Computational Model for Tree-like Fractals Used as Internal Structures for Additive Manufacturing Parts

Abstract

It is well established that the introduction of additive manufacturing in various domains has produced significant technological leaps due to the advantages over other manufacturing techniques. Furthermore, additive manufacturing allows the design of parts with complex internal structures (e.g., lattice, honeycomb) to achieve lightweight or other mechanical properties. This paper presents a computational model (integrated into a programable algorithm) designed to generate complex internal structures, using tree-like fractals, for components (mechanical parts) whose designs are achievable by additive manufacturing. The computational model is presented in detail, starting from the mathematical definition and the properties of the proposed tree-like fractals. The fractal data are computed and arranged unequivocally using table representations. Based on the fractal data, the structures are generated inside CAD parts (which are given as inputs in the algorithm). The proposed computational method is applied in different case studies to illustrate their functionality. The generated CAD components (with fractal internal structures) are intended for manufacturing (using selective laser melting) and laboratory (mechanical) testing and for finite element analysis, which in turn can validate the use of tree-like fractals as interior structures for mechanical components.