Research Papers

An Adaptive Material Mask Overlay Method: Modifications and Investigations on Binary, Well Connected Robust Compliant Continua

[+] Author and Article Information
Anupam Saxena1

Indian Institute of Technology, Kanpur 208016, Indiaanupams@iitk.ac.in


Currently at IGM, RWTH-Aachen, Germany.

J. Mech. Des 133(4), 041004 (May 09, 2011) (11 pages) doi:10.1115/1.4003804 History: Received October 18, 2010; Revised February 10, 2011; Accepted March 07, 2011; Published May 09, 2011; Online May 09, 2011

The material mask overlay strategy employs negative masks to create material voids within the design region to synthesize perfectly binary (0-1), well connected continua. Previous implementations use either a constant number of circular masks or increase the latter via a sequence of subsearches making the procedure computationally expensive. Here, a modified algorithm is presented wherein the number of masks is adaptively varied within a single search, in addition to their positions and sizes, thereby generating material voids, both efficiently and effectively. A stochastic, mutation-only search with different mutation strategies is employed. The honeycomb parameterization naturally eliminates all subregion connectivity anomalies without requiring additional suppression methods. Boundary smoothening as a new preprocessing step further facilitates accurate evaluations of intermediate and final designs with moderated notches. Thus, both material and contour boundary interpretation steps, that can alter the synthesized solutions, are avoided during postprocessing. Various features, e.g., (i) effective use of the negative masks, (ii) convergence, (iii) mesh dependency, (iv) solution dependence on the reaction force, and (v) parallel search are investigated through the synthesis of small deformation fully compliant mechanisms that are designed to be robust under the specified loads. The proposed topology search algorithm shows promise for design of single-material large deformation continua as well.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Working of the material mask overlay strategy. Circular masks (thick circles) are used for material removal. Hexagonal cells inside a circular mask are empty while those outside the masks are all filled with the desired material. Key: Fx = fixed boundary, I = input port, and Δ = expected output deformation.

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Figure 2

Algorithm for dynamic altering of number, position, and size of overlaying masks

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Figure 3

Pictorial schematic of the working of dynamic allocation of material masks in overlay strategy. The iterations are performed until the allowed number of function evaluations are exhausted.

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Figure 4

Mesh smoothening procedure for hexagonal cells at the contour boundaries

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Figure 5

An irregular hexagonal cell (left) can be mapped onto a unit hexagon (bottom). (Right) A unit hexagonal cell used to derive the shape functions.

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Figure 6

Design specifications for compliant pliers

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Figure 7

(Top, first-third columns) compliant pliers evolved with the initial number of masks as 100, 50, and 10 masks. The first row depicts the best solutions (black) obtained within 2000 evaluations. Negative overlaying masks (dashed green) are also shown. The second row shows the respective continua with smoothened boundaries. Dangling subregions are eliminated. Stress distributions are shown in the third row. (Bottom) Figure shows how the negative masks change in number as the optimization progresses; The curves in solid red, dashed green, and dotted blue represent histories for solutions 1–3, respectively. The abscissa should be multiplied by 16 to get the evaluation step. The inset depicts variation of the objective function values (P2) for the three solutions with the number of evaluations. CPU times: solution 1: 0.297 s, solution 2: 0.375 s, and solution 3: 0.36 s.

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Figure 8

Variation of pliers topologies, and corresponding stress histograms (horizontal axis: von Mises stress in N mm−2 , vertical axis: number of retained cells) with varying output spring stiffness k. CPU times: For k = 4: 0.36 s, k = 8: 0.48 s, k = 16: 0.36 s, k = 32: 0.45 s, and k = 64: 0.56 s.

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Figure 9

Intermediate and final continua (black) as optimization progresses. Masks overlaid are shown in solid green. The rightmost column depicts the final solution, the smoothened continua (below), and the corresponding stress distribution (above). The top figure exhibits the variation in the number of masks with the iterations. CPU time for the final solution: 0.28 s.

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Figure 10

(Top row) The three columns depict different solutions with overlaid masks (top), smoothened continua (middle), and stress distribution (bottom). In each case, the number of hexagonal cells used to model the domain is mentioned. (Bottom row) Figure on the left shows the convergence histories for the three solutions. The variation in the number of masks with the optimization iterations is depicted on the right. CPU times: small mesh: 0.141 s, medium mesh: 0.28 s, and large mesh: 2.98 s.

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Figure 11

Parallelization of search

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Figure 12

Design specifications for push grippers

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Figure 13

All push gripper solutions. (First three rows, left column) The continua and the mask placements. (Right column) Smoothened continua, stress contours [color code: blue (minimum), cyan, green, yellow, magenta, red (maximum)], and deformed configurations.



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