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Research Papers

Two-Step Design of Multicontact-Aided Cellular Compliant Mechanisms for Stress Relief

[+] Author and Article Information
Vipul Mehta

Graduate Student
e-mail: vipul.mehta@gmail.com

Mary Frecker

Professor
e-mail: mxf36@psu.edu
Department of Mechanical Engineering,
The Pennsylvania State University,
University Park, PA 16802

George A. Lesieutre

Professor and Head
Department of Aerospace Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: g-lesieutre@psu.edu

Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 25, 2010; final manuscript received June 20, 2012; published online October 19, 2012. Assoc. Editor: Diann Brei.

J. Mech. Des 134(12), 121001 (Oct 19, 2012) (12 pages) doi:10.1115/1.4007694 History: Received April 25, 2010; Revised June 20, 2012

A methodology for topology optimization to the design of compliant cellular mechanisms with and without internal contact is presented. A two-step procedure is pursued. First, a baseline noncontact mechanism is developed and optimized via an inverse homogenization method using the “solid isotropic material with penalization” approach. This compliant mechanism is optimized to yield specified elasticity coefficients, with the capability to sustain large effective strains by minimizing local linear elastic strain. In the second step, a system of internal contacts is designed. The initial continuum model of a noncontact mechanism is converted into a frame model, and possible contact links are defined. A computationally efficient algorithm is employed to eliminate those mechanisms having overlapping contact links. The remaining nonoverlapping designs are exhaustively investigated for stress relief. A differential evolution optimizer is used to maximize the stress relief. The results generated for a range of specified elasticity coefficients include a honeycomb-like cell, an auxetic cell, and a diamond-shaped cell. These various cell topologies have different effective properties corresponding to different structural requirements. For each such topology, a contact mechanism is devised that demonstrates stress relief. In one such case, the contact mechanism increases the strain magnification ratio by about 30%.

Copyright © 2012 by ASME
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References

Figures

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Fig. 1

An example of contact-aided cellular mechanism [8] showing a contact mechanism inside a cellular cell. The cellular cell without the contact mechanism is noncontact cellular structure.

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Fig. 2

Finite element meshing for SIMP model

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Fig. 3

Load cases required to determine the homogenized elastic coefficients

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Fig. 4

Boundary conditions and loads for local strain calculation

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Fig. 5

Symmetric perturbations for random initial guess

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Fig. 6

Conversion of continuum model into a frame structure

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Fig. 7

Schematic showing the effect of sensitivity of initial contact gap to the maximum stress in a contact-aided mechanism

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Fig. 8

Unit cell topologies similar to honeycombs

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Fig. 9

Honeycomb-similar unit cell without the local strain constraint [33]

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Fig. 10

Frame structure for honeycomb-similar cell

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Fig. 11

Stress-relieving contact mechanisms for honeycomb-similar cell with arbitrary contact gaps

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Fig. 12

Unit cell topologies for negative effective Poisson's ratio

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Fig. 13

Frame structure for an auxetic cell

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Fig. 14

Stress-relieving contact mechanisms for auxetic cell with arbitrary contact gaps

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Fig. 15

A diamond-shaped unit cell along with the unit cell and the effective properties

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Fig. 16

Frame structure, contact-aided unit cell, and contact-aided cellular configuration for the diamond-shaped unit cell

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Fig. 17

Bending stresses in the auxetic cell without contact and with a contact mechanism after the application of loads in X-direction

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