Optimization of Hybrid Composite Laminates with Distinct Ply Thicknesses Using Integer Programming

Optimization of constant-stiffness composite laminates with discrete values of fiber orientations and ply thicknesses is a nonconvex combinatorial problem. Recent studies show that this problem can be efficiently solved using the mixed integer program (MIP) by reformulating lamination parameters as functions of decision variables that represent fiber orientation and thickness choices. These formulations are limited to analyzing laminates having plies of the same thickness and material. This paper extends the previously employed lamination parameter reformulation to enable laminate designs with plies of different thicknesses and materials, thereby leading to MIP with cubic constraints. The linearization techniques are employed to convert cubic constraints of buckling load factors in terms of binary variables into sets of linear constraints that are efficiently solved with optimization algorithms for MIPs. It is shown that the use of distinct ply thicknesses in the optimization further reduces the mass of single-material laminates made with carbon-fiber-reinforced polymer when compared with previous studies using the same material. Additionally, the combination of plies made of glass-fiber-reinforced polymer and carbon-fiber-reinforced polymer with distinct thicknesses is shown to reduce the weight penalty when optimized for cost minimization in comparison to plies with uniform thickness.