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Research Papers

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

[+] Author and Article Information
Hong Zhou

Pranjal P. Killekar

Department of Mechanical and Industrial Engineering,  Texas A&M University-Kingsville, Kingsville, TX 78363pranjalkillekar@hotmail.com

J. Mech. Des 133(11), 111007 (Nov 11, 2011) (9 pages) doi:10.1115/1.4004986 History: Received January 18, 2011; Revised August 01, 2011; Published November 11, 2011; Online November 11, 2011

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical, or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary, and every design cell is either solid or void to prevent gray cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum. No postprocessing is required for topology uncertainty caused by either point connection or gray cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 6

The two possible point connections among four connected quadrilateral design cells

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Figure 7

The three-block crossover

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Figure 8

The input, output, and support ports in example 1

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Figure 9

The discretized half design domain in example 1

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The optimal topology of example 1 from the modified quadrilateral discretization

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The geometric advantage of example 1 from the modified quadrilateral discretization

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The constraints of example 1 from the modified quadrilateral discretization

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Figure 13

The optimal topology of example 1 at generation 150 from the modified quadrilateral discretization

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Figure 14

The optimal topology of example 1 from the regular quadrilateral discretization

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The geometric advantage of example 1 from the regular quadrilateral discretization

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Figure 16

The constraints of example 1 from the regular quadrilateral discretization

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Figure 17

The optimal topology of example 1 at generation 150 from the regular quadrilateral discretization

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Figure 18

The input, output, and support ports in example 2

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Figure 19

The discretized half design domain in example 2

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Figure 20

The optimal topology of example 2 from the modified quadrilateral discretization

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Figure 21

The mechanical advantage of example 2 from the modified quadrilateral discretization

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Figure 22

The constraints of example 2 from the modified quadrilateral discretization

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Figure 23

The optimal topology of example 2 at generation 150 from the modified quadrilateral discretization

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Figure 24

The optimal topology of example 2 from the regular quadrilateral discretization

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Figure 25

The mechanical advantage of example 2 from the regular quadrilateral discretization

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Figure 26

The constraints of example 2 from the regular quadrilateral discretization

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Figure 27

The optimal topology of example 2 at generation 150 from the regular quadrilateral discretization

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Figure 5

The eight triangular analysis cells in a quadrilateral design cell

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Figure 4

The modified quadrilateral discretization model

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Figure 3

The regular quadrilateral discretization model

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Figure 2

A gray cell and the potential topology uncertainty problem

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Figure 1

A point connection and the potential topology uncertainty problem

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