Consistent Frame Buckling Analysis by Finite Element Method

Abstract

Conventional element assembly process based on the initial configuration of structures does not necessarily imply the satisfaction of compatibility conditions in the deformed state. This may result in a violation to the rule that all physical relations should be specified for deformed structures in a buckling analysis. Based on an exact consideration of the interelement compatibility for structural members, one can derive a joint matrix for internally generated moments and a moment matrix for externally applied moments, in addition to the elastic and geometric stiffness matrices commonly used in nonlinear analysis. To highlight the linking between the fundamental mechanics equations and their finite element counterparts, the present derivation will be made only for planar frames that are allowed to buckle both in and out of plane. The validity of the present procedure is confirmed in the numerical examples.