流体饱和两相多孔介质拟静态问题的混合有限元方法

针对基于混合物理论的两相多孔介质模型，采用Galerkin加权残值有限元法，导出求解所静态问题的基于us-uF-P变量的混合有限元方程，由于系统方程的系数矩阵非定，进而针对该方程组提出了一种失代求解方法，并由分片试验得出节点压力插值函数的阶须低于固体相节点的位移插值函数的阶的结论，算例结果表明，采用基于u2-uF-p变量的混合法计算所得的固体相和流体相速度以及固体相的有效应力与罚方法一致，而压力值的粗度高于罚方法。

Mixed finite element method for quasi-static problems of fluid-saturated biphase porous media

Based on the fluid\|saturated biphase porous media model deduced from mixture theory, a finite element formulation with u S u F p variables for quasi\|static analysis is given out. An iterative solution method is suggested to solve the system equations whose coefficient matrices are indefinite. It is concluded from patch test that the order of interpolation function for pressure must be higher than that of displacement of solid phase. Numerical analysis of an example demonstrates that the displacements, velocities of both solid and fluid phases as well as the effective stresses in solid phase with the mixed finite element method are consistent with those obtained with penalty method, which illustrates the mixed method is correct, available and practical. It is also concluded that the pressure values obtained with mixed method are more precise than those of penalty method.