity boundary element method and the radial integration method to analyse elastodynamic problems using BEM. The latter two schemes are to treat the inertial loads in the time-domain formulation of the dynamic problem. The direct analysis with the Houbolt’s algorithm is used to perform the transient analysis. The efficient and accurate computation of the fundamental solutions has been a subject of great interest for 3D general anisotropic materials due to their mathematical complexity. A recently proposed scheme based on double Fourier series representation of these solutions is used to this end. Numerical examples are presented to demonstrate the feasibility and successful implementation of applying these schemes in synthesis to treat 3D elastodynamic problems of anisotropic materials.

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Acknowledgements

The authors would like to thank the Center for Computational Engineering and Sciences (CCES-CEPID/UNICAMP) and the National Center for High Performance Computing in São Paulo (CENAPAD-SP) for the support of computational facilities. Also to the São Paulo Research Foundation (FAPESP) Grant No. 2015/22199-9 and the National Council for the Scientific and Technological Development (CNPq) Grant No. 54283/2014-2 for the financial support of this research.

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Author notes

  1. R. Q. Rodríguez

    Present address: School of Civil Engineering, State University of Mato Grosso Campus Tangará da Serra, Tangará da Serra, MT, 78300-000, Brazil

Authors and Affiliations

  1. Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas, Campinas, SP, 13083-860, Brazil

    R. Q. Rodríguez, A. F. Galvis & P. Sollero

  2. Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON, K1S 5B6, Canada

    C. L. Tan

  3. Department of Mechanical Engineering, Faculty of Technology, University of Brasilia, Brasília, DF, 70910-900, Brazil

    E. L. Albuquerque

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  1. R. Q. Rodríguez
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  2. A. F. Galvis
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  3. P. Sollero
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  4. C. L. Tan
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  5. E. L. Albuquerque
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Correspondence to P. Sollero.

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Rodríguez, R.Q., Galvis, A.F., Sollero, P. et al. Transient dynamic analysis of generally anisotropic materials using the boundary element method. Acta Mech 229, 1893–1910 (2018). https://doi.org/10.1007/s00707-018-2108-4

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  • DOI: https://doi.org/10.1007/s00707-018-2108-4