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Research Papers

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

[+] Author and Article Information
Hong Zhou

Department of Mechanical and Industrial Engineering, Texas A&M University-Kingsville, Kingsville, TX 78363hong.zhou@tamuk.edu

J. Mech. Des 132(11), 111003 (Oct 20, 2010) (8 pages) doi:10.1115/1.4002663 History: Received January 26, 2010; Revised September 17, 2010; Published October 20, 2010; Online October 20, 2010

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Checkerboard pattern, diagonal element chain, and de facto hinge

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Figure 2

Edge and point connections in quadrilateral discretization

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Figure 3

Horizontal, vertical, and slant structural members in quadrilateral discretization

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Figure 4

Edge connections in hexagonal discretization

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Figure 5

Horizontal, vertical, and slant structural members in hexagonal discretization

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Figure 6

A subdivided design cell, a solid design cell, and a void design cell

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Figure 7

Two design cells connected in the horizontal direction

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Figure 8

Two design cells connected in the vertical direction

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Figure 9

Design cells connected in the diagonal directions

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Figure 10

The three-block crossover

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Figure 11

The input, output, and support ports in example 1

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Figure 12

The discretized half design domain in example 1

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Figure 13

The optimal topology in example 1

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The stress distribution in example 1

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The convergence history in example 1

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Figure 16

(a) The optimal topology at generation 100 in example 1 and (b) the optimal topology at generation 200 in example 1

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Figure 17

The input, output, and support ports in example 2

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Figure 18

The discretized half design domain in example 2

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Figure 19

The optimal topology in example 2

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The stress distribution in example 2

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Figure 21

The convergence history in example 2

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Figure 22

(a) The optimal topology at generation 100 in example 2 and (b) the optimal topology at generation 200 in example 2

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