Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity

Many models in polymer processing and composites manufacturing are defined in degenerated three-dimensional domains, involving plate or shell geometries. The reduction of models from 3D to 2D is not obvious when complex physics are involved. The hypotheses to be introduced for reaching this dimensionality reduction are sometimes unclear, and most of possible proposals will have a narrow interval of validity. The only getaway is to explore new discretization strategies able to circumvent or at least alleviate the drawbacks related to mesh-based discretizations of fully 3D models defined in plate or shell domains. An in-plane–out-of-plane separated representation of the involved fields within the context of the Proper Generalized Decomposition allows solving the fully 3D model by keeping a 2D characteristic computational complexity. Moreover the PGD features allow the introduction of many extra-coordinates, as for example the orientation of the different laminate plies, without affecting the solvability of the resulting multidimensional model.