Optimisation of Variable Stiffness Plates

Abstract

Variable angle tow (VAT) describes fibres in a composite lamina that have been steered curvilinearly. In so doing, substantially enlarged freedom for stiffness tailoring of composite laminates is enabled. VAT composite structures have been shown to have improved buckling and postbuckling load carrying capability when compared to straight fibre 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 fibre orientations in addition to stacking sequence considerations. In this work, an efficient two-level optim isation framework using lamination parameters as design variables has been enhanced and general ised to the design of VAT plates. 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 point-wise feasibility of lamination parameters. In addition, a small set of explicit closed-form expressions is used to define 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 optimisation methodology.