A Simple Truly Self-Starting and L-Stable Integration Algorithm for Structural Dynamics

Abstract

This paper proposes a novel composite two sub-step implicit method to effectively solve structural dynamic problems. The main highlight of the new method lies that it is truly self-starting and so avoids computing the initial acceleration vector, but the second-order accurate acceleration output can be still provided. Besides, the new method does not sacrifice other desired numerical characteristics, such as the identical second-order accuracy, unconditional stability (L-stability) and no overshoots. As with the existing Bathe algorithm, the new method also includes a unique algorithmic parameter [Formula: see text] to adjust numerical dissipation imposed in the low-frequency range. Numerical spectral analysis and examples show that the new method with [Formula: see text] is highly recommended solving various dynamical problems.