摘要:

AbstractThis paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.

ISSN:0363-9061    

DOI:10.1002/nag.1610170602

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe equations governing the elastic‐plastic deformation of granular materials are typically hyperbolic, or contain small‐magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second‐order Godunov‐type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell‐tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher‐order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step procee

ISSN:0363-9061    

DOI:10.1002/nag.1610170603

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co‐ordinates. The Lagrangian co‐ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co‐ordinates is presented, in addition to an equivalent formulation in the real co‐ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co‐ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co‐ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise.The model is validated by comparison with two dimensionless one‐dimensional solutions, one analytical for the linear case, and one numerical for the non‐linear case. Both these one‐dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentatio

ISSN:0363-9061    

DOI:10.1002/nag.1610170604

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0363-9061    

DOI:10.1002/nag.1610170605

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0363-9061    

DOI:10.1002/nag.1610170601

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY