In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional *** choose N´ed´elec edge element for...
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In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional *** choose N´ed´elec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model *** constructing multigrid algorithm,a distributive Gauss-Seidel iteration method is *** experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size h and parameter dt on regular meshes.
Behavior of a poro-elastic material bonded onto a vibrating plate is investigated in the low-frequency range. From the analysis of dissipation mechanisms, a model accounting for damping added by the porous layer on th...
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Behavior of a poro-elastic material bonded onto a vibrating plate is investigated in the low-frequency range. From the analysis of dissipation mechanisms, a model accounting for damping added by the porous layer on the plate is derived. This analysis is based on a 3-D finite element formulation including poro-elastic elements based on Biot displacement theory. First, dissipated powers related to thermal, viscous and viscoelastic dissipation are explicited. Then a generic configuration (simply-supported aluminium plate with a bonded porous layer and mechanical excitation) is studied. Thermal dissipation is found negligible. Viscous dissipation can be optimized as a function of airflow resistivity. It can be the major phenomenon within soft materials, but for most foams viscoelastic dissipation is dominant. Consequently an equivalent plate model is proposed. It includes shear in the porous layer and only viscoelasticity of the skeleton. Excellent agreement is found with the full numerical model. (C) 2002 Elsevier Science Ltd. All rights reserved.
Poro-granular materials are studied, and a model adapted to characterize their acoustic behaviour is presented. Biot's theory is used to obtain this model but a great simplification is brought to classical formula...
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Poro-granular materials are studied, and a model adapted to characterize their acoustic behaviour is presented. Biot's theory is used to obtain this model but a great simplification is brought to classical formulation. Indeed, a solid phase being made of a non-cohesive poro-granular material, a specific continuum constitutive model is used to characterize its behaviour. The macroscopic coefficient of friction that takes into account friction and collision phenomena is then neglected under specific conditions. This strong assumption does not apply for all kinds of granular materials and for any solicitations: its validity is discussed for particular materials. The solid/fluid model of Biot's theory is then transformed to an equivalent fluid/fluid model. The complexity of the classical formulation is significantly reduced since only two degrees of freedom are used: the solid and fluid pressures. A 1D case is then treated to present the simplicity of the formulation, and applied to a poro-granular material made of expanded polystyrene beads. Intrinsic parameters of this material are adjusted thanks to surface impedances measured with a stationary waves tube. Finally, a study on thermal and viscous dissipations is realized and associated with a study on pressure and velocity distribution in the sample.
Boundary value problems in thermoelasticity and poroelasticity (filtration consolidation) are solved numerically. The underlying system of equations consists of the Lam, stationary equations for displacements and nons...
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Boundary value problems in thermoelasticity and poroelasticity (filtration consolidation) are solved numerically. The underlying system of equations consists of the Lam, stationary equations for displacements and nonstationary equations for temperature or pressure in the porous medium. The numerical algorithm is based on a finite-element approximation in space. Standard stability conditions are formulated for two-level schemes with weights. Such schemes are numerically implemented by solving a system of coupled equations for displacements and temperature (pressure). Splitting schemes with respect to physical processes are constructed, in which the transition to a new time level is associated with solving separate elliptic problems for the desired displacements and temperature (pressure). Unconditionally stable additive schemes are constructed by choosing a weight of a three-level scheme.
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