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

Abstract

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%.

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“…Because a bolted joint that connects an L-shaped beam and a horizontal beam in the space frame structure in Figure 8 contains 10 bolted connections and its size is approximately one fifth of that of an L-shaped beam, the bolted joint cannot be simply modeled by a stiffness in the FE model [7]. A simple, yet accurate, linear model of a bolted connection was developed [7].…”

“…Modeling such a complex structure using simple beam elements will lead to large modeling error due to the bendingtorsion coupled vibration of a relatively short L-shaped beam and complexity of the bolted joints [7]. A more intensive model of the space frame structure with a reasonable model size needs to be developed.…”

“…A simple, yet accurate, linear model of a bolted connection was developed [7]. In the FE model of a bolted joint that connects two L-shaped beams through a bracket (Figure 9), the walls of the L-shaped beams and the bracket are modeled using shell elements, and a bolted connection is modeled by a solid cylinder [7]. The length of the solid cylinder is the sum of the distance between the two center planes of the clamped components (i.e.…”

“…With the development of modeling techniques for two common features in complex structures: fillets in thin-walled beams [6] and bolted connections [7], the main challenge associated with the modeling of complex structures can be resolved. By applying the modeling technique for fillets in thin-walled beams [6], thin-walled beams can be accurately modeled using shell and beam elements.…”

“…The higher mode vibrations of a filleted thinwalled beam, which usually cannot be captured by beam elements due to the plate-like deformations of the thin walls, can be accurately predicted by a shell and beam element model. The bolted connection modeling technique developed in [7] provides a simple, yet efficient, solution for the modeling of bolted joints. A bolted connection is modeled by a solid cylinder; the radius and elastic modulus of the cylinder can be determined by solving a contact problem using an intensive solid element model for the bolted connection.…”