Askes, H., Rodríguez-Ferran, A. and Hetherington, J. (2014) The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics. International Journal for Numerical Methods in Engineering, 101 (11). 809 - 824. ISSN 0029-5981
Abstract
In this paper, the effects of element shape on the critical time step are investigated. The common rule-of-thumb, used in practice, is that the critical time step is set by the shortest distance within an element divided by the dilatational (compressive) wave speed, with a modest safety factor. For regularly shaped elements, many analytical solutions for the critical time step are available, but this paper focusses on distorted element shapes. The main purpose is to verify whether element distortion adversely affects the critical time step or not. Two types of element distortion will be considered, namely aspect ratio distortion and angular distortion, and two particular elements will be studied: four-noded bilinear quadrilaterals and three-noded linear triangles. The maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements. The critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright © 2014 John Wiley & Sons, Ltd. This is an author produced version of a paper subsequently published in International Journal for Numerical Methods in Engineering. Uploaded in accordance with the publisher's self-archiving policy. This is the peer reviewed version of the following article: Askes, H., Rodríguez-Ferran, A. and Hetherington, J., 'The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics' which has been published in final form at http://dx.doi.org/10.1002/nme.4819. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms) |
Keywords: | explicit time integration; critical time step; eigenfrequency; element distortion; element aspect ratio |
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: | 12 May 2015 15:24 |
Last Modified: | 12 Apr 2017 10:48 |
Published Version: | http://dx.doi.org/10.1002/nme.4819 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/nme.4819 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85971 |