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Research Papers: Design Automation

Sustainable Design-Oriented Level Set Topology Optimization

[+] Author and Article Information
Jikai Liu

Department of Mechanical Engineering,
University of Alberta,
Edmonton, AB T6G 1H9, Canada
e-mail: jikai@ualberta.ca

Yongsheng Ma

Department of Mechanical Engineering,
University of Alberta,
Edmonton, AB T6G 1H9, Canada

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 15, 2016; final manuscript received October 9, 2016; published online November 11, 2016. Assoc. Editor: James K. Guest.

J. Mech. Des 139(1), 011403 (Nov 11, 2016) (8 pages) Paper No: MD-16-1037; doi: 10.1115/1.4035052 History: Received January 15, 2016; Revised October 09, 2016

This paper presents a novel sustainable design-oriented level set topology optimization method. It addresses the sustainability issue in product family design, which means an end-of-life (EoL) product can be remanufactured through subtractive machining into another lower-level model within the product family. In this way, the EoL product is recycled in an environmental-friendly and energy-saving manner. Technically, a sustainability constraint is proposed that the different product models employ the containment relationship, which is a necessary condition for the subtractive remanufacturing. A novel level set-based product family representation is proposed to realize the containment relationship, and the related topology optimization problem is formulated and solved. In addition, spatial arrangement of the input design domains is explored to prevent highly stressed material regions from reusing. Feature-based level set concept for sustainability is then used. The novelty of the proposed method is that, for the first time, the product lifecycle issue of sustainability is addressed by a topology optimization method. The effectiveness of the proposed method is proved through a few numerical examples.

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Figures

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Fig. 1

Approaches of EoL product reuse

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Fig. 2

Product family of the cube structure: (a) model 1 (volume ratio = 0.4), (b) model 2 (volume ratio = 0.3), and (c) model 3 (volume ratio = 0.2)

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Fig. 3

Strategies of product family design: (a) strategy 1, (b) strategy 2, and (c) new strategy

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Fig. 4

Multimaterial level set geometry modeling

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Fig. 5

Level set-based product family representation

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Fig. 6

Boundary conditions of (a) model 1 and (b) model 2

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Fig. 7

The independent solution of model 1

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Fig. 8

Optimization results under different weight factors. (a) Results of model 1 (compliance = 51.68), model 2 (compliance = 34.52), and the spatial overlap under the weight factor w1 = 0.9; (b) results of model 1 (compliance = 51.99), model 2 (compliance = 32.42), and the spatial overlap under the weight factor w1 = 0.8; (c) results of model 1 (compliance = 52.09), model 2 (compliance = 32.08), and the spatial overlap under the weight factor w1 = 0.7; (d) results of model 1 (compliance = 53.40), model 2 (compliance = 30.81), and the spatial overlap under the weight factor w1 = 0.6; (e) results of model 1 (compliance = 54.76), model 2 (compliance = 30.90), and the spatial overlap under the weight factor w1 = 0.5; and (f) results of model 1 (compliance = 56.21), model 2 (compliance = 30.70), and the spatial overlap under the weight factor w1 = 0.4.

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Fig. 9

Influence of the weight factor

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Fig. 10

Optimization results after changing the volume fractions: (a) results of model 1 (compliance = 52.66), model 2 (compliance = 49.41), and the spatial overlap under the weight factor w1 = 0.8; (b) results of model 1 (compliance = 54.99), model 2 (compliance = 47.18), and the spatial overlap under the weight factor w1 = 0.4

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Fig. 11

Rearrangement of the boundary condition of model 2

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Fig. 12

Optimization results after spatial arrangement: (a) results of model 1 (compliance = 51.88), model 2 (compliance = 31.74), and the spatial overlap under the weight factor w1 = 0.5; (b) results of model 1 (compliance = 56.44), model 2 (compliance = 30.83), and the spatial overlap under the weight factor w1 = 0.2

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Fig. 13

Boundary conditions of (a) model 1, (b) model 2 (given the spatial arrangement 1), and (c) model 2 (given the spatial arrangement 2)

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Fig. 14

Optimization results subject to the spatial arrangement 1: (a) results of model 1 (compliance = 80.51), model 2 (compliance = 53.57), and the spatial overlap under the weight factor w1 = 0.5; (b) results of model 1 (compliance = 89.90), model 2 (compliance = 50.03), and the spatial overlap under the weight factor w1 = 0.2

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Fig. 15

Optimization results subject to the spatial arrangement 2: (a) results of model 1 (compliance = 77.39), model 2 (compliance = 20.27), and the spatial overlap under the weight factor w1 = 0.5; (b) results of model 1 (compliance = 84.67), model 2 (compliance = 18.93), and the spatial overlap under the weight factor w1 = 0.2

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Fig. 16

The torque arm example: (a) the design domain and boundary condition of model 1; (b) the design domain and boundary condition of model 2; and (c) construction of the geometry through R-functions

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Fig. 17

Optimization results under different weight factors: (a) model 1 (w1 = 0.9), (b) model 2 (w1 = 0.9), (c) model 1 (w1 = 0.8), (d) model 2 (w1 = 0.8), (e) model 1 (w1 = 0.7), (f) model 2 (w1 = 0.7), (g) model 1 (w1 = 0.6), (h) model 2 (w1 = 0.6), (i) model 1 (w1 = 0.5), (j) model 2 (w1 = 0.5), (k) model 1 (w1 = 0.4), and (l) model 2 (w1 = 0.4)

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Fig. 18

Influence of the weight factor

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