Framework for the Buckling Optimization of Variable-Angle Tow Composite Plates

Variable-angle tow describes fibers in a composite lamina that have been steered curvilinearly. In doing so, substantially enlarged freedom for stiffness tailoring of composite laminates is enabled. Variable-angle tow composite structures have been shown to have improved buckling and postbuckling load-carrying capability when compared to straight fiber composites. However, their structural analysis and optimal design is more computationally expensive due to the exponential increase in number of variables associated with spatially varying planar fiber orientations in addition to stacking sequence considerations. In this work, an efficient two-level optimization framework using lamination parameters as design variables has been enhanced and generalized to the design of variable-angle tow plates. New explicit stiffness matrices are found in terms of component material invariants and lamination parameters. The convex hull property of B-splines is exploited to ensure pointwise feasibility of lamination parameters. In addition, a set of new explicit closed-form expressions defines the feasible region of two in-plane and two out-of-plane lamination parameters, which are used for the design of orthotropic laminates. Finally, numerical examples of plates under compression loading with different boundary conditions and aspect ratios are investigated. Reliable optimal solutions demonstrate the robustness and computational efficiency of the proposed optimization methodology.