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Research Papers

A Reduction Procedure for One-Dimensional Joint Models and Application to a Lap Joint

[+] Author and Article Information
Michael A. Guthrie1

Department of Engineering Physics, University of Wisconsin, Madison, WI 53706

Daniel C. Kammer2

Department of Engineering Physics, University of Wisconsin, Madison, WI 53706kammer@engr.wisc.edu

1

Present address: Sandia National Laboratories, Albuquerque, NM.

2

Corresponding author. Present address: 539 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706.

J. Vib. Acoust 133(3), 031002 (Mar 24, 2011) (10 pages) doi:10.1115/1.4003402 History: Received February 14, 2008; Revised September 28, 2010; Published March 24, 2011; Online March 24, 2011

A reduction procedure for joint models that was developed in earlier work is extended to allow for relative motion between surfaces, and the effect of this procedure on timestep issues is considered. A general one-dimensional structure containing a frictional interface is considered. Coulomb friction is approximated with nonlinear springs of large but finite stiffness. The system of equations describing this structure is reduced in a procedure similar to Guyan reduction by assuming that the system deforms only in the shapes that it takes when the interface is massless. The result of this procedure is that the dynamics associated with the interface region are removed from the analysis. Following the development of the reduction procedure, the reduced formulation is specialized to the case of a simple lap joint. A numerical example problem is considered in which both the full and reduced equations of motion are integrated over time. It is seen that, for the example problem considered, the reduction procedure results in tremendous computational savings with little loss of accuracy. Based on the results of the simple example problem, it appears that the proposed reduction procedure has potential to be an accurate and effective method of alleviating the timestep difficulties associated with direct finite element analysis of joints in structural dynamics applications.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Graphical (l) and mathematical (r) representations of friction law

Grahic Jump Location
Figure 2

Two flexible bars contacting one another over a portion of their length (top) and a discrete representation of this system (bottom)

Grahic Jump Location
Figure 3

Displacement at the junction between the right structural region and the interface versus time for the full and reduced formulations, fr=25 and ω=1

Grahic Jump Location
Figure 4

Displacement at the junction between the right structural region and the interface versus time for the full and reduced formulations, fr=25 and ω=2.5

Grahic Jump Location
Figure 5

Displacement at the junction between the right structural region and the interface versus time for the full and reduced formulations, fr=25 and ω=5

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