Variable stiffness composite laminates for doubly curved plates using lamination parameters

A methodology is presented for the optimisation of variable stiffness composite laminates for complex doubly curved geometries. As an example, this is here applied to a pre-twisted plate subjected to combined centrifugal and pressure loading. Lamination parameters are used to reduce the complexity of composite laminate design to a convex and continuous design space using a reduced number of variables. Lamination parameters are varied over the geometry using spline surface interpolation over a grid of control points and the optimal values found using a gradient based optimiser. A method for restricting the variation of lamination parameters over the geometry in relation to minimum turning radii of automated fibre placement heads and the distance between lamination parameter control points is discussed and demonstrated. A MATLAB script was developed to define variable angle tow paths over a doubly curved geometry. The tow paths for every ply were found using a two-stage optimisation routine. A genetic algorithm was firstly used to design the variable tow paths of each ply, this was then used as an initial design for a gradient based optimiser to further improve the tow paths of the laminate. The variable angle tow laminate designed showed good agreement to the optimal stiffness found through optimisation of the lamination parameter distribution.