Frame Buckling Analysis with Full Consideration of Joint Compatibilities

Abstract

Previous buckling analyses for three‐dimensional frames based on discrete element formulations have been criticized for the lack of equilibrium at angled joints in the buckling state. While this problem can be overcome through the introduction of the so‐called semitangential rotations and moments, this approach suffers from the drawback that the semitangential definitions are rather artificial. In this paper, it is demonstrated that the so‐called lack of equilibrium for rotated angled joints is not a physical reality, but a result of overlooking compatibility conditions for interconnected elements in the deformed position. One feature of such compatibility conditions is that they are irrelevant to any elastic deformations. In a finite element formulation, they can only be included through the external virtual work terms. In this paper, the procedure for calculating the element forces in a step‐by‐step nonlinear analysis is also discussed. The adequacy of the present approach is confirmed in the numerical study.