基于Koiter的初始后屈曲理论以及Newton法的增量迭代技术，提出了一种能够自动跟踪非线性平衡路径的降阶方法．降阶模型中摄动载荷以及主路径上变形位移的引入使摄动展开能够在平衡路径上的任意一点处进行；在每个摄动步中将求解降阶模型得到的非线性解作为结构响应的初始预测，然后采用有限元模型计算的残余力对解进行修正，最后以修正后的解作为下一个摄动步的已知展开点，并通过更新降阶模型来反映当前结构刚度的变化．算例分析表明，该方法不仅具有很高的非线性分析精度，而且需要计算的线性方程组(阶数与有限元全模型阶数相当)的数目远小于常规的非线性有限单元法．

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.