关键词: 屈曲, 降阶模型, 摄动, 非线性分析

Abstract:

Based on Koiter’S initial post-buckling theory and the incremental iterative method of the Newton method,an order reduction method that automatically tracks the nonlinear equilibrium path is proposed.In this method,the perturbation load and the deformation on the primary path are introduced to make the perturbation to expand at any point along the path.In each perturbation step,the nonlinear solution obtained from the reduced-order model is taken as an initial prediction of the structural response and is corrected with the residual lcad obtained by the FE model.Then,the corrected solution is taken as the expansion point of the next perturbation step,and the reduced-ordermodel is updated to reflect the change of structural stiffness.Numerical examples show that the proposed method is of high accuracy for the nonlinear analysis,and that the number of the linear systems of equations(the scale of which equals that of the full finite element model)needed to be solved is much less than that of the general nonlinear finite element method.

Key words: buckling, reduced-order model, perturbation, nonlinear analysis