Optimal laminate design subject to single membrane loads

In this paper we investigate optimization of laminates for maximal membrane stiffness under single in-plane loads. The design parameters are the relat ive ply thicknesses and fiber orientations of an arbitrary number of plies. The design is allowed to vary in a pointwise fashion throughout the struct ure. From prior work on lamination parameters (Hammer et al. 1997), it is known that the optimal design is given by either some sort of two ply lay-up in s pecial strain situations or otherwise by just a single rotated ply. This is exploited in the present analysis to derive analytically the unique parame ters of the optimal design (cross-ply, angle-ply or single ply) as expressi ons of the membrane forces. Both high and low shear stiffness material are treated. Furthermore the analysis covers all possible local strain or membr ane force situations. Finally, it is shown how these expressions for the optimal configuration of the laminate also appear as bounds on the principal membrane forces in ord er to obtain alignment between the numerically largest principal membrane f orce and principal strain.