Furthest reach of a uniform cantilevered elastica. (July 2017) - Plaut, Raymond H.; Virgin, Lawrence N.
Highlights: The furthest reach of an elastic cantilever is determined. A uniformly distributed load and a tip load are considered. The angle of the fixed end is optimized. Experiments are conducted to verify the analysis. Abstract: A uniform elastic cantilever is subjected to a uniformly distributed load or a concentrated load at its tip. The angle of the fixed end with the horizontal is varied until the maximum horizontal distance (projection) from the fixed end to the horizontal location of the tip is attained. The beam is modeled as an inextensible elastica, and numerical results are obtained with the use of a shooting method. For the optimal solution (furthest reach), the tip is below the level of the fixed end. Experiments are conducted to verify the analysis for a heavy cantilever (i.e., only subjected to its self-weight).