Multi-material topology optimization for additive manufacturing using polytree-based adaptive polygonal finite elements

The development of additive construction, which is an automated production process based layer-by-layer control, opens a new era for building design. It creates opportunities for novel shapes that would not have been technologically feasible in the past. The key to this revolution resides in the link between material development and computational-based optimization design tools to produce optimized structures. Topology optimization is an intelligent approach to seek the best design in many fields of computational mechanics. By analysing the information inside the determined domain, it changes the topology of such domain into a new design to satisfy the given criterion. In most of the work, ideal materials are assumed to implement the topology optimization problems. Therefore, the optimal designs are still considered as reference or theoretical solutions while the practical problems need more than that. The multi-material topology optimization (MMTOP) is established to evaluate the behaviour of many materials in a problem and give an applicable solution for design. In this study, we present a polytree-based adaptive methodology for multi-material topology optimization (MMTOP). Polytree data structure is introduced as a general recursive multi-level mesh that is automatically refined in processing based on error analysis. A new definition of filter radius is also proposed to improve the efficiency of filters and optimized results. The combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases (including void phase), but also decreases the computing time of the overall process in comparison to using the regular fine meshes. Several benchmark and practical problems are considered to show distinct features of the proposed method. 3D printed prototypes are presented to demonstrate the fabrication feasibility of this method.