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The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis

Augarde, C.E.; Deeks, A.J.

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Authors

A.J. Deeks



Abstract

The exact solution for the deflection and stresses in an end-loaded cantilever is widely used to demonstrate the capabilities of adaptive procedures, in finite elements, meshless methods and other numerical techniques. In many cases, however, the boundary conditions necessary to match the exact solution are not followed. Attempts to draw conclusions as to the effectivity of adaptive procedures is therefore compromised. In fact, the exact solution is unsuitable as a test problem for adaptive procedures as the perfect refined mesh is uniform. In this paper we discuss this problem, highlighting some errors that arise if boundary conditions are not matched exactly to the exact solution, and make comparisons with a more realistic model of a cantilever. Implications for code verification are also discussed.

Citation

Augarde, C., & Deeks, A. (2008). The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis. Finite Elements in Analysis and Design, 44(9-10), 595-601. https://doi.org/10.1016/j.finel.2008.01.010

Journal Article Type Article
Publication Date Jun 1, 2008
Deposit Date Jun 19, 2008
Publicly Available Date Apr 8, 2009
Journal Finite Elements in Analysis and Design
Print ISSN 0168-874X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 44
Issue 9-10
Pages 595-601
DOI https://doi.org/10.1016/j.finel.2008.01.010
Keywords Finite element, Adaptivity, Closed form solutions, Cantilever beam, Timoshenko.

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