Large Deflection Analysis of Beam-Columns with General Sections Using Gaussian Line-element Method
Ziemian, Ronald D.
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The finite-element analysis method implementing line-elements is extensively adopted for the analysis and design of large-scale structures. The robustness of the element derivations and formulations decidedly impact the accuracy of capturing the actual member behaviors, thereby the structure deformations. This paper develops a new and innovative beam-column element that accounts for different member complexities. The section being nonsymmetric and the twisting deformations along the element length significantly affect the section stiffness and, as a result, the element stiffness matrix. The inclined angle between the cross-section’s and the element’s local axes is varied along the element length, making the cross-section properties apparently different. To this end, the Gaussian quadrature method is adopted to summate the section stiffness; moreover, a refined Updated-Lagrangian method is introduced to account for the element total deformations. Accordingly, fewer elements to simulate the structural member can be adopted, thereby dramatically enhancing the numerical efficiency. Detailed derivations are provided, and their implementations are elaborated. Finally, several validation examples are presented to verify the accuracy and examine the robustness of the proposed method.