A continuation-based method for finding laminated composite stacking sequences

A method of recovering laminate ply stacking sequences from a set of up to twelve lamination parameters using polynomial homotopy continuation techniques is presented. The ply angles are treated as continuous variables, and are allowed to take any value between - 90 degrees and + 90 degrees. The individual plies are assumed to be orthotropic and have constant stiffness. The method is fully deterministic, and does not rely on an optimisation process to establish the stacking sequence. Polyhedral continuation methods are used to limit the solution space in which the stacking sequences are sought. The method can reliably find every stacking sequence solution that exists to achieve a precisely specified set of lamination parameter targets, with the number of real solutions to a feasible combination of target properties found to vary from 1 to over 100. The same method is also demonstrated to be able to find stacking sequences to satisfy a set of specified ABD stiffness matrix terms, as might be required following a direct-stiffness modelling design process.