PARAMETRIZATION IN LAMINATE DESIGN FOR OPTIMAL COMPLIANCE

In this paper we consider the maximal stiffness design of laminated pl ates subjected to single and multiple loads. The stiffness of the lami nates are parametrized in terms of the so-called lamination parameters . These express the relation between the material parameters for the l aminate and the laminate lay-up and are given as moments of the trigon ometric functions that appear in the well-known rotation formulae for stiffness matrices. These relations are here given in a form suitable for optimization studies. The conditions for the laminate itself to be orthotropic are also given directly in terms of the lamination parame ters. The design problem is analyzed by performing a reformulation to an equivalent problem which is local in character and it is shown how this, together with an enlargement of the design space to allow for ou t of plane chattering designs, leads to a significant simplification o f the problem. Thus, the number of variables is reduced to only four f or the stiffness problem at hand, even in the general case with coupli ng stiffnesses and multiple loads. Moreover, in the special case of in -plane loads, the optimal solution for each design element of the plat e can be realized as a single rotated ply of material or in special st rain situations by two plies. A computational solution procedure for t he simplified problem is described and several numerical examples illu strate basic features of the design approach. Copyright (C) 1996 Elsev ier Science Ltd.