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 …

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 …

Second-order unconditionally stable schemes of linear multi-step methods, and their
equivalent single-step methods, are developed in this paper. The parameters of the linear …

A family of n-sub-step composite time integration methods, which employs the trapezoidal
rule in the first n-1 n-1 sub-steps and a general formula in the last one, is discussed in this …

This paper focuses mainly on the development of composite sub-step explicit algorithms for
solving nonlinear dynamic problems. The proposed explicit algorithms are required to …

In this paper, a novel implicit family of composite two sub-step algorithms with controllable
dissipations is developed to effectively solve nonlinear structural dynamic problems. The …

This article focuses mainly on the development of explicit integration algorithms for structural
dynamics. Some known single‐step explicit schemes are first reviewed and their algorithmic …

A spectral consistent starting procedure is proposed for the first‐order‐type A‐stable linear
two‐step (LTS) time integration methods in structural dynamics analysis. The accuracy …

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 …

This paper further analyzes three Bathe algorithms (γ-Bathe, β 1∕ β 2-Bathe and ρ∞-Bathe)
with their unknown properties revealed. The analysis shows firstly that three Bathe …