An Improved Higher-Order Time Integration Algorithm for Structural Dynamics

Based on the weighted residual method, a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed, which is superior to the second-order accurate algorithms in tracking long-term dynamics. For improving such a higher-order accurate algorithm, this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable dissipation. In the proposed algorithm, a time step interval [t(k), t(k) + h] where h stands for the size of a time step is divided into two sub-steps [t(k), t(k) + gamma h] and [t(k) + gamma h, t(k) + h]. A non-dissipative fourth-order algorithm is used in the first sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to filter out the contribution of high-frequency modes. Besides, two approaches are used to design the algorithm parameter gamma. The first approach determines gamma by maximizing low-frequency accuracy and the other determines gamma for quickly damping out high frequency modes. The present algorithm uses rho(infinity) to exactly control the degree of numerical dissipation, and it is third-order accurate when 0 <= rho(infinity) < 1 and fourth-order accurate when rho(infinity) = 1. Furthermore, the proposed algorithm is self-starting and easy to implement. Some illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm.