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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

Gibson, L. J., and Ashby, M. F., 1997, Cellular Solids—Structure and Properties, 2nd ed., Cambridge University Press, Cambridge.
Scarpa, F., and Tomlinson, G., 1999, “Theoretical Characteristics of the Vibration of Sandwich Plates With In-plane Negative Poisson's Ratio Values,” J. Sound Vib., 230(1), pp. 45–67. [CrossRef]
Scarpa, F., Panayiotou, P., and Tomlinson, G., 2000, “Numerical and Experimental Uniaxial Loading on In-Plane Auxetic Honeycombs,” J. Strain Anal., 35(5), pp. 383–388. [CrossRef]
Olympio, K. R., and Gandhi, F., 2009, “Flexible Skins for Morphing Aircraft Using Cellular Honeycomb Cores,” J. Intell. Mater. Syst. Struct., 21(17), pp. 1–17. [CrossRef]
Bornengo, D., Scarpa, F., and Remillat, C., 2005, “Evaluation of Hexagonal Chiral Structure for Morphing Airfoil Concept,” Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng., 219(3), pp. 185–192. [CrossRef]
Henry, C., and McKnight, G., 2006, “Cellular Variable Stiffness Materials for Ultra-Large Reversible Deformations in Reconfigurable Structures,” Proc. SPIE, 6170, pp. 1–12. [CrossRef]
Olympio, K. R., and Gandhi, F., 2009, “Zero Poisson's Ratio Cellular Honeycombs for Flex Skins Undergoing One Dimensional Morphing,” J. Intell. Mater. Syst. Struct., 21(11), pp. 1–17. [CrossRef]
Mehta, V., Frecker, M., and Lesieutre, G. A., 2009, “Stress Relief in Contact-Aided Compliant Cellular Mechanisms,” ASME J. Mech. Des., 31(9), pp. 1–11. [CrossRef]
Bendsoe, M. P., and Sigmund, O., 2003, Topology Optimization Theory, Methods and Applications, Springer, Germany.
Bourgat, J. F., 1977, “Numerical Experiments of the Homogenization Method for Operators with Periodic Coefficients” (Lecture Notes in Mathematics), Springer Verlag, Berlin, pp. 330–356.
Guedes, J. M., and Kikuchi, N., 1990, “Preprocessing and Postprocessing for Materials Based on the Homogenization Method With Adaptive Finite Element Methods,” Comput. Methods Appl. Mech. Eng., 83, pp. 143–198. [CrossRef]
Sigmund, O., 1994, “Materials With Prescribed Constitutive Parameters: An Inverse Homogenization Problem,” Int. J. Solids Struct., 31(17), pp. 2313–2329. [CrossRef]
Sigmund, O., 1995, “Tailoring Materials With Prescribed Elastic Properties,” Mech. Mater., 20, pp. 351–368. [CrossRef]
Sigmund, O., 2000, “A New Class of Extermal Composites,” J. Mech. Phys. Solids, 48(2), pp. 397–428. [CrossRef]
Klarbring, A., Petersson, J., and Ronnqvist, M., 1995, “Truss Topology Optimization Involving Unilateral Contact,” J. Optim. Theory Appl., 87(1), pp. 1–31. [CrossRef]
Mankame, N. D., and Ananthasuresh, G. K., 2004, “A Novel Compliant Mechanism for Converting Reciprocating Translation Into Enclosing Curved Paths,” J. Mech. Des., 126, pp. 667–672. [CrossRef]
Mankame, N. D., and Ananthasuresh, G. K., 2007, “Synthesis of Contact-Aided Compliant Mechanisms for Non-Smooth Path Generation,” Int. J. Numer. Methods Eng., 69(12), pp. 2564–2605. [CrossRef]
Olympio, K. R., and Gandhi, F., 2008, “Skin Designs Using Multi-Objective Topology Optimization,” 49th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 2008-1793, pp. 1–26.
Reddy, B. V. S. N., Naik, S. V., and Saxena, A., 2012, “Systematic Synthesis of Large Displacement Contact-Aided Monolithic Compliant Mechanisms,” J. Mech. Des., 134(1), pp. 1–1. [CrossRef]
Zhang, W., Dai, G., Wang, F., Sun, S., and Bassir, H., 2007, “Using Strain Energy Based Prediction of Effective Elastic Properties in Topology Optimization of Material Microstructures,” Acta Mech. Sin., 23, pp. 77–89. [CrossRef]
Duysinx, P., and Bendsoe, M. P., 1998, “Topology Optimization of Continuum Structures With Local Stress Constraints,” Int. J. Numer. Methods Eng., 43(8), pp. 1453–1478. [CrossRef]
Cheng, G. D., and Guo, X., 1997, “ε-Relaxed Approach for Structural Topology Optimization,” Struct. Multidiscip. Optim., 13(4), pp. 258–266. [CrossRef]
Bruggi, M., 2008, “On an Alternative Approach to Stress Constraints Relaxation in Topology Optimization,” Struct. Multidiscip. Optim., 36(2), pp. 125–141. [CrossRef]
Yang, R. J., and Chen, C. J., 1996, “Stress-Based Topology Optimization,” Struct. Optim., 12, pp. 98–105. [CrossRef]
Duysinx, P., and Sigmund, O., 1998, “New Developments in Handling Stress Constraints in Optimal Material Distribution,” AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 1501–1510.
Le, C., Norato, J., Bruns, T., Ha, C., and Tortorelli, D., 2010, “Stress-Based Topology Optimization for Continua,” Struct. Multidiscip. Optim., 41(4), pp. 605–620. [CrossRef]
Haug, E. J., Choi, K. K., and Komkov, V., 1986, Design Sensitivity Analysis of Structural Systems, Academic Press, Inc., Orlando, FL.
Svanberg, K., 1987, “The Method of Moving Asymptotes: A New Method for Structural Optimization,” Int. J. Numer. Methods Eng., 24(2), pp. 359–373. [CrossRef]
Sigmund, O., and Petersson, J., 1998, “Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboard, Mesh-Independancies and Local Minima,” Struct. Optim., 16, pp. 68–75. [CrossRef]
Sigmund, O., 2007, “Morphology-Based Black and White Filters for Topology Optimization,” Struct. Multidiscip. Optim., 33, pp. 401–424. [CrossRef]
Guest, J., Prevost, J., and Belytschko, T., 2004, “Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions,” Int. J. Numer. Methods Eng., 61(2), pp. 238–254. [CrossRef]
Storn, R., and Price, K., 1997, “Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,” J. Global Optim., 11, pp. 341–359. [CrossRef]
Mehta, V., 2010, “Design, Analysis, and Applications of Cellular Contact-Aided Compliant Mechanisms,” PhD dissertation, The Pennsylvania State University, University Park, PA.

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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