A new family of two-stage explicit time integration methods with dissipation control capability for structural dynamics

•Smaller errors than Soares method and Noh and Bathe method.•Remarkably improved performance of the non-dissipative case.•True self-starting method without the initial acceleration vector.•Complete and simple control of the full range of numerical dissipation.•Improved efficiency than the central difference method. In this article, a new family of two-stage explicit time integration methods is developed for more effective analyses of linear and nonlinear problems of structural dynamics. The collocation method and special types of difference approximations with adjustable algorithmic parameters are employed to approximate the displacement and velocity vectors in time. The new two-stage explicit method is designed to possess controllable numerical dissipation like many of the recent explicit methods. Interestingly, the period error of the new two-stage explicit method is noticeably decreased when compared with the existing two-stage explicit methods. All improved and preferable features of the new two-stage explicit method are achieved without additional computational costs. Illustrative linear and nonlinear problems are solved numerically by using the new and existing methods, and numerical results are carefully compared to verify the improved performance of the new two-stage explicit method.