Optimization of multi-layered metallic shield

We investigate the problem of optimization of multi-layered metallic shield whereby the goal is to determine the sequence of materials and the thicknesses of the layers that provide the maximum ballistic limit velocity of the shield. Optimization is performed under the following constraints: fixed areal density of the shield, the upper bound on the total thickness of the shield and the bounds on the thicknesses of the plates manufactured from every material. The problem is reduced to the problem of Geometric Programming which can be solved numerically using known methods. For the most interesting in practice cases of two-layered and three-layered shields the solution is obtained in the explicit analytical form.