Reducing Finite Element Models of Bolted Joints using Spectral Submanifolds

Abstract

Bolted joints can exhibit significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric nonlinearity. Owing to the nonlinearity and high dimensionality of such models, full-order dynamic simulations are computationally expensive. In this work, we use the theory of Spectral Submanifolds (SSMs) to construct FEM-based data-driven Reduced Order Models (ROMs). The data used for constructing the model consists of a few transient trajectories of the full unforced system. Using this data, we obtain an SSM-reduced model that also predicts the forced nonlinear dynamics. We illustrate the method on a 187,920-dimensional FEM of the recent 2021 Tribomechadynamics benchmark structure. In this case, the SSM-based ROM is a 4-dimensional model that captures the internal resonance of the structure. The SSM-reduced model gives fast and accurate predictions of the experimental forced dynamics and allows to reproduce the local friction and contact stresses on the interfaces of the joint.