Abstract
For spatial stability analysis of thin-walled curved beams with non-symmetric cross sections in account for shear deformation, an improved formulation is proposed. Firstly the displacement field is introduced considering the second order terms of semitangential rotations. Next an 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. And then the potential energy due to initial stress resultants is consistently derived with accurate calculation of Wagner effect. Finally equilibrium equations and force-deformation relations are obtained using a stationary condition of total potential energy. In addition, closed-form solution for in-plane buckling of curved beams subjected to uniform compression is newly derived. In the companion paper, F. E. procedures are developed by using curved and straight beam elements with arbitrary thin-walled sections. In order to illustrate the accuracy and the reliability of this study, closed-for m and numerical solutions for instability of the structure are compared with results by available references and ABAQUS. Furthermore, the parametric study is performed on stability behaviors of curved beams.
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