A fast nonlinear dynamic analysis algorithm is proposed based on modal superposition of structural response incorporating both material and geometric nonlinearities. Because linear modal superposition has found great acceptance 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 computed 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 simulations are performed and results are demonstrated to be both accurate and efficient.
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