AN IMPROVED REDUCED-ORDER NUMERICAL SUBSTRUCTURE METHOD BASED ON NEWTON ITERATIVE ALGORITHM

Making use of the local nonlinearities of the structures under earthquakes, the numerical substructure method (NSM) transforms the original complex structural nonlinear analysis into the equivalent linear elastic analysis of a master structure based on a fixed-point iterative algorithm and nonlinear analyses of isolated substructures for yield components. However, the NSM still has a limitation due to the low convergence speed for the master structure based on the initial elastic stiffness. In this study, an improved reduced-order NSM based on a Newton algorithm is presented. In the master structure, the displacements of nonlinear degrees of freedom are taken as unknown quantities, and the nonlinear analysis process using the Newton algorithm is conducted, in which resisting forces and tangent stiffnesses of nonlinear elements are obtained from isolated substructures. Seismic elastoplastic time-history analyses of a plane 15-storey three-bay steel structure are carried out. The numerical analysis results show that: the present method is accurate and efficient, closing to the second-order convergence of the traditional Newton algorithm, and only needs to form and decompose a much smaller matrix than that in the traditional algorithm for a local nonlinear system.