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Research Papers

Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework

[+] Author and Article Information
Xu Guo

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

Weisheng Zhang, Wenliang Zhong

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

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 8, 2014; final manuscript received May 3, 2014; accepted manuscript posted May 8, 2014; published online May 22, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(8), 081009 (May 22, 2014) (12 pages) Paper No: JAM-14-1162; doi: 10.1115/1.4027609 History: Received April 08, 2014; Revised May 03, 2014; Accepted May 08, 2014

In the present work, we intend to demonstrate how to do topology optimization in an explicit and geometrical way. To this end, a new computational framework for structural topology optimization based on the concept of moving morphable components is proposed. Compared with the traditional pixel or node point-based solution framework, the proposed solution paradigm can incorporate more geometry and mechanical information into topology optimization directly and therefore render the solution process more flexibility. It also has the great potential to reduce the computational burden associated with topology optimization substantially. Some representative examples are presented to illustrate the effectiveness of the proposed approach.

Copyright © 2014 by ASME
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Figures

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Fig.1

Pixel-based topology optimization

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Fig. 2

Geometry and topology representation in CAD system

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Fig. 3

The curse of dimensionality in topology optimization

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Fig. 4

Node point-based topology optimization

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Fig. 5

Structural topology represented by the layout of structural components

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Fig. 6

Structural components as basic building blocks of topology optimization

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Fig. 7

Simple components and complex structural topologies

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Fig. 8

Rectangular structural component and its level set function (m = 6)

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Fig. 9

Topology variation through hiding mechanism of components

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Fig. 10

Approximation of curved structural components with use of straight ones

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Fig. 11

Skeleton-based topology optimization

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Fig. 12

(a) Geometry modeling of structural component with a curved geometry and (b) geometry modeling of structural components with curved geometries

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Fig. 13

XFEM analysis based on a fixed mesh

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Fig. 14

Fixed FEM mesh and adaptive narrow band FEM mesh

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Fig. 15

The short beam example

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Fig. 16

Initial design for the short beam example

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Fig. 17

Optimal topology of the short beam example (load imposed at Point A)

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Fig. 18

Some intermediate iteration steps of the short beam example (load imposed at Point A)

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Fig. 19

Optimal topology of the short beam example (load imposed at Point B)

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Fig. 20

Some intermediate iteration steps of the short beam example (load imposed at Point B)

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Fig. 22

The initial design of the MBB example

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Fig. 23

Optimal topology of the MBB example (half)

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Fig. 24

Some intermediate iteration steps of the MBB example (half)

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Fig. 25

Topological design with embedded geometrical features

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