Work

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

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12172762

Authors: Fernando Soares Carvalho, Carla Tatiana Mota Anflor

Institutions: Universidade Federal do Tocantins, Universidade de Brasília

Language: English

Topic: Topology Optimization in Engineering

Subfield: Civil and Structural Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

OpenAlex ID: W4402315846

FWCI:

Cites: 16

Cited by:

Related to: 10