Effect of double constraints on the optimization of two-component armor systems

In literature, by using Florence’s model [Florence AL. Interaction of projectiles and composite armours part II. Stanford Research Institute, Menlo Park (CA, USA), AMMRG-CR-69-15, August 1969], the optimization of plate thicknesses can be achieved for two-component armor systems by maximizing the projectile impact velocity under the constraint of the total thickness or the areal density of the armor. In this study, the design optimization of two-component armor system is viewed from a new perspective in which both the total thickness and the areal density become the constraints. The possible solutions of this problem are systematically studied, and the effect of applying both constraints on the optimal plate thicknesses and ballistic performance is discussed. The optimal solutions are obtained by numerical computation for ceramic/aluminum and ceramic/steel armor systems under the normal impact of NATO AP 7.62 rounds. Based on the results, it is concluded that depending upon the constraint conditions, the double-constraint optimization problem can be simplified to solving either one of the single-constraint problems or directly finding the intersection points between the two constraint boundaries.