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Research Papers

Design of Electrothermally Compliant MEMS With Hexagonal Cells Using Local Temperature and Stress Constraints

[+] Author and Article Information
Rajat Saxena

Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India

Anupam Saxena

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

J. Mech. Des 131(5), 051006 (Apr 06, 2009) (10 pages) doi:10.1115/1.3087544 History: Received October 13, 2008; Revised December 25, 2008; Published April 06, 2009

In this paper, meso- and microscale electrothermally compliant mechanical systems are synthesized for strength, with polysilicon as the structural material. Local temperature and/or stress constraints are imposed in the topology optimization formulation. This is done to keep the optimal solutions thermally intact and also to keep the local stresses below their allowable limit. Constraint relaxation performed on both temperature and stress constraints allows them to be ignored when the cell material densities approach their nonexisting states. As both local constraints are large in number with the number of cells, an active constraint strategy is employed with gradient based optimization. Honeycomb parametrization, which is a staggered arrangement of hexagonal cells, is used to represent the design region. This ensures at least an edge connection between any two adjacent cells, and thus prevents the appearance of both checkerboard and point flexure singularities without any additional computational load. Both SIMP and SIGMOID material assignment functions are explored to obtain the optimal solutions.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 3

(a) Representation using hexagonal cells and (b) (i) vertically-split, (ii) left-split, and (iii) right-split hexagonal cells

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Figure 4

Design domain and problem specifications of the symmetric half of ETC actuator in example 1

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Figure 8

(a) Guckle topology and (b) design domain and problem specifications

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Figure 9

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 8

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Figure 10

(a) Optimal topology and (b) deformed profile for example in Fig. 8 with local stress constraints

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Figure 11

Symmetric half of design domain for microgripper

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Figure 1

Design domain and boundary conditions for an ETC microactuator

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Figure 2

(a) Checkerboard pattern and (b) continuum segment with zero stiffness

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Figure 5

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 4

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Figure 6

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 4 without temperature boundary conditions at anchors

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Figure 7

(a) Optimal topology and (b) deformed profile of example in Fig. 4 with local stress constraints

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Figure 18

Optimal solutions from specifications in Fig. 1 using the SIGMOID material assignment. Local stress, temperature, and resource constraints are employed.

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Figure 12

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 1

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Figure 13

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 1 with local stress constraints

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Figure 14

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 4 with local temperature and stress constraints

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Figure 15

(a) Optimal topology, (b) deformed profile, and (c) temperature distribution for example in Fig. 1 with local temperature and stress constraints

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Figure 16

Optimal solutions from specifications in Fig. 4 using the SIGMOID material assignment. Local stress, temperature, and resource constraints are all employed.

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Figure 17

Optimal solutions from specifications in Fig. 8 using the SIGMOID material assignment. Local stress, temperature, and resource constraints are employed.

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