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A reduced Iwan model that includes pinning for bolted joint mechanics

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Abstract

Bolted joints are prevalent in most assembled structures; however, predictive models for their behavior do not exist. Calibrated models, such as the Iwan model, are able to predict the response of a jointed structure over a range of excitations once calibrated at a nominal load. The Iwan model, though, is not widely adopted due to the high computational expense of implementation. To address this, an analytical solution of the Iwan model is derived under the hypothesis that for an arbitrary load reversal, there is a new distribution of dry friction elements, which are now stuck, that approximately resemble a scaled version of the original distribution of dry friction elements. The dry friction elements internal to the Iwan model do not have a uniform set of parameters and are described by a distribution of parameters, i.e., which internal dry friction elements are stuck or slipping at a given load, that ultimately governs the behavior of the joint as it transitions from microslip to macroslip. This hypothesis allows the model to require no information from previous loading cycles. Additionally, the model is extended to include the pinning behavior inherent in a bolted joint. Modifications of the resulting framework are discussed to highlight how the constitutive model for friction can be changed (in the case of an Iwan–Stribeck formulation) or how the distribution of dry friction elements can be changed (as is the case for the Iwan plasticity model). The reduced Iwan plus pinning model is then applied to the Brake–Reuß beam in order to discuss methods to deduce model parameters from experimental data.

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Notes

  1. Thus, the three regimes defined above hold for a narrow range of u and \(\varphi \), including when \(u=\varphi \). Otherwise, microslip and macroslip must be defined in terms of u, and pinning must be defined in terms of \(\varphi \).

  2. Technically, Hertz’s formulation is for two cylinders contacting each other, not one cylinder inside another cylinder. However, it is assumed that this case can be represented with Hertz’s model without loss of accuracy.

  3. Though, the measurement of \(\phi _{\mathrm{MAX}}\) instead of \(F_S\) is often more practical as testing to macroslip is not always feasible.

  4. This model is proposed purely as an example of how to apply the RIPP joint formulation to other constitutive models. The burden associated with parameter estimation is too high to consider this a practical model for analysts to use.

  5. For an even more burdensome model, consider the seven-parameter friction model in [1], with the \(\rho (\phi )\) from [29]; this results in a ten-parameter Iwan model!

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Acknowledgments

The author would like to thank Rob Kuether, Caroline Nielsen, and Scott Smith for their development of the STFT algorithms used in the examples.

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Authors and Affiliations

  1. William Marsh Rice University, Houston, TX, USA

    M. R. W. Brake

  2. Sandia National Laboratories, Albuquerque, NM, USA

    M. R. W. Brake

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  1. M. R. W. Brake
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Correspondence to M. R. W. Brake.

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Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporations, for the US Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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Brake, M.R.W. A reduced Iwan model that includes pinning for bolted joint mechanics. Nonlinear Dyn 87, 1335–1349 (2017). https://doi.org/10.1007/s11071-016-3117-2

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