The use of large-deflection springs, tabs, and other compliant systems to provide integral attachment, joining, and retention is well established and may be found throughout nature and the designed world. Such systems present a challenge for mechanical analysis due to the interaction of contact mechanics with large-deflection analysis. Interlocking structures experience a variable reaction force that depends on the cantilever angle at the contact point. This paper develops the mathematical analysis of interlocking cantilevers and provides verification with finite element analysis and physical measurements. Motivated by new opportunities for nanoscale compliant systems based on ultrathin films and two-dimensional (2D) materials, we created a nondimensional analysis of retention tab systems. This analysis uses iterative and elliptic integral solutions to the moment–curvature elastica of a suspended cantilever and can be scaled to large-deflection cantilevers of any size for which continuum mechanics applies. We find that when a compliant structure is bent backward during loading, overlap increases with load, until a force maximum is reached. In a force-limited scenario, surpassing this maximum would result in snap-through motion. By using angled cantilever restraint systems, the magnitude of insertion force relative to retention force can vary by 50× or more. The mathematical theory developed in this paper provides a basis for fast analysis and design of compliant retention systems, and expands the application of elliptic integrals for nonlinear problems.
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December 2017
Research-Article
Nonlinear Mechanics of Interlocking Cantilevers
Joseph J. Brown,
Joseph J. Brown
Mem. ASME
Department of Mechanical Engineering,
University of Hawaii at Manoa,
2540 Dole St.—Holmes Hall 302,
Honolulu, HI 96822-2344
e-mail: jjbrown@hawaii.edu
Department of Mechanical Engineering,
University of Hawaii at Manoa,
2540 Dole St.—Holmes Hall 302,
Honolulu, HI 96822-2344
e-mail: jjbrown@hawaii.edu
Search for other works by this author on:
Ryan C. Mettler,
Ryan C. Mettler
Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309-0427
e-mail: ryan.mettler@colorado.edu
University of Colorado Boulder,
427 UCB
,Boulder, CO 80309-0427
e-mail: ryan.mettler@colorado.edu
Search for other works by this author on:
Omkar D. Supekar,
Omkar D. Supekar
Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309-0427
e-mail: omkar.supekar@colorado.edu
University of Colorado Boulder,
427 UCB
,Boulder, CO 80309-0427
e-mail: omkar.supekar@colorado.edu
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Victor M. Bright
Victor M. Bright
Fellow ASME
Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309-0427
e-mail: victor.bright@colorado.edu
Department of Mechanical Engineering,
University of Colorado Boulder,
427 UCB
,Boulder, CO 80309-0427
e-mail: victor.bright@colorado.edu
Search for other works by this author on:
Joseph J. Brown
Mem. ASME
Department of Mechanical Engineering,
University of Hawaii at Manoa,
2540 Dole St.—Holmes Hall 302,
Honolulu, HI 96822-2344
e-mail: jjbrown@hawaii.edu
Department of Mechanical Engineering,
University of Hawaii at Manoa,
2540 Dole St.—Holmes Hall 302,
Honolulu, HI 96822-2344
e-mail: jjbrown@hawaii.edu
Ryan C. Mettler
Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309-0427
e-mail: ryan.mettler@colorado.edu
University of Colorado Boulder,
427 UCB
,Boulder, CO 80309-0427
e-mail: ryan.mettler@colorado.edu
Omkar D. Supekar
Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309-0427
e-mail: omkar.supekar@colorado.edu
University of Colorado Boulder,
427 UCB
,Boulder, CO 80309-0427
e-mail: omkar.supekar@colorado.edu
Victor M. Bright
Fellow ASME
Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309-0427
e-mail: victor.bright@colorado.edu
Department of Mechanical Engineering,
University of Colorado Boulder,
427 UCB
,Boulder, CO 80309-0427
e-mail: victor.bright@colorado.edu
1Corresponding author.
Manuscript received August 22, 2017; final manuscript received October 11, 2017; published online October 27, 2017. Assoc. Editor: Junlan Wang.
J. Appl. Mech. Dec 2017, 84(12): 121012 (12 pages)
Published Online: October 27, 2017
Article history
Received:
August 22, 2017
Revised:
October 11, 2017
Citation
Brown, J. J., Mettler, R. C., Supekar, O. D., and Bright, V. M. (October 27, 2017). "Nonlinear Mechanics of Interlocking Cantilevers." ASME. J. Appl. Mech. December 2017; 84(12): 121012. https://doi.org/10.1115/1.4038195
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