An introduction to the topological derivative. Issue 1 (28th September 2021)

• Record Type: Journal Article
• Authors: Amstutz, Samuel
• Is Part Of: Engineering computations. Volume 39:Issue 1(2022)
• Page Start: 3
• Page End: 33
• Publication Date: 2021-09-28
• Subjects: Topology optimization -- Topological derivative -- Shape optimization; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-07-2021-0433
• Languages: English
• ISSNs: 0264-4401

Abstract

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.