利用初流量法分析有自由面渗流问题之改进

Improvement of analysis of free surface seepage problem by using initial flow method

在利用初流量法分析带有自由面的渗流问题时,常因采用高斯积分点作为结点初流量计算判断依据所带来的误差而令解出现振荡。为了减低这一因素的影响及提高计算的效率,针对常用的4结点平面单元和8结点6平面三维单元的自由面方程进行分析,提出采用坐标变换和等参变换等技术来改造结点初流量的计算,并建议按自由面穿越单元之状况引用分部积分,使其积分上、下限符合高斯积分法的格式化要求,从而可利用高斯积分法求出精确的结点初流量,而精确的结点初流量则有助于改善解的振荡及提高计算结果的精度。通过一矩形均质坝实例分析,表明该方法的稳定性和收敛性良好。

When the initial flow method is applied in solving problems of fi＇ee surface seepage, we often find an oscillating solution determined due to the error caused by taking the Gaussian integration points as the assumed nodes based on calculation of nodal initial flow. In order to reduce the impact of this factor and to improve the efficiency of computation, an analysis is made with the free surface equation commonly used by 4-node plane elements and 8-node 6-plane three-dimensional elements, a technique of transformation of coordinates as well as isoparameters is proposed to improve the calculation of the nodal initial flow, and an introduction of partial integration is also suggested according to the state of free surface penetrating elements, making the integration upper limit and lower limit in consistence with the formatting of the Gaussian requirements. Accordingly, an exact nodal initial flow integration will be obtained by using the Gaussian method, and this accurate nodal initial flow will then benefit the itself improvement of the oscillating solution and increase the precision of the calculation. Through the analysis of a homogeneous rectangular case, it is shown that a fair state of stability and convergence has been achieved by using the proposed improved method.