Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

This paper develops a family of optimized n-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first (n-1) sub-steps, and the last sub-step employs (n + 1)-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.