An improved implicit time integration algorithm: The generalized composite time integration algorithm

•The algorithm can be applied to nonlinear structural dynamics in a consistent manner.•The algorithm includes one free parameter which controls algorithmic dissipation.•The effective stiffness matrices of the first and second sub-steps become identical in linear analyses.•The algorithm provided improved solutions compared with those obtained from the Bathe method. The weighted residual method is employed to develop one- and two-step time integration schemes. Newly developed time integration schemes are combined to obtain a new second-order accurate implicit time integration algorithm whose computational structure is similar to the Bathe method (Bathe and Noh, 2012). The newly developed algorithm can control algorithmic dissipation in the high frequency limit through the optimized weighting parameters. It contains only one free parameter, and always provides an identical effective stiffness matrix to the first and second sub-steps in linear analyses, which is not provided in the algorithm proposed by Kim and Reddy (2016). Various nonlinear test problems are used to investigate performance of the new algorithm in nonlinear analyses.