Logo image
The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis
Journal article   Peer reviewed

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

C. E. Augarde and A. J. Deeks
Finite elements in analysis and design, Vol.44(9), pp.595-601
2008

Abstract

Adaptivity Beam Closed form solution Error estimation Finite element method Meshfree Meshless
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.

Details

Metrics

InCites Highlights

These are selected metrics from InCites Benchmarking & Analytics tool, related to this output

Collaboration types
Domestic collaboration
International collaboration
Citation topics
7 Engineering & Materials Science
7.63 Mechanics
7.63.1370 Meshless Method
Web Of Science research areas
Mathematics, Applied
Mechanics
ESI research areas
Engineering
Logo image