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Research Papers

Structural Topology Optimization Through Explicit Boundary Evolution

[+] Author and Article Information
Weisheng Zhang, Jianhua Zhou

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

Wanying Yang, Dong Li

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

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

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 4, 2016; final manuscript received October 7, 2016; published online November 3, 2016. Editor: Yonggang Huang.

J. Appl. Mech 84(1), 011011 (Nov 03, 2016) (10 pages) Paper No: JAM-16-1487; doi: 10.1115/1.4034972 History: Received October 04, 2016; Revised October 07, 2016

Traditional topology optimization is usually carried out with approaches where structural boundaries are represented in an implicit way. The aim of the present paper is to develop a topology optimization framework where both the shape and topology of a structure can be obtained simultaneously through an explicit boundary description and evolution. To this end, B-spline curves are used to describe the boundaries of moving morphable components (MMCs) or moving morphable voids (MMVs) in the structure and some special techniques are developed to preserve the smoothness of the structural boundary when topological change occurs. Numerical examples show that optimal designs with smooth structural boundaries can be obtained successfully with the use of the proposed approach.

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References

Figures

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Fig. 1

Representing structural topology by a set of boundary curves

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Fig. 2

A quadratic B-spline curve

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Fig. 3

Self-intersection phenomenon

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Fig. 4

The construction of a typical B-spline curve C(u) described in Eq. (2.2).

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Fig. 5

The representation of Ωs under two formulations and the treatment of intersected B-spline curves: (a) The representation of Ωs under the MMC formulation, (b) the representation of Ωs under the MMV formulation, and (c) the treatment of two intersected B-spline curves

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Fig. 6

A schematic illustration of the construction of χs

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Fig. 7

A B-spline curve constituted by several skeleton B-spline curves

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Fig. 8

B-spline representation of a structural component described in Eq. (5.1).

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Fig. 9

The short beam example

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Fig. 10

The initial designs for the short beam example: (a) Initial design for the MMC formulation and (b) initial design for the MMV formulation

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Fig. 11

Optimized structures for the short beam example: (a) optimized structure under the MMC formulation (B-spline plot and contour plot) and (b) optimized structure under the MMV formulation (B-spline plot and contour plot)

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Fig. 12

A closer look of a specific part of the structural boundary (short beam example, MMC formulation)

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Fig. 13

The L-shape beam example

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Fig. 14

The initial designs for the L-shape beam example: (a) Initial design for the MMC formulation and (b) initial design for the MMV formulation

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Fig. 15

Optimized structures for the L-shape beam example: (a) optimized structure under the MMC formulation (contour plot and B-spline plot) and (b) optimized structure under the MMC formulation (contour plot and B-spline plot)

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Fig. 16

Some intermediate iteration steps for the L-shape beam example under the MMV formulation: (a) step 3, (b) step 17, and (c) step 29

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Fig. 17

Convergence history of the L-shape beam example under the MMV formulation

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Fig. 18

A closer look of a specific part of the structural boundary (L-shape beam example, MMV formulation)

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