砂土地震液化分析中Newmark时域离散的误差评估

Temporal discretization error estimation for the Newmark scheme in sand liquefaction analysis

显式有限元存在计算精度低,对计算时间步长较敏感等缺点。基于后验误差评估的方法,给出了显式算法下Newmark时域离散误差的来源和评估方法。通过饱和砂土地震液化响应的数值算例评估了时间步长对计算结果的影响。数值分析结果表明:时间步长不同,结点位移和单元孔压的时程曲线明显不同,同时计算耗时也呈双曲线关系;相对误差主要分布在变形较大的区域,全域平均相对误差在动力响应剧烈的时间段内较大。通过对计算时间步长和离散误差的评估,可有效恰当的对计算时间步长进行取值,也为自动步长调整提供了依据。

The disadvantage of the explicit finite element method is low accuracy and sensitive to the time step size.In this paper,a posteriori error evaluation method was introduced for the explicit Newmark scheme,giving the source and estimation method of the Newmark temporal discretization error. Then,a numerical example of saturated sand liquefaction in earthquake was conducted to evaluate the influence of time step size on the calculation result.The results showed that the time step size has effects on the time histories of node displacements and element pore＇s water pressures. Moreover,the relation between the computation cost and the time step size is a hyperbolic curve.The relative error is mainly generated in the area with large deformation and the period with rapid dynamic response.The mean relative error in the entire area is larger in the time range with violent dynamic response. Through the estimated discrete error,a proper time step size can be determined to meet the desired accuracy. For automatic time step adjustment,the error estimation can provide a criterion to control the time step size.