Solution of the problem of optimizing protective properties of inhomogeneous shields during the dynamic penetration of a hard striker (based on the use of optimal control methods)

The paper presents a general formulation of the problem of finding an optimal distribution of mechanical properties of an inhomogeneous shield with minimum weight during the dynamic penetration of a hard striker. The problem is reduced to a standard form of an optimal control problem for a differential equation system. The general formulation of the problem includes a number of factors, such as an impact angle, a striker's shape, mechanical properties, etc. These factors determine mechanical behaviour of metal shields in the process of the dynamic penetration. Since the presence of a large number of factors complicates theoretical research into the process, it is necessary to investigate the effect of each factor separately. In this paper, we provide solutions for the optimization problem regarding particular variants of penetration (taking into account friction, the free surface effects, the striker's shape, the oblique impact). In accordance with the problem formulation, one of the two methods is used - either the Pontryagin maximum principle or the needle variation method. The article summarizes the main results of the research. In some cases, the final solution of the problem is provided, while in others criteria for the optimal structure of the shield are formulated. We demonstrate the effectiveness of the needle variation method in solving the problem of optimal designing of layered systems; a simple algorithm to find the optimal structure of the shield for the problem of an impact of a cone withw materials has been derived.