The optimal nose shape of a rigid projectile deeply penetrating into a solid target considering friction

Abstract

The paper deals with the optimal nose shape of a perfectly rigid axi-symmetric projectile which deeply penetrates into a semi-infinite target accounting for the dry friction between the nose surface and the target. Analytical expressions of the contact stresses at the “projectile-target” interface and of the total resistance force as well as of the final penetration depth are developed for targets described by a locked hydrostat and a linear shear failure-pressure relationship. These analytical expressions are developed using the cylindrical cavity expansion (CCE) and the spherical cavity expansion (SCE) approaches. A comparison of these approaches on the optimization problem solution is performed. The effect of dry friction on the optimal shape of the projectile nose is investigated and two main approaches to solving the problem of shape optimization are studied. Two optimization approaches are compared: the first optimization approach is based on minimizing the resistive force (MRF) acting on the projectile, and the second approach is based on maximizing the penetration depth (MPD). The optimal shapes are compared for a fixed shank radius and evaluations are carried out for different nose lengths and different values of the coefficient of friction. It is shown that friction may have a visible effect on the final penetration depth, although in all cases, the friction effect on the optimal shape of the projectile nose is negligible. The obtained optimal nose shapes are implemented in computational analysis in an own developed code that had been verified with numerous test data to examine whether these shapes actually lead to a minimum resistive force and to a maximal penetration depth. Significant effectiveness of the optimal shape performance is shown for larger radius projectiles having a defined nose length.