ON RECENT DEVELOPMENTS IN THE HOMOGENIZATION THEORY OF ELASTIC PLATESAND THEIR APPLICATION TO OPTIMAL-DESIGN .1.

The paper presents an up-to-date review of results concerning the eval uation of the stiffnesses of elastic plates with periodic structure. T he homogenization formulae of Kohn and Vogelius (1984) (model a = 1) a re viewed as the formulae of reference. The paper discusses the range of applicability of the homogenization formulae for the two-dimensiona l plate models of Kirchhoff and Reissner-Hencky. Transversely symmetri c as well as asymmetric plates are considered. Particular attention is paid to plates stiffened asymmetrically with ribs in one direction. F or this case, the closed formulae for effective membrane, reciprocal a nd bending stiffnesses are derived. The homogenization results overvie wed are a prerequisite for the discussion of the methods of regulariza tion of optimum design plate problems presented in Part II of the pape r.