An optimized three-sub-step composite time integration method with controllable numerical dissipation

摘要

This paper proposes an optimized three-sub-step composite time integration methods with controllable numerical dissipation, called the rho(infinity)-Optimal-Trapezoidal-Trapezoidal-Backward-Interpolation-Formula (rho(infinity)-OTFBIF) method. In this method, a novel Newmark-like method or four-point backward interpolation formula is employed in the third sub-step, instead of the four-point Euler backward difference method as in the Optimal-Trapezoidal-Trapezoidal-Backward-Difference-Formula (OTTBDF) method which was proposed by the present authors and co-workers. The proposed method has second-order accuracy, unconditional stability and controllable numerical dissipation, and the spectral radius rho(infinity) serves as a parameter controlling the degree of numerical dissipation. In addition, the properties of the rho(infinity)-OTTBIF method can reduce to those of the OTTBDF method when rho(infinity)similar or equal to 0. Since the low-frequency accuracy is maximized in construction, the proposed method has higher low-frequency accuracy than other methods with controllable numerical dissipation. Linear and nonlinear numerical simulations are conducted to check the advantages of the proposed method over other similar time integration methods. (C) 2020 Elsevier Ltd. All rights reserved.