Directly self-starting higher-order implicit integration algorithms with flexible dissipation control for structural dynamics

J Li, R Zhao, K Yu, X Li - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
An implicit family of composite s-sub-step integration algorithms is developed in this paper.
The proposed composite s-sub-step scheme is firstly designed to satisfy two requirements …

Three optimal families of three‐sub‐step dissipative implicit integration algorithms with either second, third, or fourth‐order accuracy for second‐order nonlinear …

J Li, K Yu, R Zhao, Y Fang - International Journal for Numerical …, 2023 - Wiley Online Library
This paper reviews the published composite three‐sub‐step implicit algorithms all of which
adopt the trapezoidal rule in the first sub‐step. Three optimal families of three‐sub‐step …

Two third-order explicit integration algorithms with controllable numerical dissipation for second-order nonlinear dynamics

J Li, K Yu, R Zhao - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
No literature has reported an explicit integration algorithm to achieve controllable numerical
dissipation and identical third-order accuracy simultaneously. This paper develops two …

A self-starting dissipative alternative to the central difference methods

R Zhao, J Li, K Yu - Archive of Applied Mechanics, 2023 - Springer
This paper focuses mainly on developing single-step explicit integration algorithms
considering the implicit treatment of velocity. A novel explicit algorithm (GSSI) is proposed …

New insights into a three-sub-step composite method and its performance on multibody systems

Y Ji, H Zhang, Y Xing - Mathematics, 2022 - mdpi.com
This paper develops a new implicit solution procedure for multibody systems based on a
three-sub-step composite method, named TTBIF (trapezoidal–trapezoidal backward …

High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems

J Li, H Li, K Yu, R Zhao - arXiv preprint arXiv:2209.13820, 2022 - arxiv.org
This paper develops an implicit family of sub-step integration algorithms, which firstly
requires identical effective stiffness matrices and third-order consistency within each sub …

On enhanced second-order explicit integration methods with controllable algorithmic dissipation and adjustable sub-step size for hyperbolic problems

J Li, H Li, Y Lian, K Yu, R Zhao - International Journal of Applied …, 2023 - World Scientific
This paper constructs and analyzes a generalized composite two-sub-step explicit method to
solve various dynamical problems effectively. Via the accuracy and dissipation analysis, the …

On second-order s-sub-step explicit algorithms with controllable dissipation and adjustable bifurcation point for second-order hyperbolic problems

J Li, H Li, R Zhao, K Yu - European Journal of Mechanics-A/Solids, 2023 - Elsevier
This paper proposes a self-starting, second-order accurate, composite s-sub-step explicit
method, within which the first five explicit members are developed, analyzed, and compared …

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

Y Ji, Y Xing - International Journal of Applied Mechanics, 2021 - World Scientific
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 …

On designing and developing single‐step second‐order implicit methods with dissipation control and zero‐order overshoots via subsidiary variables

J Li, H Li, Y Lian, K Yu, R Zhao - International Journal for …, 2023 - Wiley Online Library
Hilber and Hughes gave several competitive demands on the implicit methods in 1978.
However, there are no such integration methods in the traditional algorithm design. Via …