Assessment and improvement of precise time step integration method

Abstract

The numerical stability and the computation accuracy of precise time step integration method are discussed. The precise time step integration method is conditionally stable and this time integration scheme has inherent algorithmic damping, algorithmic period error and algorithmic amplitude decay, but the stability conditions and the computation accuracy requirements of this time integration scheme are easy to be satisfied with the discretized structural models. And the optimum values of the truncation order L and 2-division order N are presented, and the Gauss quadrature method is used to improve the computation accuracy of precise time step integration method, so a precise time step integration method is established. The method avoids the inverse matrix calculation and the simulation of the applied loading and improves the computing efficiency, and the method is independent to the quality of the matrix [H]. If the matrix [H] is singular or nearly singular, the advantage of the method is remarkable. Finally, a numerical example verified the validity of the selections of L and N and the feasibility of improvement of precise time step integration method.

詳細分析了結構動力分析的精細積分方法的穩定性、計算精度,在此基礎上提出了對現有精細積分方法的改進策略。算例證實了本文對精細積分方法改進的科學性與可行性。