不排水不可压缩条件下两相介质的两重网格算法

对于不排水、不可压缩饱和软土地基的固结问题的有限元分析，可以用Biot固结方程来考虑土体颗粒与孔隙水间的相互作用。由于受Babuska-Brezzi稳定条件的限制，用常规的等插值u-p混合有限元法求解将导致孔隙压力出现紊乱的结果。提出了基于位移和压力线性等插值函数的两重网格，但位移独立变量总数大于独立压力变量总数的计算方法，可以满足Babuska-Brezzi稳定条件，使得位移场和压力场单元插值阶数保持一致。通过几个简单算例验证了提出方法的正确性。

Double-mesh interpolation method applied to two-phase media of undrained-incompressible limit

Finite element method based on Biot consolidation equation taking into account the interaction between soil skeleton and pore fluid is always used to analyze the consolidation of saturated soft foundation with undrained-incompressible limit. Because of restriction of Babuska-Brezzi inf-sup condition, conventional FEM based on equal interpolation orders u-p formulation will give a spurious oscillation result for pore pressure. Based on displacement-pressure linear equal interpolation, a new method in which the number of the independent degree of freedom of displacement is higher than that of pore pressure, is proposed. With suggested double-mesh interpolation method, the Babuska-Brezzi stability condition will be satisfied; and it is possible to use equal interpolation orders u-p formulation. Several examples are presented to verify the suggested method.