Stability Analysis of Curved Beams Based on First-Order Shear Deformation Theory and Moving Least-Squares Approximation

Based on the first-order shear deformation theory (FSDT) and moving least-squares approximation (MLS), a new meshfree method that considers the effects of geometric nonlinearity and the pre- and post-buckling behaviors of curved beams is proposed. An incremental equilibrium equation is established with the Updated Lagrangian (UL) formulation under the von Karman deflection theory. The proposed method is applied to several numerical examples, and the results are compared with those from previous studies to demonstrate its convergence and accuracy. The pre- and post-buckling behaviors of the curved beam with different parameters, such as vector span ratios, bending forms, inclusion angles, boundary conditions, slenderness ratios, and axial shear stiffness ratios, are also investigated. The effects of the parameters on the buckling response are demonstrated. The proposed method can be extended to the study of double nonlinearities of curved beams in the future. This extension will provide a more scientific reference basis for the structural selection of curved girder structures in practical engineering.