Wilson-θ法两种积分格式的稳定性探讨  

Stability discussion of two integration formats for Wilson-θ Method

作　　者：方德平[1] 王全凤[1] 

机构地区：[1]华侨大学土木工程学院,福建泉州362021

出　　处：《计算力学学报》2008年第4期539-541,共3页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50578066/E080507);福建省自然科学基金(E0410023E0540005);厦门市科技计划项目(3502Z20074039)资助项目

摘　　要：Wilson-θ法分为加速度未经过和经过动力平衡方程修正的Wilson-θ①法和Wilson-θ②法;推导了单自由度体系的Wilson-θ①、②法的状态传递算子,由传递算子的谱半径来判断Wilson-θ①、②法的稳定性。计算结果表明:Wilson-θ①法的稳定性是无条件的,Wilson-θ②法的稳定性不是无条件的;并给出了Wilson-θ②法的稳定范围。There remain two kinds of Wilson-θ methods, namely, Wilson-θ （1） and （2） methods. In Wilson-θ （1） method, the accelerations are not modified by the dynamic equilibrium equations at the time t＋ △t; in Wilson-θ （2） method, the accelerations are modified. The modal superposition method can reduce the response of a multi-degree-of-freedom （MDOF） system to the superposition of the single-degree-of-freedom （SDOF） system responses for each mode, thus the stability for a SDOF system is equivalent to the stability for a MDOF system. In order to simplify the equation expression, only SDOF system is considered. The amplification matrixes of Wilson-θ （1） and （2） methods for SDOF system are derived. The stabilities of Wilson-θ （1） and （2） methods are examined hy the spectral radii of the amplification matrixes. The stability of Wilson-θ （1） method is unconditional. The calculation results indicate： the stability of Wilson-θ （2） method is not unconditional. The stability ranges of Wilson-θ （2） method are also put forward. The conclusion corrects a mistake in some references where both Wilson-θ （1） and （2） methods are wrongly considered as unconditional stability.

关 键 词：WILSON-Θ法 稳定性 状态传递算子 谱半径 

分 类 号：TU311.3[建筑科学—结构工程]