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Topological Derivative-Based Topology Optimization of Plate Structures Under Bending Effects

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Abstract

In this work, the topological derivatives of L2 and energy norms associated with the solution to Kirchhoff and Reissner-Mindlin plate bending models are introduced. Based on existing theoretical results, closed forms of the sensitivities are presented. A zero-order term is introduced in the equilibrium equations, which allows for adapting the obtained sensitivities to the context of topology optimization of plates under elastic support and free vibration condition as well. The resulting analytical formulae are used together with a level-set domain representation method to devise a simple topology design algorithm. Several finite element-based representative numerical experiments are presented showing its applications to the compliance minimization and eigenvalue maximization of Kirchhoff as well as Reissner-Mindlin plate structures under bending effects.

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Funding

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).

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Authors and Affiliations

  1. Group of Experimental and Computational Mechanics, University of Brasilia, Gama, Brazil

    F. S. Carvalho, D. Ruscheinsky & C. T. M. Anflor

  2. Facultad Regional Córdoba UTN-FRC / CONICET, Universidad Tecnológica Nacional, Maestro M. López esq. Cruz Roja Argentina, X5016ZAA, Córdoba, Argentina

    S. M. Giusti

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

    A. A. Novotny

Authors
  1. F. S. Carvalho
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  2. D. Ruscheinsky
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  3. S. M. Giusti
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  4. C. T. M. Anflor
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  5. A. A. Novotny
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Correspondence to C. T. M. Anflor.

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Responsible Editor: Palaniappan Ramu

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Carvalho, F.S., Ruscheinsky, D., Giusti, S.M. et al. Topological Derivative-Based Topology Optimization of Plate Structures Under Bending Effects. Struct Multidisc Optim 63, 617–630 (2021). https://doi.org/10.1007/s00158-020-02710-4

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  • DOI: https://doi.org/10.1007/s00158-020-02710-4

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