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Research Papers: Design Automation

Hinge-Free Compliant Mechanism Design Via the Topological Level-Set

[+] Author and Article Information
Anirudh Krishnakumar

Department of Mechanical Engineering,
UW-Madison,
Madison, WI 53706

Krishnan Suresh

Department of Mechanical Engineering,
UW-Madison,
Madison, WI 53706
e-mail: suresh@engr.wisc.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 16, 2013; final manuscript received October 24, 2014; published online January 30, 2015. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 137(3), 031406 (Mar 01, 2015) (10 pages) Paper No: MD-13-1264; doi: 10.1115/1.4029335 History: Received June 16, 2013; Revised October 24, 2014; Online January 30, 2015

The objective of this paper is to introduce and demonstrate a new method for the topology optimization of compliant mechanisms. The proposed method relies on exploiting the topological derivative, and exhibits numerous desirable properties including: (1) the mechanisms are hinge-free; (2) mechanisms with different geometric and mechanical advantages (GA and MA) can be generated by varying a single control parameter; (3) a target volume fraction need not be specified, instead numerous designs, of decreasing volume fractions, are generated in a single optimization run; and (4) the underlying finite element stiffness matrices are well-conditioned. The proposed method and implementation are illustrated through numerical experiments in 2D and 3D.

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Figures

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Fig. 1

Classic inverter problem

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Fig. 2

The primary input problem

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Fig. 3

The secondary output problem

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Fig. 4

A hypothetical topological change

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Fig. 5

A hypothetical shape change

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Fig. 6

The three topological sensitivity fields. (a) Input topological sensitivity, (b) Output topological sensitivity fields, and (c) Mutual topological sensitivity.

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Fig. 7

Topological sensitivity field for w = (0,0,1). (a) Topological sensitivity field and a cutting plane and (b) Induced domain Ωτ.

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Fig. 8

Fixed point iteration

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Fig. 9

A finite element model with bilinear quad elements

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Fig. 10

A new topology with reduced volume fraction

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Fig. 11

Estimating the topological sensitivities over the out elements. (a) Compute field over in-elements, (b) Estimate field over the nodes, and (c) Estimate over ‘out’ elements near boundary.

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Fig. 12

Pathological case of a disconnected mesh

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Fig. 13

The proposed algorithm

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Fig. 14

2D finite element model for the inverter problem

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Fig. 15

The inverter design; deformation in (b) is scaled for clarity. (a) Final design and (b) Un-deformed and deformed mesh.

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Fig. 16

Mechanism history for the inverter. (a) Geometric and mechanical advantages and (b) Objective function.

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Fig. 17

Intermediate designs for the inverter at volume fractions of 0.3 and 0.4

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Fig. 18

Symmetric inverter problem

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Fig. 19

Symmetric inverter for 500 elements (η = 0.5)

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Fig. 20

History of the GA and MA for the symmetric inverter

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Fig. 21

Symmetric inverter for 1000 elements

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Fig. 23

Cruncher design for η = 0.5. (a) Final design and (b) Geometric and mechanical advantages.

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Fig. 24

Cruncher for η = 0.6. (a) Final design and (b) Geometric and mechanical advantages.

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Fig. 25

Grasper problem. (a) Full model and (b) Model exploiting symmetry.

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Fig. 27

3D inverter problem

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Fig. 28

Finite element discretization with 2000 elements

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Fig. 29

3D inverter design. (a) Un-deformed and (b) Deformed.

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