I NTRODUCTl ON
Optimization techniques have now been applied to structural design for nearly thirty years. However, the great majority of this work has been limited to research activities directed at developing the methods, improving algorithms, and understanding their capabilities and limitations. Optimization methods are only now becoming generally accepted as a practical design tool, and are beginning to be taught more widely in engineering schools. For this reason, the methodology used here may be unfamiliar to many readers, and so a brief outline of the numerical optimization process will be given below.
Even though optimization methods have not yet received the attention of other computerbased design methods such as CAD, they offer a remarkably versatile design tool. Also, the development of these methods has reached a point where they can be comfortably used by nonspecialists by coupling available optimization codes with user-provided analysis codes. Thus, much of the motivation for this discussion is to encourage the use of optimization as a design tool of composite structures.
The majoriy of the work in structural optimization has dealt with isotropic structures and survey papers by Ashley.' Schmit' and Vanderplaats3 offer many references to the theory and applications, as well as referencing numerous other survey papers. The typical problem addressed is the design of a structure for minimum weight, subject to limits on strength, deflections, vibration, static and aeroelastic stability, and dynamic response. The design variables typically include member dimensions and geometric (shape) variables.
In the area of composite structures, the design variables include ply thickness (number of plies) and occasionally ply orientation. In some cases, the number of plies is treated as a discrete variable, but more often it is treated as a continuous variable which is then rounded up to the next integer number of plies at the optimum. Ply orientation as a design variable creates a relative complexity in that the objective function (weight) is not a function of ply orientation, but the constraints are. More importantly, it is easily seen from the constitutive relationships that treating ply orientations as variable introduces relative minima into the optimization task. Finally, ply stacking sequence has not been addressed as part of the optimization task, since this introduces combinatorial aspects into the problem that are not well understood.
While it is clear from this that optimization of composite structures is a difficult task, the rewards are so great that considerable effort is justified. To begin with, there is relatively little experience available that can be relied upon to guide us in new designs. Also, the number of