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Upper and lower bound limit analysis of plates using FEM and second-order cone programming

Le, C.V., Nguyen-Xuan, H. and Nguyen-Dang, H. (2010) Upper and lower bound limit analysis of plates using FEM and second-order cone programming. Computers & Structures, 88 (1-2). pp. 65-73. ISSN 0045-7949

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Abstract

This paper presents two novel numerical procedures to determine upper and lower bounds on the actual collapse load multiplier for plates in bending. The conforming Hsieh–Clough–Tocher (HCT) and enhanced Morley (EM) elements are used to discrete the problem fields. A Morley element with enhanced moment fields is used. The constant moment fields is added a quadratic mode in which the pressure is equilibrated by corner loads only, ensuring that exact equilibrium relations associated with a uniform pressure can be obtained. Once the displacement or moment fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization. In this paper, the optimization problems are formulated in the form of a standard second-order cone programming which can be solved using highly efficient interior point solvers. The procedures are tested by applying it to several benchmark plate problems and are found good agreement between the present upper and lower bound solutions and results in the literature.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2009 Elsevier Ltd. This is an author produced version of a paper published in 'Computers & Structures'. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Limit analysis; Upper and lower bounds; Displacement and equilibrium models; Criterion of mean; Second order cone programming
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield)
Depositing User: Dr Canh Le
Date Deposited: 18 May 2010 16:39
Last Modified: 08 Feb 2013 17:00
Published Version: http://dx.doi.org/10.1016/j.compstruc.2009.08.011
Status: Published
Publisher: Elsevier Ltd
Refereed: Yes
Identification Number: 10.1016/j.compstruc.2009.08.011
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/10744

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