Approximations for warp free laminate configurations

The relationship between laminates exhibiting thermal warping characteristics and the required strain in flattening a warped plate is described. Upper limits on these strains are proposed and subsequently used to define the boundaries of a feasible region from which coupled laminates approximating a warp free condition may be safely chosen. The study also characterizes the growth of this feasible region as a function of the allowable strain for laminates with standard ply angles (±45, 0 and 90 degrees), for all possible layups with up to 10 plies. The results show that symmetric configurations significantly reduce design freedom, particularly as the number of plies increase. A simple, yet intuitive, design approach incorporating non-symmetric subsequences is therefore developed