Summary: ARTICLE IN PRESS
Finite Elements in Analysis and Design ( )
The use of Timoshenko's exact solution for a cantilever beam in adaptive
Charles E. Augardea,
, Andrew J. Deeksb
aSchool of Engineering, Durham University, South Road, Durham DH1 3LE, UK
bSchool of Civil & Resource Engineering, The University of Western Australia, Crawley Western Australia 6009, Australia
Received 29 May 2007; received in revised form 17 January 2008; accepted 18 January 2008
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.
2008 Elsevier B.V. All rights reserved.
Keywords: Adaptivity; Finite element method; Meshless; Closed form solution; Beam; Error estimation; Meshfree