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Solid Displacements (solid + displacement)
Selected AbstractsCoupled simulation of wave propagation and water flow in soil induced by high-speed trainsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2008P. Kettil Abstract The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water-saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd. [source] Time domain 3D fundamental solutions for saturated poroelastic media with incompressible constituentsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008Mohsen Kamalian Abstract This paper presents simple time domain fundamental solutions for the three-dimensional (3D) well known u,p formulation of saturated porous media, neglecting the compressibility of fluid and solid particles. At first, the corresponding boundary integral equations as well as the explicit Laplace transform domain fundamental solutions are obtained in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Time 2D fundamental solution for saturated porous media with incompressible fluidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2005Behrouz Gatmiri Abstract The derivation of analytical transient two-dimensional fundamental solution for porous media saturated with incompressible fluid in u-p formulation is discussed in detail. First, the explicit Laplace transform solution in terms of solid displacements and fluid pressure are obtained. Then, the closed-form time-dependent fundamental solution is derived by the analytical inversion of the Laplace transform solution. Finally, a set of numerical results is presented to investigate the accuracy of the proposed solution. It is shown that this solution can be considered as a good approximation of exact solution, especially for the long time. Copyright © 2004 John Wiley & Sons, Ltd. [source] Hybrid and enhanced finite element methods for problems of soil consolidationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007X. X. Zhou Abstract Hybrid and enhanced finite element methods with bi-linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation. Both plane strain and axisymmetric problems are studied. It is found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures can be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented. It is also shown that for some situations, such as problems involving high Poisson's ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods are superior to that of the conventional displacement-based method. The results from the hybrid method are better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation, the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement-based finite element method. The present enhanced method and hybrid method can be easily extended to non-linear consolidation problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Homogenizing the acoustic properties of a porous matrix containing an incompressible inviscid fluidMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2003J. L. Ferrin We undertake a rigorous derivation of the Biot's law for a porous elastic solid containing an inviscid fluid. We consider small displacements of a linear elastic solid being itself a connected periodic skeleton containing a pore structure of the characteristic size ,. It is completely saturated by an incompressible inviscid fluid. The model is described by the equations of the linear elasticity coupled with the linearized incompressible Euler system. We study the homogenization limit when the pore size ,tends to zero. The main difficulty is obtaining an a priori estimate for the gradient of the fluid velocity in the pore structure. Under the assumption that the solid part is connected and using results on the first order elliptic systems, we obtain the required estimate. It allows us to apply appropriate results from the 2-scale convergence. Then it is proved that the microscopic displacements and the fluid pressure converge in 2-scales towards a linear hyperbolic system for an effective displacement and an effective pressure field. Using correctors, we also give a strong convergence result. The obtained system is then compared with the Biot's law. It is found that there is a constitutive relation linking the effective pressure with the divergences of the effective fluid and solid displacements. Then we prove that the homogenized model coincides with the Biot's equations but with the added mass ,a being a matrix, which is calculated through an auxiliary problem in the periodic cell for the tortuosity. Furthermore, we get formulas for the matricial coefficients in the Biot's effective stress,strain relations. Finally, we consider the degenerate case when the fluid part is not connected and obtain Biot's model with the relative fluid displacement equal to zero. Copyright © 2003 John Wiley & Sons, Ltd. [source] Poroelastodynamic Boundary Element Method in Time Domain: Numerical AspectsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Martin Schanz Based on Biot's theory the governing equations for a poroelastic continuum are given as a coupled set of partial differential equations (PDEs) for the unknowns solid displacements and pore pressure. Using the Convolution Quadrature Method (CQM) proposed by Lubich a boundary time stepping procedure is established based only on the fundamental solutions in Laplace domain. To improve the numerical behavior of the CQM-based Boundary Element Method (BEM) dimensionless variables are introduced and different choices studied. This will be performed as a numerical study at the example of a poroelastic column. Summarizing the results, the normalization to time and spatial variable as well as on Young's modulus yields the best numerical behavior. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A Poroelastic Mindlin-PlatePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Anke Busse Dipl.Ing The numerical treatment of noise insulation of solid walls has been an object of scientific research for many years. The main noise source is the bending vibration of the walls usually modeled as plates. Generally, walls consist of porous material, for instance concrete or bricks. Therefore, a poroelastic plate theory is necessary. A theory of dynamic poroelasticity was developed by Biot using the solid displacements and the pore pressure as unknowns. After formulating the poroelastic theory for thick plates, Mindlin's theory, a variational principle for this poroelastic thick plate model is developed. This is the basis of a Finite Element formulation. [source] Influence of Incompressibility on Different Wave Types in Porous MediaPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Dobromil Pryl Dipl.-Ing. There are three wave types in poroelastic continua, the fast compressional wave, with solid and fluid moving inphase, the shear wave, and the second (slow) compressional wave, which has no equivalent in elastic materials, with solid and fluid moving in opposite directions. The fast compressional wave propagates with infinite speed if both constituents are modelled incompressible. Numerical results of BEM calculations showing the influence of incompressible constituents will be presented as well as elements employing different shape functions for the solid displacements and the pore pressure. [source] Material Modelling of Porous Media for Wave Propagation ProblemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003M. Schanz PD Dr.-Ing. Under the assumption of a linear geometry description and linear constitutive equations, the governing equations are derived for two poroelastic theories, Biot's theory and Theory of Porous Media (TPM), using solid displacements and pore pressure as unknowns. In both theories, this is only possible in the Laplace domain. Comparing the sets of differential equations of Biot's theory and of TPM, they show different constant coefficients but the same structure of coupled differential equations. Identifying these coefficients with the material data and correlating them leads to the known problem with Biot's ,apparent mass density'. Further, in trying to find a correlation between Biot's stress coefficient to parameters used in TPM yet unsolved inconsistencies are found. For studying the numerical effect of these differences, wave propagation results of a one-dimensional poroelastic column are analysed. Differences between both theories are resolved only for compressible constituents. [source] | ||||||||||