Abstract
The propagation of errors in the response calculation of nonviscous damped systems by the increase of time-step-size can cause tremendous numerical problems in the analysis. In this article, the precise time integration method (PTIM) is proposed for the response calculations of large-scale dynamic systems. The state-space scheme of the nonviscous system by utilizing an anelastic displacement field model (ADF) is derived. Then, the PTIM based on the state-space and piecewise linear interpolation schemes is developed. The proposed PTIM in terms of accuracy, precision, and implementation is discussed. The inherent algorithmic damping and amplitude decay of the proposed PTIM are proved by utilizing a single-degree-of-freedom system. The computational accuracy, efficiency, and time-step-size sensitivity of the proposed PTIM are investigated by using a multi-degrees-of-freedom system and a continuum system with much higher degrees of freedom. It is indicated that the proposed PTIM can give precise numerical results approaching the exact solution at the integration points for various time steps. It is also indicated that the linear displacement–velocity-based direct integration method (DIM-LDV) is sensitive compared to the PTIM as the time-step size is increased on large-scale problems. The performance of PTIM in terms of computational efficiency is much higher than the mode superposition method (MSM) and DIM-LDV.
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