Shape optimization of impactors against a finite width shield using a modified method of local variations

We suggest a modification of the method of local variations of Banichuk and Chernous'ko that expands further the scope of applications of this method beyond the applications considered in our previous study. This modification allows us to solve numerically the variational problem of determining the shape of the impactor having a minimum ballistic limit velocity (BLV) when the criterion of optimization is a double integral with an integrand including a double integral over a variable area. The integrands in both integrals depend on the unknown function determining the generatrix of the impactor. We found that impactors with flat or conical nose have a minimum BLV and derived an analytical criterion that determines the choice between these two shapes depending on the parameters describing the size of the impactor's nose and properties of the material of the shield. The proposed approach can be useful in solving other optimization problems.