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Analysis of the Problem of Harmonic Waves in Elastic Bodies and its h-Adaptive Finite-Element Approximation

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We formulate a variational problem for harmonic waves in a viscoelastic body with short-term memory generated by distributed loads of a given frequency. The conditions of its well-posedness and equivalence to the saddle-point problem for the corresponding Lagrangian are established. We construct an h -adaptive scheme of the finite-element method for the solution of the formulated problem with an a posteriori error estimator determined element by element and a criterion for the local improvement of Delaunay triangulations used for the evaluation of approximations with prescribed accuracy. The efficiency of the proposed methods is illustrated by an example of numerical investigation of the resonance frequencies of a square plate containing a square hole.

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Authors and Affiliations

  1. I. Franko National University of Lviv, Lviv, Ukraine

    H. А. Kvasnytsia & H. А. Shynkarenko

  2. Opole University of Technology, Opole, Poland

    H. А. Shynkarenko

Authors
  1. H. А. Kvasnytsia
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  2. H. А. Shynkarenko
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Correspondence to H. А. Kvasnytsia.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 52–64, January–March, 2020.

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Kvasnytsia, H.А., Shynkarenko, H.А. Analysis of the Problem of Harmonic Waves in Elastic Bodies and its h-Adaptive Finite-Element Approximation. J Math Sci 270, 59–75 (2023). https://doi.org/10.1007/s10958-023-06332-1

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  • DOI: https://doi.org/10.1007/s10958-023-06332-1

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