Nonlinear thermoelastic buckling analysis of thin-walled structures using a reduced-order method with mixed nonlinear kinematics

The initial temperature field adds to the complexity of the geometrically nonlinear response, especially for the thin-walled structures in the presence of buckling. The conventional finite element method requires plenty of computational resources to solve the full-order finite element (FE) model using a Newton-Raphson incremental- iterative solution procedure. Although the reduced-order method inspired by the Koiter asymptotic theory remarkably decreases the number of degrees of freedom (DOFs) of the analysis model, the up to the fourth- order strain energy variations are still computationally prohibited when the fully nonlinear kinematics are adopted. In this work, a reduced-order method with the mixed nonlinear kinematics is proposed for nonlinear thermoelastic buckling analysis of thin-walled structures. The mixed kinematics are developed to simplify the high-order strain energy variations and involve the nonlinear thermoelastic effect. A reduced-order model is constructed using the mixed kinematics, in which the initial temperature field is converted to be an additional degree of freedom. The nonlinear thermoelastic response can be automatically traced using the predictor- corrector strategy based on the reduced FE system. The numerical examples, including flat plates and curved shells with various geometries and loadings, demonstrate the accuracy and high efficiency of the proposed method.