摘要
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 ,导出求解拟静态问题的基于 u S- u F- p变量的混合有限元方程 ,由于系统方程的系数矩阵非正定 ,进而针对该方程组提出了一种迭代求解方法 ,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位移插值函数的阶的结论。算例结果表明 ,采用基于 u S- u F- 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 ,而压力值的精度高于罚方法。
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.
出处
《计算力学学报》
CAS
CSCD
北大核心
2001年第2期127-132,共6页
Chinese Journal of Computational Mechanics
