Optimisation of composite structures – Enforcing the feasibility of lamination parameter constraints with computationally-efficient maps

Composite materials are increasingly used in high performance structural applications because of their high strength and stiffness to weight ratios together with their significant tailoring capabilities. The stiffness of a monolithic laminate can be expressed as a linear combination of material invariants, one thickness variable, and twelve lamination parameters, which is an efficient alternative to using fibre angles as design variables. However, feasibility constraints originating from the interdependency between lamination parameters must be satisfied to obtain laminates with realistic stiffness properties. Currently, enforcing these feasibility constraints is a computationally intensive task. In this paper we propose to use normalised design variables that inherently map (i.e. correspond) to feasible lamination parameters, effectively removing the need to evaluate feasibility constraints altogether. To this end, linear and B-spline maps of the feasible lamination parameter subspace are proposed and evaluated. Results of 2D and 4D benchmark analyses and optimisation studies suggest that the proposed methodology does successfully provide an efficient means of achieving feasible results at lower computational costs.