Smith, C.C. orcid.org/0000-0002-0611-9227 and Gilbert, M. orcid.org/0000-0003-4633-2839 (2022) The stress function basis of the upper bound theorem of plasticity. International Journal of Solids and Structures, 244-245. 111565. ISSN 0020-7683
Abstract
The discontinuous slip-line form of upper bound plasticity analysis is considered using an equilibrium of forces approach. It is demonstrated that the underlying basis of the approach can be written in terms of stress functions that provide a continuum stress state interpretation of the upper bound solution. An alternative proof of the upper bound theorem, applicable to both associative and non-associative materials, using stress functions is presented. The broader nature of the equilibrium form and the strict conditions under which it is valid are discussed, including examination of the apparent omission of moment equilibrium and associativity in many equilibrium form solutions. Finally, the relationship of the stress function formulation to the output of the computational limit analysis method discontinuity layout optimisation (DLO) and the potential to use the stress function formulation to derive a form of lower bound solution from an upper bound analysis are demonstrated.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Elsevier Ltd. This is an author produced version of a paper subsequently published in International Journal of Solids and Structures. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Plasticity; Limit analysis; Upper bound; Stress function |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Sciences Research Council EP/T001305/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Apr 2022 12:33 |
Last Modified: | 19 Mar 2023 01:13 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.ijsolstr.2022.111565 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:185448 |