In structural optimization of laminated composites, the complexity of some design problems can be significantly reduced by introducing lamination parameters as design variables. The value of each lamination parameter is not truly independent and instead are interlinked by a particular lamination (lay-up). Although the feasible region of 12 lamination parameters has already been shown to be convex, the explicit relations between the parameters are generally unknown. In the design of variable angle tow (VAT) composite laminates, the lamination parameters vary as a function of x, y coordinates. The value of each lamination parameter continuously varies in a smooth manner and their constraints should be satisfied at all points. Consequently, accurate bounds for the feasible region of lamination parameters are necessary to describe the design constraints in the optimization of VAT laminates. This paper presents a set of explicit closed-form expressions to define the feasible region of two in-plane and two out-of-plane lamination parameters, which can be applied to the design of orthotropic VAT laminates. A preliminary buckling optimization of a square orthotropic VAT panel is presented using lamination parameters that are represented by a polynomial series. The distribution of lamination parameters are pointwise constrained by the closed-form nonlinear inequalities. The optimum results demonstrate the applicability of the presented expressions for lamination parameters in the design of VAT panels. Finally, corresponding fibre angles distributions are generated from the optimal lamination parameters using a genetic algorithm (GA).
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