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Multiscale Topology Optimization Combining Density-Based Optimization and Lattice Enhancement for Additive Manufacturing

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A Correction to this article was published on 26 January 2021

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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.

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Abbreviations

f :

Structural compliance

K :

Global stiffness matrix

F :

Load vector

u :

Displacement vector.

ρ :

Pseudo density in macroscale TO

V f :

Target volume fraction in macroscale TO

E 0 :

Elastic modulus of solid material

E i :

Elementary elastic modulus in macroscale TO

ρ i :

Elementary pseudo density in macroscale TO

N e :

The number of finite elements in macroscale TO

d j :

Diameter of the j-th strut in microscale TO

V j :

The strut volume fraction in microscale TO

N s :

The number of struts in microscale TO

d min :

The minimum strut diameter in microscale TO

d max :

The maximum strut diameter in microscale TO

ρ * :

Reduced pseudo density in multiscale TO

d * :

Strut diameter in multiscale TO

V f * :

Reduced target volume fraction in multiscale TO

V r :

The volume of the remaining struts after integration in multiscale TO

N r :

The number of remaining struts after integration in multiscale TO

α :

Scale factor to consider the strut overlapping in multiscale TO

δ max :

The maximum vertical displacement

F max :

The maximum compressive force

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Acknowledgements

This work was supported by a Korea Institute of Machinery & Materials grant (Grant no.: NK224I) and a National Research Foundation of Korea (NRF) grant (Grant no.: 2019R1A2C1002799) funded by the by the Ministry of Science and ICT, Republic of Korea.

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  1. Department of Mechanical System Design Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul, 01811, Republic of Korea

    Jae-Eun Kim & Keun Park

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Correspondence to Keun Park.

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The original online version of this article was revised: Due to an unfortunate oversight, the colour bar of fig. 7 has been given erroneously.

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Kim, JE., Park, K. Multiscale Topology Optimization Combining Density-Based Optimization and Lattice Enhancement for Additive Manufacturing. Int. J. of Precis. Eng. and Manuf.-Green Tech. 8, 1197–1208 (2021). https://doi.org/10.1007/s40684-020-00289-1

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