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Damage identification in plate structures based on the topological derivative method

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Abstract

In this work, a novel approach for solving a damage identification problem in plate structures based on the topological derivative method is proposed. The forward problems are governed by the elastodynamic Kirchhoff and Reissner–Mindlin plate bending models in the frequency domain. The inverse problem consists in finding a set of damages from pointwise domain measurements of the plate displacement field. The damage is represented by a variation in the plate thickness, which is assumed to be given by a piecewise constant function. A shape functional measuring the misfit between the available data (measurements) and the displacements computed from the model is minimized with respect to the geometrical support of the unknown damage distribution, by using the topological derivative method. Finally, some numerical experiments are presented, showing different features of the proposed approach in detecting and locating damages of varying sizes and shapes by taking into account noisy data.

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Acknowledgements

This research was partly supported by CNPq (Brazilian Research Council), CAPES (Brazilian Higher Education Staff Training Agency), and FAPERJ (Research Foundation of the State of Rio de Janeiro). These financial support are gratefully acknowledged. We would like also to thanks the referees for the impressive and nice comments that strongly contribute to improve the final version of the manuscript.

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  1. Laboratório Nacional de Computação Científica LNCC/MCTI, Coordenação de Métodos Matemáticos e Computacionais, Av. Getúlio Vargas 333, Petrópolis, RJ, 25651-075, Brazil

    A. A. M. da Silva & A. A. Novotny

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  1. A. A. M. da Silva
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  2. A. A. Novotny
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Correspondence to A. A. Novotny.

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da Silva, A.A.M., Novotny, A.A. Damage identification in plate structures based on the topological derivative method. Struct Multidisc Optim 65, 7 (2022). https://doi.org/10.1007/s00158-021-03145-1

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