The use of Timoshenkoʹs exact solution for a cantilever beam in adaptive analysis

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.