Spatial Stability of Shear Deformable Nonsymmetric Thin-Walled Curved Beams: A Centroid-Shear Center Formulation

Abstract

An improved shear deformable curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled stability analysis of thin-walled curved beams with nonsymmetric cross sections. For this, the displacement field is introduced considering the second order terms of semitangential rotations. Next the elastic strain energy is newly derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. Then the potential energy due to initial stress resultants is consistently derived with accurate calculation of the Wagner effect. Finally, equilibrium equations and force–deformation relations are obtained using a stationary condition of total potential energy. The closed-form solutions for in-plane and out-of-plane buckling of curved beams subjected to uniform compression and pure bending are newly derived. Additionally, finite-element procedures are developed by using curved beam elements with arbitrary thin-walled sections. In order to illustrate the accuracy and the practical usefulness of this study, closed-form and numerical solutions for spatial buckling are compared with results by available references and ABAQUS’ shell elements.