Coupled, Nonconservative Stability-Finite Element

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Abstract
Coupled bending-torsion instabilities in columns are investigated through application of the Ritz finite element method. Conditions for dynamic divergence and flutter instabilities generated by nonconservative follower forces are determined for columns with cross-sectional assymetry. Both inertial and stiffness coupling are considered in the formulation of nonself-adjoint eigenvalue problems. Critical loading conditions based on observation of eigenvalue trajectories are examined for a cantilevered channel and an I-beam subjected to end loading and for a simply supported beam loaded in the plane of maximum stiffness. The results clearly indicate that: (1) Critical loads can be significantly reduced by bending-torsion coupling and (2) critical load and instability mechanism (static or dynamic) calculation are sensitive to system modeling; therefore, accurate discretization procedures are essential for critical load prediction.

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