Multiscale Topology Optimization Combining Density-Based Optimization and Lattice Enhancement for Additive Manufacturing
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Multiscale Topology Optimization Combining Density‑Based Optimization and Lattice Enhancement for Additive Manufacturing Jae‑Eun Kim1 · Keun Park1 Received: 21 July 2020 / Revised: 22 October 2020 / Accepted: 10 November 2020 © Korean Society for Precision Engineering 2020
Abstract Topology optimization (TO) is a shape optimization method based on finite element (FE) analysis, and has recently been used in lightweight design on the basis of the rapid advances of additive manufacturing (AM). While the conventional TO has been applied to obtain the optimal pseudo density in a macroscale domain, microscale TO involving optimization of the strut diameters of a lattice structure has also been studied. In this study, a multiscale TO method was developed by performing the conventional macroscale TO with additional enhancement of microscale lattices. To compare the structural efficiency of the proposed multiscale TO with that of the macroscale and microscale TOs, three optimization methods were applied to a meta-sandwich beam under a three-point bending load condition. Structural FE analyses were then conducted for the three optimized beams, and their deformation behaviors were compared in terms of the structural stiffness and safety. Three optimized beams were then fabricated by the photo-polymerization type AM process using an acrylic photopolymer, and bending experiments were conducted to investigate their deformation behaviors. From the results, the multiscale TO showed the highest structural stiffness and strength owing to the enhancement of microscale lattices. The energy absorption capability was also improved compared to the result of the macroscale TO. These results demonstrate that the multiscale TO is advantageous in the design of efficient lightweight structures with enhanced structural stiffness and safety compared to the conventional macroscale and microscale TO methods. Keywords Additive manufacturing · 3D printing · Lightweight design · Topology optimization · Lattice optimization · Finite element analysis List of Symbols f Structural compliance K Global stiffness matrix F Load vector u Displacement vector. ρ Pseudo density in macroscale TO Vf Target volume fraction in macroscale TO E0 Elastic modulus of solid material Ei Elementary elastic modulus in macroscale TO ρi Elementary pseudo density in macroscale TO Ne The number of finite elements in macroscale TO dj Diameter of the j-th strut in microscale TO Vj The strut volume fraction in microscale TO Ns The number of struts in microscale TO * Keun Park [email protected] 1
Department of Mechanical System Design Engineering, Seoul National University of Science and Technology, 232 Gongneung‑ro, Nowon‑gu, Seoul 01811, Republic of Korea
dmin The minimum strut diameter in microscale TO dmax The maximum strut diameter in microscale TO ρ* Reduced pseudo density in multiscale TO d* Strut diameter in multiscale TO Vf* Reduced target volume fraction in multiscale TO Vr The volum
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