Generative design of hierarchical truss structures with desired stiffness and strength: Recursive multiscale topology optimization based on powder bed fusion

Abstract

The stiffness and strength of uniaxial compressive material can be equivalently realized by a hierarchical truss structure. This work fills the conceptual gap between weight minimization of single truss and the design of hierarchical truss metamaterial, resulting in the formulation of heterogeneous non-periodic structures. Multiscale topology optimization integrated with additive manufacturing (AM) leads to disruptive innovation in construction. The structural hierarchy plays a pivotal role in the creation of bulk material properties. Therefore, a systematic understanding of the cross-level behavior is critical. A rod with the desired stiffness and strength is implemented with an optimized truss with equivalent mechanical properties while using less material. Euler’s critical problem is transformed into the global buckling problem of the truss at the lower level of hierarchy. The recursive algorithm constructs and simultaneously searches for the best structure of multi-level hierarchy. A series of uniaxial compression tests compared the differences between the theoretical model and the specimens produced by powder bed fusion (PBF). The truss joint geometry for PBF was tuned to approximate the stiffness and stability predicated by the mathematical model. Despite the AM imperfection, the statistical mechanical properties are consistent across specimens. 3D-printed trusses can be assembled by welding or bolting connections into larger structures in practice. Compared with solid material with equivalent stiffness and strength, the hierarchical fusiform trusses save significant amounts of material. The cross-level map between the mechanical behavior from neighboring levels of hierarchy facilitates the estimation of the upper bound of the levels of hierarchy.