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Research Papers: Design Automation

A Moving Morphable Component Based Topology Optimization Approach for Rib-Stiffened Structures Considering Buckling Constraints

[+] Author and Article Information
Weisheng Zhang

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

Ying Liu, Yichao Zhu

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

Zongliang Du

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
International Research Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116023, China;
Structural Engineering Department,
University of California, San Diego,
San Diego, CA 92093

Xu Guo

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

1Corresponding authors.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 3, 2018; final manuscript received July 31, 2018; published online September 7, 2018. Assoc. Editor: Andres Tovar.

J. Mech. Des 140(11), 111404 (Sep 07, 2018) (12 pages) Paper No: MD-18-1182; doi: 10.1115/1.4041052 History: Received March 03, 2018; Revised July 31, 2018

Stiffened structures are widely used in industry. However, how to optimally distribute the stiffening ribs on a given base plate remains a challenging issue, partially because the topology and geometry of stiffening ribs are often represented in a geometrically implicit way in traditional approaches. This implicit treatment may lead to problems such as high computational cost (caused by the large number of design variables, geometry constraints in optimization, and large degrees-of-freedom (DOF) in finite element analysis (FEA)) and the issue of manufacturability. This paper presents a moving morphable component (MMC)-based approach for topology optimization of rib-stiffened structures, where the topology and the geometry of stiffening ribs are explicitly described. The proposed approach displays several prominent advantages, such as (1) both the numbers of design variables and DOF in FEA are reduced substantially; (2) the proper manufacture-related geometry requirements of stiffening ribs can be readily satisfied without introducing any additional constraint. The effectiveness of the proposed approach is further demonstrated with numerical examples on topology optimization of rib-stiffened structures with buckling constraints.

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Figures

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Fig. 1

The basic idea of the MMC-based topology optimization approach with (a) a two-dimensional case and (b) a 3D case

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Fig. 2

A schematic illustration of the construction of a rib-stiffened structure

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Fig. 3

A schematic illustration of the DOF removal technique in FEA

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Fig. 4

The cantilever beam example

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Fig. 5

The initial design for the cantilever beam example

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Fig. 6

The optimized structure for the cantilever beam example

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Fig. 7

The history of the CPU time for FEA in each iteration step

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Fig. 8

Some intermediate designs for the cantilever beam example

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Fig. 9

The history of the values of objective function and volume constraint in each iteration step

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Fig. 10

The torsion beam example

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Fig. 11

The initial design for the torsion beam example

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Fig. 12

The optimized structure for the torsion beam example with (a) the contour plot and (b) the CAD plot

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Fig. 13

The optimized structure for the torsion beam example (L3=8) with (a) the contour plot and (b) the CAD plot

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Fig. 14

The 3D column-like structure example

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Fig. 15

The initial design for the 3D column-like structure example

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Fig. 16

The optimized structure without buckling load factor constraint for the 3D column-like structure

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Fig. 17

The optimized structure with buckling load factor constraint for the 3D column-like structure (λ¯=0.8)

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Fig. 18

The optimized structure with buckling load factor constraint for the 3D column-like structure (λ¯=1.0)

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Fig. 19

The optimized structure with buckling load factor constraint for the 3D column-like structure (λ¯=1.2)

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Fig. 20

The optimized structure with buckling load factor constraint for the 3D column-like structure (λ¯=1.4)

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Fig. 21

The optimized structure with buckling load factor constraint for the 3D column-like structure (λ¯=1.0, L3=16)

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Fig. 22

The history of the values of objective function, volume and buckling load factor constraints in each iteration step (λ¯=1.0)

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Fig. 23

Some intermediate designs with buckling load factor constraint for the 3D column-like structure (λ¯=1.0)

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Fig. 24

The optimized structure without considering DOF removal technique (λ¯=1.0)

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Fig. 25

The 3D perforated structure example

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Fig. 26

The initial design for the 3D perforated structure example

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Fig. 27

The optimized structure without buckling load factor constraint for the 3D perforated structure

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Fig. 28

The optimized structure with buckling load factor constraint for the 3D perforated structure example (λ¯=1.1) with (a) the contour plot and (b) the CAD plot

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