Nonlinear Dynamic Analysis of Structures Using Modal Superposition
Kevin K. Wong
A fast nonlinear dynamic analysis algorithm based on modal superposition of structural response incorporating both material and geometric nonlinearities is proposed. Because linear modal superposition has found great acceptances in performance-based seismic engineering, it is here extended to the nonlinear domain by using the force analogy method to address material nonlinearity, where the stiffness force is quantified by a change in displacement instead of using the traditional way of changing stiffness. Geometric nonlinearity is incorporated into the analysis using stability functions. State space method is used to explicitly calculate the dynamic responses of each modal single-degree-of-freedom system. Through the combination of force analogy method, stability functions, state space method, and modal superposition, numerical simulation is performed and results are demonstrated to contain both accuracy and efficiency.