Maximum Principle in the Optimal Design of Plates with Stratified Thickness

An optimal design problem for a plate governed by a linear, elliptic equation with bounded thickness varying only in a single prescribed direction and with unilateral isoperimetrical-type constraints is considered. Using Murat–Tartars homogenization theory for stratified plates and Young-measure relaxation theory, smoothness of the extended cost and constraint functionals is proved, and then the maximum principle necessary for an optimal relaxed design is derived.