Weldeyesus, A.G., Gondzio, J., He, L. et al. (3 more authors) (2019) Adaptive solution of truss layout optimization problems with global stability constraints. Structural and Multidisciplinary Optimization, 60 (5). pp. 2093-2111. ISSN 1615-147X
Abstract
Truss layout optimization problems with global stability constraints are nonlinear and nonconvex and hence very challenging to solve, particularly when problems become large. In this paper, a relaxation of the nonlinear problem is modelled as a (linear) semidefinite programming problem for which we describe an efficient primal-dual interior point method capable of solving problems of a scale that would be prohibitively expensive to solve using standard methods. The proposed method exploits the sparse structure and low-rank property of the stiffness matrices involved, greatly reducing the computational effort required to process the associated linear systems. Moreover, an adaptive ‘member adding’ technique is employed which involves solving a sequence of much smaller problems, with the process ultimately converging on the solution for the original problem. Finally, a warm-start strategy is used when successive problems display sufficient similarity, leading to fewer interior point iterations being required. We perform several numerical experiments to show the efficiency of the method and discuss the status of the solutions obtained.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 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. |
Keywords: | Truss structures; Global stability; Semidefinite programming; Interior point methods |
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) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 11 Jun 2019 08:49 |
Last Modified: | 07 Dec 2021 09:07 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s00158-019-02312-9 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147177 |
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