3D-2D asymptotic analysis for inhomogeneous thin films

A dimension reduction analysis is undertaken using Gamma -convergence techn iques within a relaxation theory for 3D nonlinear elastic thin domains of t he form Omega (epsilon) := {(x(1), x(2), x(3)) : (x(1), x(2)) is an element of omeg a, /x(3)/ < epsilon f(epsilon) (x(1), x(2))}, where omega is a bounded domain of R-2 and f(epsilon) is an epsilon -depend ent profile. An abstract representation of the effective 2D energy is obtai ned, and specific characterizations are found for nonhomogeneous plate mode ls, periodic profiles, and within the context of optimal design for thin fi lms.