Additive manufacturing (AM) is now capable of fabricating geometrically complex geometries such as a variable-density lattice structure. This ability to handle geometric complexity provides the designer an opportunity to rethink the design method. In this work, a novel topology optimization algorithm is proposed to design variable-density lattice infill to maximize the first eigenfrequency of the structure. To make the method efficient, the lattice infill is treated as a continuum material with equivalent elastic properties obtained from asymptotic homogenization (AH), and the topology optimization is employed to find the optimum density distribution of the lattice structure. Specifically, the AH method is employed to calculate the effective mechanical properties of a predefined lattice structure as a function of its relative densities. Once the optimal density distribution is obtained, a continuous mapping technique is used to convert the optimal density distribution into variable-density lattice structured design. Two three-dimensional (3D) examples are used to validate the proposed method, where the designs are printed by the EOS direct metal laser sintering (DMLS) process in Ti6Al4V. Experimental results obtained from dynamical testing of the printed samples and detailed simulation results are in good agreement with the homogenized model results, which demonstrates the accuracy and efficiency of the proposed method.
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October 2018
Design Innovation Paper
Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation
Lin Cheng,
Lin Cheng
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
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Xuan Liang,
Xuan Liang
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
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Eric Belski,
Eric Belski
Aerotech,
Pittsburgh, PA 15238
101 Zeta Drive
,Pittsburgh, PA 15238
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Xue Wang,
Xue Wang
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
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Jennifer M. Sietins,
Jennifer M. Sietins
Materials Manufacturing Technology Branch,
Army Research Laboratory,
Aberdeen, MD 21005
Army Research Laboratory,
Aberdeen Proving Ground
,Aberdeen, MD 21005
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Steve Ludwick,
Steve Ludwick
Aerotech,
Pittsburgh, PA 15238
101 Zeta Drive
,Pittsburgh, PA 15238
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Albert To
Albert To
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: albertto@pitt.edu
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: albertto@pitt.edu
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Lin Cheng
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
Xuan Liang
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
Eric Belski
Aerotech,
Pittsburgh, PA 15238
101 Zeta Drive
,Pittsburgh, PA 15238
Xue Wang
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
Jennifer M. Sietins
Materials Manufacturing Technology Branch,
Army Research Laboratory,
Aberdeen, MD 21005
Army Research Laboratory,
Aberdeen Proving Ground
,Aberdeen, MD 21005
Steve Ludwick
Aerotech,
Pittsburgh, PA 15238
101 Zeta Drive
,Pittsburgh, PA 15238
Albert To
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: albertto@pitt.edu
and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: albertto@pitt.edu
Manuscript received October 10, 2017; final manuscript received June 15, 2018; published online July 27, 2018. Assoc. Editor: Qiang Huang. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.
J. Manuf. Sci. Eng. Oct 2018, 140(10): 105002 (16 pages)
Published Online: July 27, 2018
Article history
Received:
October 10, 2017
Revised:
June 15, 2018
Citation
Cheng, L., Liang, X., Belski, E., Wang, X., Sietins, J. M., Ludwick, S., and To, A. (July 27, 2018). "Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation." ASME. J. Manuf. Sci. Eng. October 2018; 140(10): 105002. https://doi.org/10.1115/1.4040622
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