Proper generalized decomposition solutions for composite laminates parametrized with fibre orientations

Composite materials are gaining popularity as an alternative to classical materials in many different applications. Moreover, their design is even more flexible due to the potential of additive manufacturing. Thus, one can produce a tailored composite laminate with the optimal values of some design parameters providing the desired mechanical performance. In this context, having a parametric numerical model for the mechanical response of the composite laminate is essential to compute the optimal parameters. In the present paper, the design parameters under consideration are the angles describing the orientation of the reinforcement fibers in different layers or patches of the composite laminates. We obtain a generalized solution using Proper Generalized Decomposition (PGD) which is adopted to provide solutions with explicit parametric dependence. The Tsai-Wu failure criterion is used to estimate first ply failure. In this context, Tsai-Wu criterion is used as the objective function for the optimization of the fibre orientations in the laminate. The PGD solution provides also sensitivities for a gradient-based optimization algorithm. The potentiality and efficiency of the presented approach is demonstrated through some numerical tests.