EFFECTIVE STIFFNESSES OF TRANSVERSELY NONHOMOGENEOUS PLATES WITH UNIDIRECTIONAL PERIODIC STRUCTURE

This paper presents a derivation and analysis of closed formulae for t he membrane, bending and reciprocal effective stiffnesses of elastic o rthotropic and transversely asymmetric plates with microstructures per iodic in one direction. The derivation is based on the concept of impo sing Hencky-type displacement constraints on the solutions to the Cail lerie-Kohn-Vogelius local homogenization problems. Reduction of the di mension of the problems by one makes it possible to solve the new appr oximate local problems exactly, thus enabling one to find the relevant formulae in closed form, ready for engineering applications as well a s for optimization and sensitivity studies. This paper generalizes the previous results of the author [Int. J. Solids Structures 29, 309-326 (1992)], concerning the bending of transversely symmetric periodic pl ates.