Series solutions for spatially coupled buckling anlaysis of thin-walled Timoshenko curved beam on elastic foundation

The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thicknesscurvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and forcedeformation relationships are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers