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

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 topo...

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Bibliographic Details
Published in:Mathematics
Main Authors: Fernando Soares Carvalho, Carla Tatiana Mota Anflor
Format: Article
Language:English
Published: MDPI AG 2024-09-01
Subjects:
optimal design of plane structures
topological derivative
first eigenvalue maximization
Online Access:https://www.mdpi.com/2227-7390/12/17/2762
Description
Summary: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.
ISSN:2227-7390

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