Stochastic Iwan-Type Models for Joint Variability Modeling

Abstract

This chapter focuses overall on the development and validation of stochastic models to describe the dissipation and stiffness properties of a bolted joint for which experimental data, i.e., stiffness and dissipation measurements obtained in harmonic testing of nine nominally identical bolted joints, is available and exhibits a large scatter. The four-parameter Iwan model is considered first for this effort and it is found to characterize accurately either dissipation or stiffness properties but not both. Accordingly, two extensions of this model are investigated. The first one, referred to as the split four-parameter model, adopts the four-parameter Iwan representation but with different parameters for the dissipation and stiffness properties. The second extension of the four-parameter Iwan model involves dynamic and static coefficients of friction differing from each other and thus leading to a five-parameter representation. The applicability of this latter extension is investigated using this data and is found to provide very good fits of the experimental data for each bolted joint, notwithstanding the significant variability of their behavior. This finding suggests that this variability can be simulated through the randomization of only the parameters of the proposed extended Iwan-type models (split four-parameter and five-parameter). The distribution of these parameters is next selected based on maximum entropy concepts and their corresponding parameters, i.e., the hyperparameters of the model, are identified using a maximum likelihood strategy. Proceeding with Monte Carlo simulations of the stochastic Iwan models demonstrates that the experimental data fits well within the uncertainty bands corresponding to the 5th and 95th percentiles of the model predictions which well supports the adequacy of either model.