Optimal shapes of axisymmetric bodies penetrating into soil

This paper presents the results of a study of the shapes of axisymmetric bodies with minimum penetration resistance and maximum depth of penetration into the plastic soils. Optimum shapes of bodies of revolution of predetermined length and cross-sectional radius with generatrices represented by line segments are obtained by a modified method of local variations. The problem is solved using a binomial quadratic model of local interaction, including inertial and strength terms containing constant and Coulomb frictions. The resistance forces and the depth of penetration of cones and the obtained bodies of optimal shape are determined at different penetration velocities.