饱和土体中稳态渗流的高效无网格分析

利用稳定节点积分思想,构造一种求解饱和土体中稳态渗流问题的快速Galerkin无网格方法.该方法通过建立非局部光滑节点水力梯度,具有节点积分高效的特点,同时避免形函数在节点上直接求导,为稳态渗流分析提供有效的稳定保障.均匀渗流与自由面渗流算例的计算结果表明,该方法分析渗流问题高效且准确,能精确模拟任意均匀渗流场,在求解自由面迭代问题时,能避免有限元求解迭代问题时重划网格的工作,迭代收敛速度快.

An Efficient Meshfree Method for Steady Seepage Analysis in Saturated Soils

An efficient Galerkin meshfree method using the technique of stabilized conforming nodal integration is presented for the steady Darcy seepage analysis in saturated soil media. In this method, the seepage stiffness is integrated nodally with a smoothed nodal hydraulic gradient. This smoothed gradient is obtained as a volume average of the hydraulic gradient in the associated nodal representative domain. No derivatives of the meshfree shape functions are involved in the whole computation process. It turns out that, this method exactly meets the integration constraint for linear exactness, which corresponds to the requirement to reproduce the solution of uniform seepage problems regardless of meshfree discretization patterns. Both computational efficiency and stability are achieved. Two ease numerical tests, the uniform seepage problem and the free surface seepage problem, demonstrated that the present method is very accurate and also fast convergent.