Research Papers

An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms

[+] Author and Article Information
Chandini Jain, Anupam Saxena

 Indian Institute of Technology, Kanpur 208016, India

J. Mech. Des 132(6), 061006 (May 25, 2010) (10 pages) doi:10.1115/1.4001530 History: Received July 01, 2009; Revised January 29, 2010; Published May 25, 2010; Online May 25, 2010

The honeycomb-based domain representation directly yields checkerboard and point flexure free optimal solutions to various topology design problems without requiring any supplementary suppression method. This is because the root cause behind the appearance of these pathologies, namely, the permitted single-point connectivity between contiguous subregions in rectangular-cell-based representation, is eliminated. The mesh-free material-mask overlay method further promises unadulterated “black and white” solutions in contrast to density interpolation schemes where the material is modeled between the “void” and “filled” states. Here, we propose improvements to the material-mask overlay method by judiciously increasing the number of material masks during a sequence of subsearches for the best solution. We used an alternative, mutation-based zero-order stochastic search, which, through a small population of solution vectors, can yield multiple solutions from a single search for nonconvex topology optimization formulations. Wachspress hexagonal cells are used as finite elements since they offer rich displacement interpolation functions. Singular solutions are penalized and filtered. With the improved material-mask overlay method, we showcase the synthesis using two classical small displacement problems each on optimal stiff structures and compliant mechanisms to illustrate the extraction of pathology-free, “black and white,” and multiple solutions.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 3

Topology determination of a stiff simply supported beam. (a) Specifications, (b) solution obtained using the improved material-mask overlay method with hexagonal cells, (c) positions of material masks over the domain, and (d) convergence history for the solution in (b).

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Figure 4

Topology determination of a beam fixed at two left corners. (a) Specifications, ((b)–(e)) solutions obtained using the adaptive material-mask overlay method with hexagonal cells, ((f)–(i)) placement of the masks over respective solutions. Solution (e) is the best with the lowest objective value.

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Figure 5

Topology optimization of a compliant displacement inverter. (a) Specifications, ((b)–(d))) three different solutions obtained using the same sequence of subsearches. Also shown are the respective deformation profiles, (e)–(g). ((h)–(j)) Placement of masks (dotted circles).

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Figure 6

Topology optimization of the symmetric upper half of a compliant crimper. (a) Specifications, ((b)–(d)) three different solutions obtained using the same sequence of subsearches. Also shown are the respective deformation profiles. (e) A result from a separate search with exponents changed in (P2).

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Figure 7

Boundary processing before candidate solutions are evaluated

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Figure 1

Specifications, domain discretization, and material assignment through overlaid masks

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Figure 2

Flowchart describing adjustment in the number of material masks and sequence of subsearches with the function-based hill climber method



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