Finite Element Modeling of Structures With L-Shaped Beams and Bolted Joints

Due to bending-torsion coupled vibrations of the L-shaped beams and numerous uncertainties associated with the bolted joints, modeling structures with L-shaped beams and bolted joints is a challenging task. With the recent development of the modeling techniques for L-shaped beams by the authors (He and Zhu, 2009, “Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements,” ASME J. Vibr. Acoust., 131(5), p. 051002), this work focuses on developing new finite element (FE) models for bolted joints in these structures. While the complicated behavior of a single bolted connection can be analyzed using commercial FE software, it is computationally expensive and inefficient to directly simulate the global dynamic response of an assembled structure with bolted joints, and it is necessary to develop relatively simple and accurate models for bolted joints. Three new approaches, two model updating approaches and a predictive modeling approach, are developed in this work to capture the stiffness and mass effects of bolted joints on the global dynamic response of assembled structures. The unknown parameters of the models in the model updating approaches are determined by comparing the calculated and measured natural frequencies. In the predictive modeling approach, the effective area of a bolted connection is determined using contact FE models and an analytical beam model; its associated stiffnesses can also be determined. The models developed for the bolted joints have relatively small sizes and can be easily embedded into a FE model of an assembled structure. For the structures studied, including a three-bay space frame structure with L-shaped beams and bolted joints, and some of its components, the errors between the calculated and measured natural frequencies are within 2% for at least the first 13 elastic modes, and the associated modal assurance criterion values are all over 94%.