Search

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better ac-curacy than the classical methods. By considering this assumption and employing two pa-rameters ô and a, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the ac-curacy of the proposed method. Second order accuracy is achieved for all values of ô and a. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-8, and generalized-a methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally sta-ble methods, namely, Newmark's average acceleration, Wilson-0, and generalized-a. methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step du-ration, the proposed method is shown to be faster in comparison with the other methods. [ABSTRACT FROM AUTHOR]