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Research Papers

Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation

[+] Author and Article Information
Pu Zhang, Jakub Toman, Yiqi Yu, Emre Biyikli, Markus Chmielus

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261

Mesut Kirca

Department of Mechanical Engineering,
Istanbul Technical University,
Istanbul 34437, Turkey

Albert C. To

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: albertto@pitt.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received April 14, 2014; final manuscript received September 21, 2014; published online December 12, 2014. Assoc. Editor: David L. Bourell.

J. Manuf. Sci. Eng 137(2), 021004 (Apr 01, 2015) (8 pages) Paper No: MANU-14-1172; doi: 10.1115/1.4028724 History: Received April 14, 2014; Revised September 21, 2014; Online December 12, 2014

Cellular structures are promising candidates for additive manufacturing (AM) due to their lower material and energy consumption. In this work, an efficient method is proposed for optimizing the topology of variable-density cellular structures to be fabricated by certain AM process. The method gains accuracy by relating the cellular structure's microstructure to continuous micromechanics models and achieves efficiency through conducting continuum topology optimization at macroscopic scale. The explicit cellular structure is then finally reconstructed by mapping the optimized continuous parameters (e.g., density) to cell structural parameters (e.g., strut diameter). The proposed method is validated by both finite element analysis and experimental tests on specimens manufactured by stereolithography.

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Figures

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Fig. 1

Schematic illustration of the HOC steps during the design-optimization process of an AM cellular structure: (a) material property modeling based on computational micromechanics model. (b) Continuous solid model based on obtained homogenized material properties. (c) Topology optimization for the continuous solid model (darker gray scales indicate higher local density of material). (d) Explicit cellular structure obtained from cell construction step.

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Fig. 2

Flowchart of the design-optimization process of a cellular structured component produced by AM

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Fig. 3

Material property scaling law of cellular structures with hexagonal lattice and circular holes: (a) C11/C11* and (b) C33/C33*. Solid curves indicate fitted functions shown in Eq. (2) while triangular markers show results from FEA simulation. The Hashin–Shtrikman (H–S) lower and upper bounds are indicated by dash curves for comparison.

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Fig. 4

Cellular structure construction for a variable-density hexagonal lattice structure. (a) A map with overlapping FEA square elements and hexagonal lattice points. One hexagon cell with a circular hole is constructed as an example. (b) An example of the corresponding cellular structure constructed by using the proposed algorithm.

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Fig. 5

Schematic illustration of a simply supported beam with its cross section

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Fig. 6

Optimized density distribution and constructed cellular structures of a simply supported beam

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Fig. 7

Comparison of the flexural stiffness k obtained from continuous model and constructed cellular structures

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Fig. 8

Photos of the AM cellular beams manufactured by SLA. Only a half of each beam is presented to show the cell structures clearly. (a) Uniform cellular structure. (b) Optimized cellular structure.

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Fig. 9

Loading curves of cellular structured beams obtained from three-point bending test

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