This paper presents a recently developed constrained shell finite element method (termed as fFEM in this paper) towards the elastic buckling analysis of thin-walled members and its applicability toward tapered steel sections using a set of numerical examples. Tapered sections have a wide application in steel structures. However, their stability behaviors could be complex and numerical analysis is commonly required to fully capture it (though some simplified analytical solutions may be possible). For thin-walled tapered members, they will also be subjected to the commonly categorized buckling modes: Global (G), Distortional (D), and Local (L) modes. Recently, a fFEM was developed using a force-based approach by defining the GDL modes utilizing the displacement and force characteristics of each mode. The method was then implemented with shell element formulations in ANSYS, which is capable of providing constrained solutions for the elastic buckling analysis of thin-walled members including prismatic and curved sections - either open or closed. Since the mode definitions of the developed fFEM utilize the stiffness of the linear elastic analysis of the member and the restraints are enforced through the degrees of freedom, these definitions and implementation are revisited and their applicability to tapered sections are justified. Then, numerical examples are demonstrated on a set of thin-walled tapered members, including a tapered I-section and a tapered lipped channel section. The complicated buckling behaviors of these members are accordingly investigated through the modal decomposition and identification of fFEM. All these numerical examples demonstrate the potential and applicability of the developed fFEM in analyzing the stability of tapered steel members.
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