Theoretical optimal shape of a longest reach cantilever

Abstract

The problem of finding the shape of initially straight elastic cantilever that minimizes volume, and satisfies certain condition at the free end is analyzed. The recently analyzed longest reach problem follows as a special case. New results are presented about shape of the cantilever, having prescribed volume and having longest reach. The Pontryagin's maximum principle with cross-sectional area as "control" is used in the optimization procedure.