流体饱和多孔介质的动力学Gurtin型变分原理和有限元模拟

基于多孔介质理论。在两相不可压和小变形的假设下，建立了流体饱和弹性多孔介质的动力学Gurtin型变分原理，并导出了以此变分原理为基础的有限元离散公式，由于Gurtin型变分原理是卷积型的空间积分泛函，空间的有限元离散导致一个关于时间的对称微分—积分方程组，在一般条件下。该积分—微分方程组可转化为对称的微分方程组，这组方程有别于标准Galerkin有限元的非对称离散方程组，作为数值例子，分析了流体饱和弹性多孔介质中一维纵向波的传播和反射，其结果进一步揭示了饱和多孔介质中波的传播特性。

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problems of dynamical response of fluid-saturated el as tic porous media is developed by assuming infinitesimal deformation and incompre ssible constitutes of solid and fluid phase. The associated finite element form ulation based on this variational principle is also derived. As functional of t he variational principle is a spatial integral of the convolution formulation, t he general finite element discretization in space results in symmetrical differe ntial-integral equations in time domain. In some situations, the differential -i ntegral equations can be reduced to symmetrical differential equations, and, as numerical examples, is employed to analyze the reflection of one-dimensional lo n gitudinal wave in a fluid-saturated porous solid. The numerical results can pr ovide the further understanding of the wave propagation in porous media.