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

Fernando Soares Carvalho () and Carla Tatiana Mota Anflor
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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

Mathematics, 2024, vol. 12, issue 17, 1-20

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.

Keywords: optimal design of plane structures; topological derivative; first eigenvalue maximization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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