Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements

Fillets are commonly found in thin-walled beams. Ignoring the presence of a fillet in a finite element (FE) model of a thin-walled beam can significantly change the natural frequencies and mode shapes of the structure. A large number of solid elements are required to accurately represent the shape and the stiffness of a fillet in a FE model, which makes the size of the FE model unnecessarily large for global dynamic and static analyses. In this work the equivalent stiffness effects of a fillet in a thin-walled beam are decomposed into in-plane and out-of-plane effects. The in-plane effects of a fillet are analyzed using the wide-beam and curved-beam theories, and the out-of-plane effects of the fillet are analyzed by modeling the whole fillet section as a slender bar with an irregular cross section. A simple shell/plate and beam element model is developed to capture the in-plane and out-of-plane effects of a fillet on a thin-walled beam. The natural frequencies and mode shapes of a thin-walled L-shaped beam specimen calculated using the new methodology are compared with its experimental results for 28 modes. The maximum error between the calculated and measured natural frequencies for all the modes is less than 2%, and the associated modal assurance criterion values are all over 95%. The methodology is also applied to other thin-walled beams, and excellent agreement is achieved between the natural frequencies from the shell/plate and beam element models and those from the solid element models. While the shell/plate and beam element models provide the same level of accuracy as the intensive solid element models, the degrees of freedom of the shell/plate and beam element models of the thin-walled beams are only about 10% or less of those of the solid element models.