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Research Papers: Design Automation

Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints

[+] Author and Article Information
Zongliang Du

Structural Engineering Department,
University of California, San Diego,
San Diego, CA 92093
e-mail: zodu@eng.ucsd.edu

Xiao-Yi Zhou

School of Engineering,
Cardiff University,
Cardiff CF24 3AA, UK
e-mail: zhoux19@cf.ac.uk

Renato Picelli

School of Engineering,
Cardiff University,
Cardiff CF24 3AA, UK
e-mail: PicelliR@cardiff.ac.uk

H. Alicia Kim

Structural Engineering Department,
University of California, San Diego,
San Diego, CA 92093;
School of Engineering,
Cardiff University,
Cardiff CF24 3AA, UK
e-mail: alicia@ucsd.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 1, 2018; final manuscript received August 6, 2018; published online October 1, 2018. Assoc. Editor: James K. Guest.

J. Mech. Des 140(11), 111417 (Oct 01, 2018) (12 pages) Paper No: MD-18-1272; doi: 10.1115/1.4041176 History: Received April 01, 2018; Revised August 06, 2018

With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities.

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Figures

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Fig. 1

An illustration of multiscale topology optimization without connectivity

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Fig. 2

An L-beam example with (a) the design domain, (b) the initial macroscale structure, and (c) the initial microstructure

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Fig. 3

Multiscale optimization solution of the L beam example (a) optimized macroscale structure and (b) optimized microstructures illustrating the connectivity challenges

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Fig. 4

An illustration of the proposed connectivity measure, where yellow structure on the left represents one-unit cell and the green structure on the right represents the adjacent unit cell, and the light red strips represent the interface regions used to quantify the connectivity between the two cells

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Fig. 5

Two test cases obtained by microstructural optimization via homogenization, (a) maximum shear modulus and bulk modulus solutions and (b) maximum D11H and D22H solutions

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Fig. 11

Optimization history of cantilevered beam 2:3

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Fig. 10

Illustrations of the connected cellular materials of the cantilevered beams (a) design domain 1:3 and (b) design domain 2:3

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Fig. 15

Optimized solution for case 3 (a) macrostructure and (b) microstructure and (c) an illustration of the optimized structure–material system

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Fig. 16

Optimization history of L-beam case 3

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Fig. 8

(a) Illustration of the self-connectivity index and (b) maximum shear and bulk modulus microstructure designs with self-connectivity constraints

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Fig. 7

The maximum shear and bulk microstructure design

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Fig. 6

(a) Initial design with five circular holes, (b) optimized unit cell with maximum shear modulus, (c) optimized unit cell with maximum bulk modulus, and (d) optimized unit cell with maximum D22H

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Fig. 12

Optimized solution for case 1 (a) macrostructure and (b) microstructure

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Fig. 13

The optimized multiscale structure of case (3) with (a) the optimized macrostructure and (b) the optimized microstructures

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Fig. 14

Optimization history of L-beam case 2

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