Constrained Shell Finite Element Method for Stability Analysis of Thin-Walled Steel Members with Tapered Sections

This paper presents a recently developed constrained shell finite element method (cFEM) 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 behavior 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 steel members, they will also be subjected to the commonly categorized buckling modes: Global (G), Distortional (D), and Local (L) modes. Recently, a cFEM 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, which is capable of providing constrained stability solutions of thin-walled members including prismatic and curved sections - either open or closed. Since the mode definitions of the developed cFEM utilize the stiffness of the linear elastic analysis of the member and the restraints are enforced through the degree of freedoms, 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 steel members, including a tapered lipped channel section, a tapered circular section, and a tapered I-section. The complicated buckling behaviors of these members are accordingly investigated through the modal decomposition and identification of cFEM. All these numerical examples demonstrate the potential and applicability of the cFEM in stability analyses of tapered steel members.

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