An introduction to the topological derivative
ISSN: 0264-4401
Article publication date: 28 September 2021
Issue publication date: 1 February 2022
Abstract
Purpose
This paper provides a self-contained introduction to the mathematical aspects of the topological derivative.
Design/methodology/approach
Full justifications are given on simple model problems following a modern approach based on the averaged adjoint state technique. Extensions are discussed in relation with the literature on the field.
Findings
Closed expressions of topological derivatives are obtained and commented.
Originality/value
Several cases are covered in a unified and didactic presentation. Some elements of proof are novel.
Keywords
Acknowledgements
The author benefited from the supports of the chair “Modeling advanced polymers for innovative material solutions” led by the Ecole polytechnique and the Fondation de l’Ecole polytechnique and sponsored by Arkema, and of the project ANR-18-CE40-0013 SHAPO financed by the Agence Nationale de la Recherche.
Citation
Amstutz, S. (2022), "An introduction to the topological derivative", Engineering Computations, Vol. 39 No. 1, pp. 3-33. https://doi.org/10.1108/EC-07-2021-0433
Publisher
:Emerald Publishing Limited
Copyright © 2021, Emerald Publishing Limited