Fail-safe optimization concerning partial damage—a comparison of rigid plastic and linear elastic material models

Abstract

Existing studies on stress-constrained fail-safe optimization concerning partial damage with elastic material models have shown that the partial degradation of a member may cause a worse objective function than complete removal. This brief note compares the results of a simple formulation using a rigid plastic material with those of the existing elastic problem, using a three-bar example as an illustration. It is demonstrated that the plastic formulation resolves the singularity issues, and the underlying characteristics of both formulations can be understood from both a mathematical and an intuitive engineering perspective. As well as remaining continuous at complete damage, plastic load redistribution enables optimum volumes to be 80% lower than the elastic optimum in cases approaching complete damage. Investigations into the workings of the problems unveil their inherent strengths and weaknesses, and thus areas for future improvement.

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Item Type:	Article
Authors/Creators:	Whiteside, E.A. Fairclough, H.E. https://orcid.org/0000-0003-3133-1534 Rigby, S.E.
Copyright, Publisher and Additional Information:	© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords:	Fail-safe optimization; Partial damage; Disproportionate collapse; Size optimization
Dates:	Submitted: 27 January 2026 Accepted: 15 May 2026 Published (online): 13 June 2026 Published: June 2026
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Engineering (Sheffield) > School of Mechanical, Aerospace and Civil Engineering
Date Deposited:	30 Jun 2026 10:14
Last Modified:	30 Jun 2026 10:14
Status:	Published
Publisher:	Springer Science and Business Media LLC
Refereed:	Yes
Identification Number:	10.1007/s00158-026-04360-4
Related URLs:	Author
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:242686

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Fail-safe optimization concerning partial damage—a comparison of rigid plastic and linear elastic material models

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