A mode superposition method for approximately solving the dynamic response of viscously damped nonlinear structural systems is presented, which is characterized by high accuracy and low computational cost. The method is based on an incremental decomposition procedure to formulate the motion of the discrete system, which is established by finite element theory for spatial dependence and both geometric and material nonlinearities are considered. The accuracy and efficiency are studied through two practical problems. By comparing the results using the present method with those using the direct time integration, it is found that the error is negligible and the computational effort can be significantly reduced.

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