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Research Papers: Design Automation

Design and Optimization of Graded Cellular Structures With Triply Periodic Level Surface-Based Topological Shapes

[+] Author and Article Information
Dawei Li

College of Mechanical and Electrical Engineering,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: davidlee@nuaa.edu.cn

Ning Dai

College of Mechanical and Electrical Engineering,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: dai_ning@nuaa.edu.cn

Yunlong Tang

Department of Mechanical Engineering,
McGill University,
Montreal, Quebec, Canada H3A 0G4
e-mail: tang.yunlong@mail.mcgill.ca

Guoying Dong

Department of Mechanical Engineering,
McGill University,
Montreal, Quebec, Canada H3A 0G4
e-mail: guoying.dong@mail.mcgill.ca

Yaoyao Fiona Zhao

Department of Mechanical Engineering,
McGill University,
Montreal, Quebec, Canada H3A 0G4
e-mail: yaoyao.zhao@mcgill.ca

1Corresponding authors.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received June 27, 2018; final manuscript received January 14, 2019; published online March 13, 2019. Assoc. Editor: Xu Guo.

J. Mech. Des 141(7), 071402 (Mar 13, 2019) (13 pages) Paper No: MD-18-1491; doi: 10.1115/1.4042617 History: Received June 27, 2018; Accepted January 15, 2019

Periodic cellular structures with excellent mechanical properties widely exist in nature. A generative design and optimization method for triply periodic level surface (TPLS)-based functionally graded cellular structures is developed in this work. In the proposed method, by controlling the density distribution, the designed TPLS-based cellular structures can achieve better structural or thermal performances without increasing its weight. The proposed technique can be divided into four steps. First, the modified 3D implicit functions of the triply periodic minimal surfaces are developed to design different types of cellular structures parametrically and generate spatially graded cellular structures. Second, the numerical homogenization method is employed to calculate the elastic tensor and the thermal conductivity tensor of the cellular structures with different densities. Third, the optimal relative density distribution of the object is computed by the scaling laws of the TPLS-based cellular structures added optimization algorithm. Finally, the relative density of the numerical results of structure optimization is mapped into the modified parametric 3D implicit functions, which generates an optimum lightweight cellular structure. The optimized results are validated subjected to different design specifications. The effectiveness and robustness of the obtained structures is analyzed through finite element analysis and experiments. The results show that the functional gradient cellular structure is much stiffer and has better heat conductivity than the uniform cellular structure.

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Figures

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Fig. 1

Procedures for TPLS-based functionally graded cellular structures design and optimization

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Fig. 2

Library of TPLS-based cellular structures: (a) G, D, P, and W level surfaces and (b) cellular structures with 3 × 3 × 3 unit cells

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Fig. 3

Scaling laws of the relative density of G-, D-, P-, and W-based cellular structures (R2: coefficient of determination)

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Fig. 4

Example of functionally graded cellular structures of G (a), D (b), P (c), and W (d) along the y-axis direction

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Fig. 5

Asymptotic homogenization concept of a cellular structure

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Fig. 6

Elastic tensor and thermal conductivity tensor scaling laws for TPLS-based cellular structures: (a) Gyroid, (b) diamond, (c) primitive, and (d) iWP

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Fig. 7

The procedure of the relative density mapping methodology

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Fig. 8

(a) A cubic block of 30 × 30 × 30 mm, (b) boundary conditions for stress deformation analysis, (c) boundary conditions for thermal analysis, and (d)–(l) the number of units along a single direction are 1, 2, 3, 4, 5, 6, 8, 10, and 12

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Fig. 9

(a) Maximum of the total deformation associated with unit cell number along one direction and (b) maximum temperature associated with unit cell number along one direction

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Fig. 10

(a) The design domain and boundary conditions, (b) and (c) an optimized cantilever beam and its cross section area, and (d)–(f) different filling densities, density intervals, and their results of compliance, respectively (ρ is the relative density and c is the compliance)

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Fig. 11

Comparison between the homogenization result and full-scale simulation of the optimized cantilever beam (kstiffness is the stiffness of the linear elastic region, Case 1 and Case 2 are the examples)

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Fig. 12

Illustration of local material damage: (a) standard topology optimization, the uniform gyroid-based cellular structure, and our proposed optimized cellular structures, respectively, (b) deficiencies in different areas (A, B, and C), and (c) displacement results with different design strategies and different deficiencies. (ρ is the relative density, c is the compliance).

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Fig. 13

Heat-sink optimization and full-scale simulation results: (a) design domain and boundary conditions, (b) the uniform gyroid structure with the volume fraction of 30%, (c) our optimized result with a density range of 0.1–0.8, and (d) our optimized result with a density range of 0.1–0.9

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