In this talk I will discuss a geometric constraint, called accessibility constraint, for shape and topology optimization of structures built by additive manufacturing. The motivation comes from the use of sacrificial supports to maintain a structure, submitted to intense thermal residual stresses during its building process. Once the building stage is finished, the supports are of no more use and should be removed. However, such a removal can be very difficult or even impossible if the supports are hidden deep inside the complex geometry of the structure. A rule of thumb for evaluating the ease of support removal is to ask that the contact zone between the structure and its supports can be accessed from the exterior by a straight line which does not cross another part of the structure. It represents the possibility to cut the head of the supports attached to the structure with some cutting tool. We propose a new mathematical approach to evaluate such an accessibility constraint, which is based on distance functions, solutions of eikonal equations. The main advantage is the possibility of computing shape derivatives of such a criterion with respect to both the structure and the support. We numerically demonstrate in 2D and 3D that, in the context of the level-set method for topology
optimization, our algorithm can optimize simultaneously the mechanical performance of a structure and the accessibility of its building supports, guaranteeing its additive manufacturing.There remain open questions about the precise mathematical definition of the adjoint and the rigorous proof of shape differentiation for our accessibility measure.
This is a joint work with M. Bihr, B. Bogosel and M. Godoy.
Maxime Laborde
