Research Papers

Multiscale Topology Optimization for Additively Manufactured Objects

[+] Author and Article Information
John C. Steuben

Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology,
U.S. Naval Research Laboratory,
Washington, DC 20375

Athanasios P. Iliopoulos

Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology
U.S. Naval Research Laboratory,
Washington, DC 20375

John G. Michopoulos

Fellow ASME
Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology,
U.S. Naval Research Laboratory,
Washington, DC 20375

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 15, 2017; final manuscript received January 23, 2018; published online June 12, 2018. Assoc. Editor: Jitesh H. Panchal.

J. Comput. Inf. Sci. Eng 18(3), 031002 (Jun 12, 2018) (10 pages) Paper No: JCISE-17-1229; doi: 10.1115/1.4039312 History: Received October 15, 2017; Revised January 23, 2018

The precise control of mass and energy deposition associated with additive manufacturing (AM) processes enables the topological specification and realization of how space can be filled by material in multiple scales. Consequently, AM can be pursued in a manner that is optimized such that fabricated objects can best realize performance specifications. In the present work, we propose a computational multiscale method that utilizes the unique meso-scale structuring capabilities of implicit slicers for AM, in conjunction with existing topology optimization (TO) tools for the macro-scale, in order to generate structurally optimized components. The use of this method is demonstrated on two example objects including a load bearing bracket and a hand tool. This paper also includes discussion concerning the applications of this methodology, its current limitations, a recasting of the AM digital thread, and the future work required to enable its widespread use.

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Grahic Jump Location
Fig. 1

An overview of the AM “digital thread” concept

Grahic Jump Location
Fig. 2

Illustration of toolpath concepts. Note the perimeter shells (black) that enclose a sparse infill pattern (red); this combination of path types is commonly used in AM applications.

Grahic Jump Location
Fig. 3

Example of implicit slicing. At top, the input geometry and applied force F. At center, the von Mises stress in the part, as calculated using FEA. At bottom, the toolpath produced by the implicit slicer.

Grahic Jump Location
Fig. 4

Flowchart of the workflow demonstrating the stages of the proposed multiscale methodology for TO

Grahic Jump Location
Fig. 5

TO example. At top (a) the original domain and boundary conditions are shown. At center (b), the output ρd is shown, with the cutoff value ρd=ρmin highlighted. At the bottom (c), the output domain Ω corresponding to ρd≥ρmin is highlighted: (a) TO domain, (b) results of TO, and (c) output domain from TO.

Grahic Jump Location
Fig. 6

Steps for computing the 2D and 3D domains: (a) 2Γρ, (b) 2Γρ ∪ 2Γ0, (c) Γ=2Γρ ∪ 2Γ0¯, and (d) 2Ω, and (e) 3Γ

Grahic Jump Location
Fig. 7

TO example. (a) the density field from the topology optimizer. (b, c) the corresponding linear infill function defined over the first and second layers. (d, e) the modulated infill function for the first and second layers. (f) contours corresponding to the infill for the first two layers superimposed, along with the perimeter contours: (a) ρd(x), (b) Hlin(x) for z = 0, (c) Hlin(x) for z=lt, (d) Hin(x) for z = 0, (e) Hin(x) for z=lt, and (f) superimposed infill for first two layers.

Grahic Jump Location
Fig. 8

Complete bracket toolpath in 3D space. All slices are of the same bounding geometry, resulting in a 2.5D part.

Grahic Jump Location
Fig. 9

Illustration of the graph formulation for optimal toolpath sequencing. The original toolpath segments are shown in bold, with the vertices Vi on either end. The negative-weight edges connecting the endpoints of the original segments are bold and dashed. The positive weight edges representing movement between toolpath segments are shown by light dashed lines.

Grahic Jump Location
Fig. 10

The fastener that the spanner must drive (top), and the corresponding dimensions and boundary conditions on the outer envelope of the spanner wrench

Grahic Jump Location
Fig. 11

Multiscale TO of the wrench. At top (a), the density function is computed by the topology optimizer. Below (b) is the domain Ω upon which the implicit slicer operates. The infill function Hin is shown, for the first two layers, in (c). In (d) and (e) the output toolpath can be seen. At bottom (f), the FDM-manufactured wrench is photographed: (a) ρd(x), (b) Ω, (c) Hin for z = 0 and z=lt, (d) ρd(x) with gin∪gpr superimposed, (e) output toolpath, and (f) photograph of as-manufactured wrench.

Grahic Jump Location
Fig. 12

The reinterpreted digital thread incorporating an optimization environment




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