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- Title
The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures.
- Authors
Carvalho, Fernando Soares; Anflor, Carla Tatiana Mota
- 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.
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 17, p2762
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12172762