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Technical Briefs

The Discrete Topology Optimization of Structures Using the Improved Hybrid Discretization Model

[+] Author and Article Information
Hong Zhou

e-mail: hong.zhou@tamuk.edu

Rutesh B. Patil

e-mail: rutesh.patil@gmail.com
Department of Mechanical and
Industrial Engineering, Texas A&M University-Kingsville,
Kingsville, TX 78363

Contributed by the Design Education Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 29, 2012; final manuscript received September 12, 2012; published online October 26, 2012. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 134(12), 124503 (Nov 15, 2012) (8 pages) doi:10.1115/1.4007841 History: Received February 29, 2012; Revised September 12, 2012

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty caused by any intermediate material state. In this paper, the improved hybrid discretization model is introduced for the discrete topology optimization of structures. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. The dangling and redundant solid design cells are completely eliminated from topology solutions in the improved hybrid discretization model to avoid sharp protrusions. The local stress constraint is directly imposed on each triangular analysis cell to make the designed structure safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. The presented discrete topology optimization procedure is illustrated by two topology optimization examples of structures.

Copyright © 2012 by ASME
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Figures

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Fig. 1

A subdivided quadrilateral design cell and its inner and corner triangular analysis cells

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Fig. 2

The four corner triangles between two neighboring quadrilateral design cells

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Fig. 3

Two solid neighboring quadrilateral design cells in different directions

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Fig. 4

The quadrilateral design cells and the subdivided triangular analysis cells in a hybrid discretization model

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Fig. 5

The quadrilateral design cells and the triangular analysis cells of a topology

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Fig. 6

The topology of Fig. 5 after dangling design cells are removed

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Fig. 7

The topology of Fig. 6 after redundant design cells are removed

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Fig. 8

The topology of Fig. 5 after all dangling and redundant design cells are removed

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Fig. 9

The eight neighboring design cells around a design cell

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Fig. 10

The design domain in example 1

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Fig. 11

The discretization in example 1

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Fig. 12

The subdivision in example 1

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Fig. 13

The topology optimization results of example 1 from the improved hybrid discretization

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Fig. 14

The stiffness of example 1 from the improved hybrid discretization

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Fig. 15

The constraints of example 1 from the improved hybrid discretization

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Fig. 16

The topology optimization results of example 1 from the quadrilateral discretization

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Fig. 17

The stiffness of example 1 from the quadrilateral discretization

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Fig. 18

The constraints of example 1 from the quadrilateral discretization

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Fig. 19

The design domain in example 2

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Fig. 20

The discretization in example 2

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Fig. 21

The subdivision in example 2

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Fig. 22

The topology optimization results of example 2 from the improved hybrid discretization

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Fig. 23

The stiffness of example 2 from the improved hybrid discretization

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Fig. 24

The constraints of example 2 from the improved hybrid discretization

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Fig. 25

The topology optimization results of example 2 from the quadrilateral discretization

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Fig. 26

The stiffness of example 2 from the quadrilateral discretization

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Fig. 27

The constraints of example 2 from the quadrilateral discretization

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