Research Papers: Mechanisms and Robotics

A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization

[+] Author and Article Information
Anupam Saxena

 Indian Institute of Technology, Kanpur, India, 208016

J. Mech. Des 130(8), 082304 (Jul 14, 2008) (9 pages) doi:10.1115/1.2936891 History: Received May 04, 2007; Revised December 04, 2007; Published July 14, 2008

This paper proposes novel honeycomb tessellation and material-mask overlay methods to obtain optimal single-material compliant topologies free from checkerboard and point-flexure pathologies. The presence of strain-free rotation regions in rectangular cell based discretization is identified to be a cardinal cause for appearance of such singularities. With each hexagonal cell sharing an edge with its neighboring cells, strain-free displacements are not permitted anywhere in the continuum. The new material assignment approach manipulates material within a subregion of cells as opposed to a single cell thereby reducing the number of variables making optimization efficient. Cells are allowed to get filled with only the chosen material or they can remain void. Optimal solutions obtained are free from intermediate material states and can be manufactured requiring no material interpretation and less postprocessing. Though the hexagonal cells do not allow strain-free rotations, some subregions undergoing large strain deformations can still be present within the design. The proposed procedure is illustrated using three classical examples in compliant mechanisms solved using genetic algorithm.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Schematic representation of domain discretization used in the homogenization and SIMP approaches for fixed grid topology optimization

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Figure 2

(a) Honeycomb, a regular tessellation using hexagonal cells that provides edge connectivity between cells. (b) A hexagonal cell can be divided into two bilinear four-node finite elements in any of the three possible ways shown.

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Figure 3

A generic design domain represented using a honeycomb tessellation with material masks overlaid

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Figure 4

A flow chart for the genetic algorithm used

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Figure 5

(a) Design specifications for the compliant crimper; (b) optimal topology with deformed profile. (c) Histories of variation of the objective, output displacement (MSE), strain energy (SE), and the normalized volume V∕V*. (d) A prototype of the optimal solution.

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Figure 6

(a) Design specifications for the compliant pliers; (b) optimal topology with deformed profile. (c) Histories of variation of the objective, output displacement (MSE), strain energy (SE), and the normalized volume V∕V*. (d) An alternative solution with the same design specifications showing distributivity in compliant mechanisms cannot always be achieved with hexagonal cells. (e) A prototype of the solution in (b).

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Figure 7

Synthesis example of the displacement inverter with different numbers of a priori chosen material masks. (a) Design specifications; (b)–(f) optimal solutions with 10, 20, 30, 50, and 100 masks, respectively.

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Figure 8

A notch between two contiguous hexagonal cells can be replaced by an arc passing through the notch and the midpoints of two edges forming the notch




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