An adaptive numerical scheme based on the Craig–Bampton method for the dynamic analysis of tall buildings

A new numerical scheme is proposed to perform a nonlinear dynamic analysis for tall buildings. The structural components (beams and columns) of tall buildings gradually enter the inelastic phase under strong seismic excitation. Because the distribution of nonlinear components is initially unknown due to the randomness of earthquake inputs, a group of linear and nonlinear substructures are automatically figured out during the time-history analysis of a structure. Then a modified Craig–Bampton method is proposed to condense the DOFs of the linear substructures in modal coordinates at each time step while keeping the governing equation of the nonlinear substructure in physical coordinates. The dominant modes of the linear substructures are selected to capture the main dynamic characteristics of the structure. The time step integration analysis is used to solve the governing equation of the structures in hybrid coordinates. A 20-story building is employed as the numerical simulation test to validate the feasibility and effectiveness of the proposed numerical scheme. This scheme provides a new method for the nonlinear dynamic analysis of tall buildings with acceptable simulation accuracy and high computational efficiency.