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The meshless finite point method for transient elastodynamic problems

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Abstract

In this paper, the application of the meshless finite point method (FPM) to solve elastodynamic problems through an explicit velocity–Verlet time integration method is investigated. Strong form-based methods, such as the FPM, are generally less stable and accurate in terms of satisfaction of Neumann boundary conditions than weak form-based methods. This is due to the fact that in such types of methods, Neumann boundary conditions must be imposed by a series of equations which are different from the governing equations in the problem domain. In this paper, keeping all the advantages of FPM in terms of simplicity and efficiency, a new simple strategy for proper satisfaction of Neumann boundary conditions in time for elastodynamic problems is investigated. The method is described in detail, and several numerical examples are presented. Moreover, the accuracy of the method with reference to the solution of some 3D problems is discussed.

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Acknowledgements

The support of the ‘Visiting Scientist’ scheme of Padua university is gratefully acknowledged.

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Authors and Affiliations

  1. Industrial Engineering Department, University of Padova, v. Venezia 1, 35131, Padua, Italy

    Arman Shojaei, Mirco Zaccariotto & Ugo Galvanetto

  2. Center of Studies and Activities for Space (CISAS)-“G. Colombo”, v. Venezia 15, 35131, Padua, Italy

    Arman Shojaei, Mirco Zaccariotto & Ugo Galvanetto

  3. Department of Civil Engineering, University of Isfahan, Isfahan, 81744-73441, Iran

    Farshid Mossaiby

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  1. Arman Shojaei
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  2. Farshid Mossaiby
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  3. Mirco Zaccariotto
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  4. Ugo Galvanetto
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Correspondence to Farshid Mossaiby.

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Shojaei, A., Mossaiby, F., Zaccariotto, M. et al. The meshless finite point method for transient elastodynamic problems. Acta Mech 228, 3581–3593 (2017). https://doi.org/10.1007/s00707-017-1894-4

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  • DOI: https://doi.org/10.1007/s00707-017-1894-4

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