An Implicit Unconditionally Stable Integration Method for Nonlinear Structural Dynamics and Earthquake Engineering Problems

摘要

A novel time integration procedure is designed in order to solve the differential equation of motion of dynamics and earthquake engineering problems. The procedure is constituted on the principle of impulse-momentum, leading to a lesser number of assumed fields. The algorithmic properties of the procedure are determined by stability and accuracy analyses. Overshooting tendency, which is not related to stability and accuracy characteristic of a method, and order of accuracy are also examined. It is displayed that the new method is unconditionally stable and non-dissipative. Also, the numerical dispersion of the proposed algorithm appears to be much less than the commonly used integration methods. The method has no tendency to overshoot both the displacement and velocity response solutions. Its order of accuracy is around four as compared to two of the other methods considered in the study. A few numerical examples consisting of both single and multi-degree of freedom systems with linear and nonlinear characteristics are performed to see the overall behavior of the method in various practical problems. The numerical results of the proposed method obtained from these examples coincide well with the simulated exact results.