Non-conservative dynamic stiffness analysis of axial-lateral buckling

Abstract

The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method is extended to analyze the lateral buckling of thin wall columns under the influence of a follower axial force and the in-plane moment. The constant in-plane moment weakens the flexural mode so that, at certain critical applied moments, the flexural mode buckles as the fundamental flexural frequency reaches zero. However, the constant in-plane moment hardens the torsional mode so that the torsional mode never buckles. When both torsion and flexure are considered, the interaction of the flexural characteristic curves and the torsional characteristic curves becomes very complex. Since the dynamic stiffness is exact in the classical sense, the interaction can be studied easily. Numerical examples are given to show the complexity of the characteristic diagrams. The dynamic stiffness is given explicitly for uniform beams of symmetric cross-section with one bending stiffness being taken as infinite and with negligible warping stiffness, a follower external axial end force and a follower external bending end moment about the stiff cross-sectional axis.