Topology optimisation of architected cellular materials from additive manufacturing: Analysis, design, and experiments

Abstract

This work deals with an experimental/numerical validation of the optimised topologies found through a special density-based topology optimisation (TO) method wherein the topological descriptor, i.e., the pseudo-density field, is represented through a non-uniform rational basis spline (NURBS) hyper-surface. The framework is that of multi-scale TO methods to design architected cellular materials (ACMs). Specifically, in the most general case, the topological variables are defined at the scale of the representative volume element (RVE) of the ACM and at the macroscopic scale of the structure. The transition among scales is performed via a numerical homogenisation scheme based on the strain energy of elements. The proposed formulation exploits the properties of NURBS entities to determine the relationships occurring among the topological variables defined at different scales to correctly state the optimisation problem and to satisfy the hypotheses at the basis of the homogenisation method. Three design cases are considered: in the first one, TO is performed only at the macroscopic scale; in the second one, TO is performed only at the RVE scale; in the last one, TO is performed simultaneously at both scales. Multiple design requirements related to lightness, scale separation condition (to ensure the validity of the results of the homogenisation method) and minimum printable size are included in the problem formulation. Particularly, the last two requirements are implicitly satisfied by controlling the integer parameters of the NURBS entity (describing the pseudo-density field at each scale) without introducing explicit optimisation constraints. The multi-scale TO strategy is applied to a structure made of ACM subject to three-point bending test-like boundary conditions: for each design case, the optimised topology is manufactured through stereo-lithography and a comparison between experimental and numerical results (obtained through non-linear analysis conducted a posteriori on the optimised topology) is performed to assess the effectiveness of the approach.