A WOODBURY NONLINEAR ANALYSIS APPROACH BASED ON THE SUBSTRUCTURING METHOD

Nonlinear analysis is an important means to study structural performance. Accurate and efficient simulation of nonlinear behavior is of great significance for evaluating structural safety. Material nonlinear behavior generally occurs in some local regions for most engineering structures. The computational efficiency of nonlinear analyses can be greatly improved by taking advantage of the characteristics of local nonlinearity. The Woodbury formula has been employed by multiple numerical algorithms to efficiently solve structural analysis problems with local nonlinearity. The use of the Woodbury formula only needs to factorize a small-scale Schur complement matrix and the corresponding operation of the global stiffness can be avoided. However, because the Schur complement matrix is dense and its dimension depends on the scale of the nonlinear domains, the achievement of high efficiency of the Woodbury formula requires the condition of local nonlinearity to be satisfied. To overcome the limitation of the Woodbury formula, a Woodbury nonlinear analysis approach based on the substructuring method is proposed, in which the order of the Schur complement matrix is considerably reduced by partitioning the matrix into several submatrices. The proposed method is applied to the dynamic nonlinear analysis of a steel frame structure, and a comparison is made with conventional structural analysis methods based on the Woodbury for mulain terms of accuracy and efficiency. The results show that the proposed method is sufficiently accurate and improves the computational performance of the Woodbury formula so that its scope of application is broadened.