On the shape of minimum-resistance solids of revolution moving in plastically compressible and elastic-plastic media (Q1107355)

A variational problem on the shape of minimum-drag thin solids of revolution moving at a constant velocity in plastically compressible and elastic-plastic media simulating soil and metals, respectively, is formulated and solved under the assumption of the validity of the plane section hypothesis. Optimal solid of revolution shapes are found when there is friction in the medium. Optimal body shapes and their resistance are computed on a computer for real soils under different isoperimetric conditions. It is shown that a cone is not the optimal solid in a number of cases.