Strength and mass optimisation of variable-stiffness composites in the polar parameters space

A general theoretical and numerical framework for the strength and mass optimisation of variable-stiffness composite laminates (VSCLs) is presented in this work. The optimisation is performed in the context of the first-level problem of the multi-scale two-level optimisation strategy (MS2LOS) for VSCLs. Both the failure load maximisation problem (subject to a constraint on the mass) and the mass minimisation one (with a constraint on the VSCL strength) are solved for two benchmark structures. The effect of the presence of a constraint on the maximum tow curvature is also investigated. The solutions are searched by means of a deterministic algorithm by considering different scenarios in terms of the VSCL macroscopic behaviour: the orthotropy type and shape, the direction of the main orthotropy axis and the thickness of the laminate are tailored either globally (uniform over the structure) or locally. The polar method is used to represent the point-wise elastic response of the VSCL at the macroscopic scale. The distributions of the polar parameters and of the thickness are described through B-spline entities: their properties are exploited in computing physical and geometrical response functions of the VSCL as well as their gradient. The VSCL strength at the macroscopic scale is assessed using a laminate-level failure criterion in the space of polar parameters. Numerical results show considerable improvements with respect to both quasi-homogeneous isotropic structures and an optimised VSCL solution taken from the literature obtained by using the design approach based on lamination parameters. These results confirm the effectiveness of the proposed strategy and the great potential of VSCLs.