Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal d...Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.展开更多
基金Project supported by the National Nattural Science Foundation of China(No.10272070)
文摘Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.
