Stacking sequence optimisation of variable stiffness laminates with manufacturing constraints

The fibre paths of variable stiffness laminates are described through the fibre angles at the nodes of a finite element (FE) representation of the structure. An algorithm is presented to optimise the fibre angles efficiently. To reduce the number of required FE analyses a multi-level approach is used: the exact solution is first approximated in laminate stiffness space. The second level approximation is a Gauss-Newton quadratic approximation in fibre angle space. To ensure manufacturability, a steering constraint is introduced: the norm of the gradient of the fibre angle distribution is constrained. Two formulations are proposed: either the average steering is constrained; or the local element-wise steering is constrained. The resulting quadratically constrained quadratic optimisation problem is solved using an interior-point method. It is shown that the local steering constraint performs best, at the cost of increasing the size of the problem.