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The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures

Author

Listed:
  • Fernando Soares Carvalho

    (Department of Mathematics, Federal University of Tocantins, Palmas 77650-000, Brazil)

  • Carla Tatiana Mota Anflor

    (Group of Experimental and Computational Mechanics, University of Brasilia, Brasilia 70910-900, Brazil
    Arraias 77330-000, Brazil.)

Abstract

This paper presents the topological derivative of the first eigenvalue for the free vibration model of plane structures. We conduct a topological asymptotic analysis to account for perturbations in the domain caused by inserting a small inclusion. The paper includes a rigorous derivation of the topological derivative for the eigenvalue problem along with a proof of its existence. Additionally, we provide numerical examples that illustrate the application of the proposed methodology for maximizing the first eigenvalue in plane structures. The results demonstrate that multiple eigenvalues were not encountered.

Suggested Citation

  • Fernando Soares Carvalho & Carla Tatiana Mota Anflor, 2024. "The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures," Mathematics, MDPI, vol. 12(17), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2762-:d:1472820
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    References listed on IDEAS

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    1. Samuel Amstutz, 2011. "Augmented Lagrangian for cone constrained topology optimization," Computational Optimization and Applications, Springer, vol. 49(1), pages 101-122, May.
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