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Research Papers

Nonlinear Algebraic Reduction for Snap-Fit Simulation

[+] Author and Article Information
Kavous Jorabchi

Department of Mechanical Engineering, University of Wisconsin, Madison, WI 53706kjorabchi@wisc.edu

Krishnan Suresh

Department of Mechanical Engineering, University of Wisconsin, Madison, WI 53706suresh@engr.wisc.edu

J. Mech. Des 131(6), 061004 (Apr 28, 2009) (8 pages) doi:10.1115/1.3116342 History: Received September 06, 2008; Revised January 25, 2009; Published April 28, 2009

Snap-fits are often preferred over other traditional methods of assembly since they reduce part count, assembly/disassembly time, and manufacturing cost. A typical simulation of a snap-fit assembly entails two critical steps: contact detection and nonlinear deformation analysis, which are strongly coupled. One could rely on standard 3D contact detectors and standard 3D finite element analysis (FEA) to simulate the two steps. However, since snap-fits are slender, 3D FEA tends to be inefficient and slow. On the other hand, one could rely on an explicit 1D beam reduction for simulation. This is highly efficient for large deformation analysis, but contact detection can pose challenges. Moreover, for complex snap-fits, extracting cross-sectional properties for 1D formulation is nontrivial. We propose here a nonlinear algebraic dimensional reduction method that offers the “best of both worlds.” In the proposed method, a 3D model is used for contact detection. However, to speed-up deformation analysis, the 3D model is implicitly reduced to a 1D beam model via an algebraic process. Thus, it offers the generality of 3D simulation and the computational efficiency of 1D simulation, as confirmed by the numerical experiments and optimization studies.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Typical snap-fit (cantilever hook)

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Figure 2

Complex snap-fit (cantilever hook)

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Figure 3

A typical snap-fit simulation process

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Figure 4

A tetrahedral mesh of the snap-fit

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Figure 5

7-DOF beam element

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Figure 6

Co-rotational formulation for the beam

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Figure 7

Nonlinear analysis algorithm

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Figure 8

Simple cantilever hook (all dimensions in meters)

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Figure 9

Insertion force versus displacement

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Figure 10

Complex snap-fit (all dimensions in meters)

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Figure 11

Maximum insertion force versus design parameters

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Figure 12

The initial and optimized snap-fits

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