Mixed Integer Linear Programming formulations of the stacking sequence and blending optimisation of composite structures

This manuscript proposes two novel formulations for the manufacturable stacking sequence retrieval of laminated composite structures. Detailed sizing of composite structures is commonly tackled by a two-stage optimisation approach, the first stage being a weight minimisation resulting in a continuous thickness and stiffness distribution of the structure. The second stage, which is the focus of the current paper, aims at retrieving stacking sequences that match the optimised target thickness and stiffness characteristics of the first stage, while also fulfilling a set of predefined design and manufacturing rules, with blending being one of the most crucial ones. The problem of retrieving layered designs that meet all of the prescribed composite rules is formulated as two Mixed Integer Linear Programming instances which mainly differ in how the blending is treated. Using either of the two formulations, mathematical programming algorithms can be employed to solve the problem to global optimality. Results show that both formulations can produce manufacturable solutions that fulfil the imposed composite rules. High-quality solutions can be obtained consistently, while benefiting from increased design freedom concerning the blending formulation.