两相多孔介质动力问题的混合有限元及其解法

针对基于混合物理论的流体饱和两相多孔质模型,采用Ｇａｌｅｒｋｉｎ加权残值有限元方法导出基于ｕ＾Ｓ－ｕ＾Ｆ－ｐ３个变量的混合有限元动力平衡方程。这种方法克服了 限元方法选择恰当的罚参数的困难,且计算得到的压力分布的精度高于罚有限元方法。由分片试验得出节点压力插值函数的阶须高于固体相节点位移插值函数的阶的重要结论。

Mixed Finite Element Method for Dynamic Problems of Fluid Saturated Biphasic Porous Media

Based on the fluid saturated biphasic porous media model deduced from mixture theory,a finite element formulation with u S u F p variables for dynamic response analysis is given out.This method overcomes the difficulty of choosing suitable penalty parameter in penalty finite element method,and the accuracy of pressure distribution obtained with the mixed finite element method is higher than the penalty finile element method.An iterative solution method is suggested to solve the system of equations whose coefficient matrices are non positive definite.It is concluded from patch test that the order of interpolation function for pressure variables must be higher than that of displacement variables of solid phase.