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Research Papers

Additive Manufacturing-Oriented Design of Graded Lattice Structures Through Explicit Topology Optimization

[+] Author and Article Information
Chang Liu, Zongliang Du, Weisheng Zhang, Yichao Zhu

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
International Research Center for
Computational Mechanics,
Dalian University of Technology,
Dalian 116023, China

Xu Guo

State Key Laboratory of Structural Analysis for
Industrial Equipment, Department of
Engineering Mechanics,
International Research Center for
Computational Mechanics,
Dalian University of Technology,
Dalian 116023, China
e-mail: guoxu@dlut.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 24, 2017; final manuscript received May 29, 2017; published online June 16, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(8), 081008 (Jun 16, 2017) (12 pages) Paper No: JAM-17-1271; doi: 10.1115/1.4036941 History: Received May 24, 2017; Revised May 29, 2017

In the present work, a new approach for designing graded lattice structures is developed under the moving morphable components/voids (MMC/MMV) topology optimization framework. The essential idea is to make a coordinate perturbation to the topology description functions (TDF) that are employed for the description of component/void geometries in the design domain. Then, the optimal graded structure design can be obtained by optimizing the coefficients in the perturbed basis functions. Our numerical examples show that the proposed approach enables a concurrent optimization of both the primitive cell and the graded material distribution in a straightforward and computationally effective way. Moreover, the proposed approach also shows its potential in finding the optimal configuration of complex graded lattice structures with a very small number of design variables employed under various loading conditions and coordinate systems.

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References

Figures

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Fig. 1

A print with graded patterns [26]

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Fig. 2

Generating a periodic lattice structure through a primitive cell

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Fig. 3

Generating graded lattice structures using different approaches

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Fig. 4

Generating graded effect through coordinate transformation

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Fig. 5

The simply supported beam example

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Fig. 6

Numerical results of the simply supported beam example: (a) and (f) initial designs for the two cases, respectively; (b)–(d) and (g)–(i) some intermediate results for the two cases, respectively; (e) and (j) the optimized structures

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Fig. 7

Convergence history of the values of the objective function: (a) case 1 and (b) case 2

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Fig. 8

A circle region under distributed pressure

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Fig. 9

Numerical results of the pressured circle region example: (a) initial design; (b)–(e) some intermediate results; (f) optimized structure

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Fig. 10

Convergence history of the values of the objective function for the pressured circle region example

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Fig. 11

A torque arm example

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Fig. 12

Initial designs for the torque arm example

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Fig. 13

Optimized graded lattice structure of the torque arm

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