The purpose of this work is to introduce a new constraint functional for shape optimization problems, which enforces the constructibility by means of additive manufacturing processes, and helps in preventing the appearance of overhang features - large regions hanging over void which are notoriously difficult to assemble using such technologies. The proposed constraint relies on a simplified model for the construction process: it involves a continuum of shapes, namely the intermediate shapes corresponding to the stages of the construction process where the total, final shape is erected only up to a certain level. The shape differentiability of this constraint functional is analyzed - which is not a standard issue because of its peculiar structure. Several numerical strategies and examples are then presented. This is a joint work with G. Allaire, R. Estevez, A. Faure and G. Michailidis.
