Design of variable–stiffness laminates using lamination parameters

Benefits of the directional properties of fiber reinforced composites could be fully utilized by proper placement of the fibers in their optimal spatial orientations. This paper investigates the optimal design of fiber reinforced rectangular composite plates for minimum compliance. The classical minimum compliance design problem is formulated in the lamination parameters space. The use of lamination parameters guarantees that the obtained solutions represent the best possible performance of the structure since there are no restrictions on the possible lamination sequence. Two types of designs are considered: constant–stiffness designs where the lamination parameters are constant over the plate domain, and variable-stiffness designs where the laminations parameters are allowed to vary in a continuous manner over the domain. The optimality conditions for the problem are reformulated as a local design rule. The local design rule assumes the form of a convex optimization problem and is solved using a feasible sequential quadratic programming. Optimal designs for both constant and variable–stiffness plates are obtained. It is shown that significant improvements in stiffness can be gained by using variable–stiffness design.