Design of variable stiffness panels for maximum strength using lamination parameters

Tailoring of laminated composite structures by changing ply angle and thickness locally provides a unique opportunity to take full advantage of anisotropic properties of composite materials. Variable stiffness design has become more attractive with the development of industrial fibre placement machines. Strength design is one of the areas where fibre steering is advantageous. Design methods that consist of directly optimising fibre angles or fibre path coefficients can lead to local optima and/or non-continuous solutions. These problems can be alleviated by using lamination parameters as design variables, which provide a compact definition of laminate stiffness. Additionally these parameters are continuous and the design space has shown to be convex. Dependency of strength failure criteria on ply angles may preclude using lamination parameters as design variables. Here, a recently developed method which incorporates the strength failure criteria in the lamination parameter space by using a conservative failure envelope for all ply angles is utilised. A hybrid approximation for the failure index is developed and is guaranteed to be convex using a convexifying approach. As an example strength maximisation of a panel with a central hole under uniaxial tension is investigated. Numerical results show improvements in strength with respect to the quasi-isotropic design. Although there is a common belief that design for stiffness can be served as a surrogate for strength design, it is shown that considering the strength as a design criteria especially for structures with large stress gradients is very important.