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.

Introduction

Step-by-step direct time integration methods [1,2] are essential tools for numerical analyses of structural dynamics. For many decades, time integration methods have been improved not only to give more accurate predictions but also to perform specific functions, such as the elimination of the spurious high-frequency mode and the conservation of the total energy, more effectively. Traditionally, the role of numerical dissipation in implicit methods has been emphasized for the effective elimination of the spurious highfrequency mode and the stabilization of highly nonlinear problems. In general, implicit methods are unconditionally stable, and time steps can be chosen independently without stability considerations [3]. By utilizing unconditional stability and numerical dissipation of implicit methods, the spurious high-frequency mode can be effectively eliminated without additional processes. The Houbolt [4] method, the Park method [5], and the Bathe and Baig (BB) method [6] have strong numerical dissipation which is useful for filtering of the spurious highfrequency mode in numerical solutions. Other than the capability of filtering the spurious high-frequency mode, the capability of conserving the total energy of dynamic systems has also been regarded as an essential attribute of a good time integration method in many of practical analyses [7,8]. The Houbolt, Park, and BB methods were effective for filtering the spurious highfrequency mode in numerical solutions, but these methods also introduced a certain amount of numerical damping into the important low-frequency mode. When large time steps were used for a long duration of time, they could distort predictions seriously as discussed in Ref. [9].