Non‐linear dynamic analysis using one‐dimensional updated subspaces

The purpose of this paper is to improve the effectiveness of ordinary reduction methods performance, in nonlinear dynamic analysis. In this paper, the error vector due to linear and nonlinear dynamic analysis in generalized subspaces is extracted, and is decomposed into two independent components, namely outside and inside components. Based on the inside error component, a new iterative reduction method, one‐dimensional generalized subspace procedure (ODGS), is proposed where an innovative criterion is defined for updating the base vectors necessary for stiffness changes in nonlinear dynamic analysis. In this study, the performance of ODGS for linear and nonlinear analysis of elastodynamic systems including non‐proportional damping based on the Ritz generalized subspace has been proposed. Numerical examples show the competency of the proposed method in both economy and exactness. Time saving gained from the ODGS method could be recompensed to get much more accurate results consuming the same CPU time. This iterative method is more effective than the ordinary reduction methods. Since the method is directly derived from the discrete model based on the finite element method (FEM), the complexity of the structure does not affect directly the effectiveness of ODGS. Therefore, whenever the FEM is effectively capable to represent the topology of the structure, the ODGS results will also represent the system response properly. Same as any other reduction methods, accuracy of this iterative reduction method is directly related to the number of selected Ritz vectors, according to convergence criterion.