A general B-Spline surfaces theoretical framework for optimisation of variable angle-tow laminates

This work deals with the optimum design of variable angle-tow (VAT) composites in the theoretical framework of B-Spline surfaces. The design problem is formulated as a constrained optimisation problem in the context of the multi-scale two-level (MS2L) optimisation methodology. The proposed approach aims at optimising all parameters characterising the VAT laminate at each pertinent scale (mesoscopic and macroscopic ones). In particular, this study focuses on the first level of the MS2L optimisation strategy that aims at determining, at the VAT laminate macroscopic scale, the optimum distribution of the laminate mechanical properties over the structure. At this stage, the behaviour of the VAT composite is described by means of the polar formalism and the spatial distribution of the polar parameters is represented through a set of suitable B-Spline surfaces. The expression of the gradient of objective and constraint functions is determined in a closed form by exploiting the properties of the B-Spline surfaces. Moreover, the effect of the discrete variables tuning the shape of the B-Spline surfaces (mainly the number of control points) on the quality of the optimum solution is investigated. The effectiveness of the proposed approach is tested through some meaningful benchmarks taken from literature.