有阻尼体系显式积分格式的计算精度研究

结构动力反应计算中的显式积分格式是一种重要的时域逐步积分方法。对于有阻尼单自由度体系,由于时间离散,质点的反应计算值与理论值存在一定差异。本文通过特征向量矩阵对积分格式的传递矩阵进行分解,采用周期延长率和相邻正/负波峰值递减率作为计算精度的衡量指标,建立了有阻尼体系显式积分格式计算精度的一种新方法。应用该方法分析ABAQUS/Explicit积分格式的计算精度,推得单自由度体系质点振动的周期延长率、峰值递减率随频率、阻尼比及计算时间步长变化的解析表达式,并采用工程结构常用的阻尼比取值对计算精度进行定量分析。结果表明,本文提出的方法可行有效,并可推广应用于其它有阻尼体系显式积分格式计算精度的定量分析。

Research on the computational accuracy of explicit integration method with damping

Explicit integration scheme is an important step-by-step time-integration method in dynamic anal-ysis. Due to time discretization, the calculated response values are different from the theoretical ones for a single degree of freedom system with damping. In this paper, the transfer matrix in the integration scheme is decomposed by use of eigenvector matrix, and percentage period elongation and percentage peak value decay of adjacent positive/negative waves are defined as the accuracy indexes. In this way a new method for the accuracy analysis of explicit integration scheme is proposed. This method is applied in the accuracy analysis of ABAQUS/Explicit. The analytical formulae of the two accuracy indexes with frequency, damp-ing ratio and time step are derived. Quantitative analysis of the computation accuracy is also carried out in the usual range of damping ratio of engineering structures. The results show that the method proposed in this paper is feasible and effevtive, and can be applied to the accuracy study of other explicit integration scheme.