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TECHNICAL PAPERS

A Four-Parameter Iwan Model for Lap-Type Joints

[+] Author and Article Information
Daniel J. Segalman

 Sandia National Laboratories, Albuquerque, NM 87185djsegal@sandia.gov

J. Appl. Mech 72(5), 752-760 (Feb 08, 2005) (9 pages) doi:10.1115/1.1989354 History: Received July 15, 2004; Revised February 08, 2005

The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in built-up structures. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured through direct numerical simulation (DNS) of the contact mechanics within a structural dynamics analysis. The difficulties of DNS manifest themselves either in terms of Courant times that are orders of magnitude smaller than that necessary for structural dynamics analysis or as intractable conditioning problems. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. In this way, development of constitutive models for joint response is a prerequisite for a predictive structural dynamics capability. A four-parameter model, built on a framework developed by Iwan, is used to reproduce the qualitative and quantitative properties of lap-type joints. In the development presented here, the parameters are deduced by matching joint stiffness under low load, the force necessary to initiate macroslip, and experimental values of energy dissipation in harmonic loading. All the necessary experiments can be performed on real hardware or virtually via fine-resolution, nonlinear quasistatic finite elements. The resulting constitutive model can then be used to predict the force/displacement results from arbitrary load histories.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

A parallel-series Iwan system is a parallel arrangement of springs and sliders (Jenkins) elements

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Figure 2

The dissipation resulting from small amplitude harmonic loading tends to behave as a power of the force amplitude

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Figure 3

The monotonic pull of a simple lap joint shows the force saturates at FS as the displacement passes a critical value

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Figure 4

The numerical predictions of a finely meshed system containing a single lap joint illustrate how interface displacements are obscured by the large compliance of the elastic response of the attached members. In the figure at top, both sides of the system are clamped, and stretched horizontally. In the figure below that, the left side is clamped and a zero-slope boundary condition is imposed on the right.

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Figure 5

Typically the force displacement conditions on elastic systems containing joints is as dominated at low loads by the elastic compliance (Region A). As the applied load approaches that necessary to initiate macroslip the force displacement curve begins to flatten (Region B). In macroslip the force-displacement curve is exactly flat (Region C). The only useful information about the joint available from such experiments is identification of the force necessary to initiate macroslip.

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Figure 6

A spectrum that is the sum of a truncated power law distribution and a Dirac delta function can be selected to satisfy asymptotic behavior at small and large force amplitudes

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Figure 7

The dimensionless force-displacement curve for monotonic pull for the four-parameter model for χ=−1∕2 and for three values of β

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Figure 12

The leg section of the mockup. To the left is a finite-element mesh of the full leg section, in the middle is the actual leg section in the test apparatus, and to the right is a sketch indicating the interface being modeled by the four-parameter model.

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Figure 13

A stepped specimen shows qualitatively different dissipation than a simple half-lap joint. The difference may be due to the near singular traction that develops at the edges of the contact patch.

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Figure 14

Comparison of dissipation prediction of Eq. 35 with the quadrature of Eqs. 44 through 46

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Figure 11

Fit to dissipation data from a stepped specimen. In this case, there is appreciable curvature in the log-log plot of dissipation per cycle versus force amplitude. The dimensionless parameters employed were χ=−0.304 and β=0.613.

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Figure 10

Fit to dissipation data from a single leg of a component mass mockup. In this case, there is almost no curvature in the log-log plot of dissipation per cycle versus force amplitude, consistent with a power-law relationship. The dimensionless parameters employed were χ=−0.632 and β=3.68.

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Figure 9

The dimensionless dissipation per cycle as a function of normalized force for the four-parameter model for χ=−1∕2 and for three values of β

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Figure 8

The dimensionless hysteresis curves for the four-parameter model for χ=−1∕2 and for two values of β are shown in gray. The maximum and minimum extensions are set to 3∕4 of that associated with the inception of macroslip. The corresponding curves for the unidirectional extension of a virgin material (backbone curves) are shown in black.

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