We consider the Bathe implicit time integration method and focus on the time step splitting
ratio and the spectral radius at large time steps to improve and generalize the scheme. The …

In this paper we further consider the Bathe method for the direct time integration in structural
dynamics and wave propagations. The method uses two sub-steps per time step and is an …

The objective in this paper is to present some new insights into an implicit direct time
integration scheme, the Bathe method, for the solution of the finite element equations of …

In this paper we focus on the L-stable β 1/β 2-Bathe time integration method to obtain new
insights for transient and wave propagation solutions. The method is a specific case of the …

In this paper, a new family of controllably dissipative composite algorithms is developed to
obtain reliable numerical response of structural dynamic problems. The proposed algorithm …

A comprehensive study of the two sub‐steps composite implicit time integration scheme for
the structural dynamics is presented in this paper. A framework is proposed for the …

In this paper we introduce the explicit β 1/β 2-Bathe method for solving dynamic problems, in
particular wave propagations. Like for the implicit β 1/β 2-Bathe method, the proposed …

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 …

This paper constructs a composite s-sub-step explicit method and analyzes second-order
accuracy, conditional stability, and dissipation control at the bifurcation point. In the present s …