Nonlinear stability analysis of thin-walled I-section laminated composite curved beams with elastic end restraints

Semi-analytical solution for critical buckling load and nonlinear load-deflection relationship of I-section laminated composite curved beams with elastic end restraints is presented. The governing differential equations of thin-walled curved beams are derived from the principle of virtual displacement with full consideration of curvature effect. The elastic end restraints of laminated curved beams for practical engineering is adopted, and the characteristic displacement functions of pinned-pinned and clamped-clamped are linearly combined to describe the stability behavior of end-restrained curved beams. The Galerkin method is used to solve the governing differential equations for stability analysis of laminated curved beams. Accuracy of the present semi analytical solution for predicting critical buckling load is verified with available solutions in the literature, and its effectiveness for nonlinear stability analysis is illustrated in comparison with the finite element method using ABAQUS. The in-plane and out-of-plane behaviors of laminated composite curved beams are compared. Finally, the effects of geometry of section, initial imperfection, central angle of curved beam (the ratio of arc length to radius), layup in flange and web, and stiffness of elastic end restraints are evaluated to shed light on nonlinear stability behavior. The present semi-analytical solution for nonlinear stability analysis of thin-walled I section laminated composite curved beams can be used effectively and efficiently in design analysis and optimization of thin-walled curved beam structures.