Koiter–Newton Reduced-Order Method Using Mixed Kinematics for Nonlinear Buckling Analysis

Abstract

The Koiter–Newton method improves the computational efficiency of nonlinear buckling analysis; however, the construction of reduced-order models using fully nonlinear kinematics is still a tedious and time-consuming work. In this paper, the Koiter–Newton reduced-order method using mixed nonlinear kinematics is presented for the geometrically nonlinear buckling analysis of thin-walled structures. Strain energy variations up to the fourth order were achieved using mixed kinematics for the improved Koiter theory. Corotational kinematics, which is inconvenient for high-order variations, was applied to calculate the first- and second-order variations for the internal force and tangent stiffness, respectively, whereas the third- and fourth-order strain energy variations were facilitated by explicit algebraic formulations using updated von Kármán kinematics. A reduced-order model with 1+m degrees of freedom was established, of which m perturbation loads were considered to make the method applicable for buckling problems. The geometrically nonlinear response was traced using a predictor–corrector strategy by combining the nonlinear prediction solved by the reduced-order model and the correction using Newton iterations. Numerical examples of structures with various buckling behaviors demonstrate that the performance of the proposed method is not obviously affected by using simplified kinematics, and sometimes it even exhibits a superior capability for path-following analysis.