GRADIENT RELIABILITY-BASED DESIGN OPTIMIZATION OF A COMPOSITE PLATE THROUGH MULTI-SCALE DESIGN SPACES

The inherent incertitudes linked to the manufacturing processs call for a reliability-based approach to structural optimisation. In this case, one faces optimization in a mesoscopic space where design variables (i.e., the orientations) are many, discrete, and often bear some uncertainty. In some cases, it seems more advantageous to work on some homogeneous macroscopic space (e.g., the laminations parameters) instead of using orientations. Indeed, this allows a reduction of the problem dimension and naturally exploits regular gradients information. Once the optimal design is obtained in the macroscopic space, an inverse problem must be solved to identify a corresponding optimized set of mesoscopic design parameters. This identification is far from trivial in standard optimization frameworks because of non-uniqueness issues and it often relies on meta-heuristic methods. In the context of reliability-based design optimization, an uncertainty quantification from the mesoscopic to the macroscopic space is necessary, requiring a scaling up to transport the impact of these uncertainties. An optimization carried out in the macroscopic space and accounting for uncertainties now requires solving an inverse problem at each iteration to correctly identify an optimized set of mesoscopic parameters in terms of the statistical description of the macroscopic solution. This expensive search must be reiterated, necessitating highly efficient propagation of uncertainties. To this end, a particular orthonormal basis has been constructed with Fourier chaos expansion. Moreover, due to the modal nature of the aeroelastic quantity of interest (i.e., the flutter velocity), a surrogate model strategy is implemented by combining the Kriging method and a classification. This approach is applied to a composite plate optimization with uncertain ply angles to promote the wing’s flexibility while remaining reliable with respect to the flutter phenomenon. The preliminary results show a good convergence of this optimization approach with a significant improvement in the reliability relative to the deterministic optimized design.