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Design Innovation Paper

Natural Frequency Optimization of Variable-Density Additively Manufactured Lattice Structure: Theory and Experimental Validation

[+] Author and Article Information
Lin Cheng

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261
chenglin9003@gmail.com

Xuan Liang

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261
XUL31@pitt.edu

Eric Belski

Aerotech, 101 Zeta Drive, Pittsburgh, PA 15238
ebelski@aerotech.com

Xue Wang

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261
wangxue.dlut@gmail.com

Jennifer Sietins

Materials Manufacturing Technology Branch, Army Research Laboratory, Aberdeen Proving Ground, MD 21005
jennifer.m.sietins.civ@mail.mil

Stephen Ludwick

Aerotech, 101 Zeta Drive, Pittsburgh, PA 15238
sludwick@aerotech.com

Albert C. To

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

1Corresponding author.

ASME doi:10.1115/1.4040622 History: Received October 10, 2017; Revised June 15, 2018

Abstract

Additive manufacturing is now capable of fabricating complex geometries, such as a variable-density lattice structures. 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 a structure. To make the method efficient, the lattice infill is treated as a continuum material with equivalent elastic properties obtained from asymptotic homogenization, and the topology optimization is employed to find the optimum density distribution of the lattice structure. Specifically, the asymptotic homogenization 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 examples printed in Ti6Al4V by the direct metal laser sintering process are used to validate the proposed method. Experimental results obtained from dynamic 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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