Becque, J., Li, X. and Davison, B. (2019) Modal decomposition of coupled instabilities: The method of the equivalent nodal forces. Thin-Walled Structures, 143. 106229. ISSN 0263-8231
Abstract
A solution to the ‘modal decomposition problem’ encountered within the context of the stability analysis of thin-walled structural members is presented. The proposed method achieves decomposition of a randomly deformed shape into a number of constituent modes, which have the physical meaning of the classical local, distortional and global buckling modes, augmented with two additional classes of shear and transverse extension modes. The basis vectors of these five classes are created by defining sets of nodal forces which, when applied to the member in a first order linear elastic problem, generate shapes commensurate with specific mechanical criteria defining the local, distortional, global, shear and transverse extension modes. In a second step the basis vectors of a given class are used to define a constrained stability problem, where the solution is restricted to a linear combination of these basis vectors, in order to obtain the buckled shapes under a given loading. The full set of buckling modes spanning the five classes forms an orthonormal basis of the complete deformation space. Consequently, decomposition can be achieved by projecting the shape which is to be decomposed onto the basis vectors. Two examples are provided to illustrate the method.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier. This is an author produced version of a paper subsequently published in Thin-Walled 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: | Coupled instabilities; Decomposition; Buckling modes; Local buckling; Distortional buckling; Global buckling |
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 08:56 |
Last Modified: | 08 Jun 2020 00:40 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.tws.2019.106229 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147178 |