Automated shape differentiation in the Unified Form Language

Ham, David A.; Mitchell, Lawrence; Paganini, Alberto; Wechsung, Florian

doi:10.1007/s00158-019-02281-z

Automated shape differentiation in the Unified Form Language

Ham, David A.; Mitchell, Lawrence; Paganini, Alberto; Wechsung, Florian

Authors

David A. Ham

Lawrence Mitchell

Alberto Paganini

Florian Wechsung

Abstract

We discuss automating the calculation of weak shape derivatives in the Unified Form Language (JAMA 40(2):9:1–9:37 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes Gâteaux derivatives with respect to the coordinate field. We illustrate the ease of use with several examples.

Citation

Ham, D. A., Mitchell, L., Paganini, A., & Wechsung, F. (2019). Automated shape differentiation in the Unified Form Language. Structural and Multidisciplinary Optimization, 60(5), 1813-1820. https://doi.org/10.1007/s00158-019-02281-z

Journal Article Type	Article
Acceptance Date	Apr 9, 2019
Online Publication Date	Aug 2, 2019
Publication Date	Nov 30, 2019
Deposit Date	Aug 29, 2018
Publicly Available Date	Aug 6, 2019
Journal	Structural and Multidisciplinary Optimization
Print ISSN	1615-147X
Electronic ISSN	1615-1488
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	60
Issue	5
Pages	1813-1820
DOI	https://doi.org/10.1007/s00158-019-02281-z
Related Public URLs	https://arxiv.org/pdf/1808.08083.pdf

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Advance online version © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.