Vers une nouvelle stratégie PGD pour la simulation numérique de structures élancées

Effective models for slender structures derived from well-known theories are justified within the limit of a small thickness, and may therefore prove limited for intermediate slenderness. On the other hand, direct 3D simulation of such structures is sub-optimal because it does not take advantage of the presence of small dimensions in some directions and is sometimes too costly. In this context, the Proper Generalized Decomposition (PGD) method, a model order reduction method based on a modal representation of the solution with separation of variables, makes it possible to obtain a 3D solution with 2D resolution complexity. In this work, an analysis of the links between the PGD reduced-order model and the solution provided by plate theory is carried out using asymptotic expansion. It is shown that, in the limit of large slenderness, the first mode of the PGD exhibits Kirchhoff-Love type kinematics, but only corresponds to this model in very special cases of loading and boundary conditions. To capture the asymptotic solution, a new PGD strategy is introduced, consisting of computing the first two modes simultaneously. Numerical experiments are provided, demonstrating the interest of this approach and confirming the theoretical analysis.