Research Papers: Design Automation

Generating Constructal Networks for Area-to-Point Conduction Problems Via Moving Morphable Components Approach

[+] Author and Article Information
Baotong Li, Chengbin Xuan, Guoguang Liu

Key Laboratory of Education Ministry for
Modern Design and Rotor-Bearing System,
School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China

Jun Hong

Key Laboratory of Education Ministry for
Modern Design and Rotor-Bearing System,
School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: jhong_email@163.com

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 13, 2018; final manuscript received November 7, 2018; published online January 11, 2019. Assoc. Editor: Samy Missoum.

J. Mech. Des 141(5), 051401 (Jan 11, 2019) (16 pages) Paper No: MD-18-1450; doi: 10.1115/1.4042020 History: Received June 13, 2018; Revised November 07, 2018

In this article, we focus on a generative design algorithm for area-to-point (AP) conduction problems in a Lagrangian framework. A physically meaningful continuous area to point path solution is generated through an adaptive growth procedure, which starts from the source point and extends spreading the whole conduction domain. This is achieved by using a set of special moving morphable components (MMCs) whose contour and skeleton are described explicitly by parameterized level-set surfaces. Unlike in the conventional methods where topology optimization was carried out in an Eulerian framework, the proposed optimizer is Lagrangian in nature, which is consistent with classical shape optimization approaches, giving great potential to reduce the total number of design variables significantly and also yielding more flexible modeling capability to control the structural feature sizes. By doing this, the growth elements are separated from the underlying finite element method (FEM) grids so that they can grow toward an arbitrary direction to form an optimized area-to-point path solution. The method is tested on an electromagnetic bandgap (EBG) power plane design example; both simulation and experiment verified the effectiveness of the proposed method.

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Fig. 1

Transformation from PDN design problem to equivalent AP problem

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Fig. 2

(a) Polygonal shaped growth element and its level-set function and (b) description of the element geometry with explicit parameters

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Fig. 3

Finite element method modeling of growth elements

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Fig. 4

Flowchart of the generative algorithm

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Fig. 5

Design domain of case 1

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Fig. 6

Growth process of case 1

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Fig. 7

Changing process of Umin

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Fig. 8

Design domain of case 2

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Fig. 9

Growth history of case 2

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Fig. 10

Illustration of design domain

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Fig. 11

Changing history of the level-set functions for growth elements

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Fig. 12

Variation of the minimum voltage across over the entire domain during the simulation

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Fig. 13

Geometry representation utilized in the SIMP method and the growth-based method

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Fig. 14

Comparison of the results obtained by the growth-based method and the SIMP method (note: the SIMP algorithm utilized in the above computation is cited from Ref. [18])

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Fig. 15

Numerical comparison of the synthesized designs (note: the type of EBG structure cells utilized in the simulation is cited from Ref. [12])

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Fig. 16

Numerical comparison of the synthesized designs (note: the type of EBG structure cells utilized in the simulation is cited from Ref. [27])

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Fig. 17

S21 simulation results for design_1 and design_2

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Fig. 18

S21 simulation results for design_3 and design_4

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Fig. 19

Experimental setup for S21 analysis

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Fig. 20

Comparison of simulated and measured values of S21



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