Virtual charts for shape optimization of structures

The paper presents the concept of "Virtual Charts" applied to computational structural mechanics. Based on the Proper Generalized Decomposition (PGD), a model reduction method, the idea is to create a numerical tool to help engineers to perform shape optimization, where quantities of interest, computed for all the geometrical configurations, will be stored. Two different approaches have been developed in order to introduce geometry variations as parameters in the PGD. Promising results were obtained for academic examples.