Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity. Issue 1 (14th December 2021)

• Record Type: Journal Article
• Authors: Baumann, Phillip; Sturm, Kevin
• Is Part Of: Engineering computations. Volume 39:Issue 1(2022)
• Page Start: 60
• Page End: 114
• Publication Date: 2021-12-14
• Subjects: Topological derivative -- Topology optimisation -- Elasticity; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-07-2021-0407
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals. Design/methodology/approach: The authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model. Findings: The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method. Originality/value: In contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.