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Abstrakty
A deformation problem of an isotropic elastic liquid-saturated porous medium has been discussed by finding a general solution to the field equations of poroelasticity under axisymmetric conditions. An eigenvalue approach using the Laplace and the Hankel transforms is applied to get the solution. To show the utility of the solution obtained, an application of an infinite space with a concentrated point force acting at some interior point of the medium has been considered. The transformed solutions are inverted numerically, using a numerical inversion technique to invert the Laplace and the Hankel transforms. The results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model.
Rocznik
Tom
Strony
1009--1025
Opis fizyczny
Bibliogr. 21 poz., wykr.
Twórcy
autor
autor
autor
- Department of Mathematics Kurukshetra University Kurukshetra - 136 119 Haryana, INDIA, miglani_aseem@rediffmail.com
Bibliografia
- Altay G.A. and Dokmeci M.C. (1998): A uniqueness theorem in Biot's poroelasticity theory. - ZAMP, vol.49, No.5, pp.838-846.
- Armero F. and Callari C. (1999): An analysis of strong discontinuities in a saturated poroelastic solid. - International Journal of Numerical Methods and Engineering, vol.46, No.10, pp.1673-1698.
- Biot M.A. (1956a): General solution of the equations of elasticity and consolidation for a porous material. - J. Appl. Mech., vol.23, pp.91-95.
- Biot M.A. (1956b): The theory of propagation of elastic waves in a fluid-saturated porous solid. - J. Acoust. Soc. Am. vol.28, pp.168-191.
- Burridge R. and Vargas C.A. (1979): The fundamental solution in dynamic poroelasticity. - Geophysical Journal of the Royal Astronomical Society, vol.58, pp.61-90.
- Chiarella C. and Booker J.R. (1975): The time settlement behaviour of a rigid die resting on a deep clay layer. - Q. J. Mech. Appl. Math., vol.28, No.3, pp.317-328.
- Deresiewicz H. and Skalak R. (1963): On uniquesness in dynamic poro-elasticity. - Bulletin of the Seismological Society of America, vol.53, pp.783-789.
- Fellah Z.E.A. and Depollier C. (2000): Transient acoustic wave propagation in rigid porous media: A time domain approach. - Journal of the Acoustical Society of America, vol.107, No.2, pp.683-688.
- Honig G. and Hirdes U. (1984): A method for the numerical inversion of the Laplace transform. - J. Comp. Appl. Math., vol.10, pp.113-132.
- Kumar R., Miglani A. and Garg N.R. (2000): Plain strain problem of poroelasticity using eigenvalue approach. - Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences), vol.109, pp.371-380.
- Kumar R., Miglani A. and Garg N.R. (2003): Mechanical response of an anisotropic liquid-saturated porous medium. - Acta Mechanica, vol.162, pp.41-56.
- Pal P.C. (1983): On the disturbance produced by an impulsive shearing stress on the surface of a semi-infinte poroelastic medium. - Journal of the Acoustical Society of America, vol.74, No.2, pp.586-590.
- Paul S. (1976a): On the displacements produced in a porous elastic half-space by an impulsive line load (Non-dissipative case). - Pure and Applied Geophysics, vol.114, pp.605-614.
- Paul S. (1976b): On the disturbance produced in a semi-infinte poroelastic medium by a surface load. - Pure and Applied Geophysics, vol.114, pp.615-627.
- Philippacopolous A.J. (1988): Lamb'sproblem for fluid-saturated porous media. - Bulletin of the Seismological Society of America, vol.78, pp.908-923.
- Press W.H., Teukolsky S.A., Vellering W.T. and Flannery B.P. (1986): Numerical Recipes. - Cambridge: Cambridge University Press.
- Reddy P.M. and Tajjuddin M. (2000): Exact analysis of the plain strain viberations of thick walled hollow poroelastic cylinders. - International Journal of Solids and Structures, vol.37, pp.3439-3456.
- Sabin G.C.W. (1989): Behaviour of a poroelastic seabed under normal and shear loads. - J. Offshore Mech. Arctic Eng., vol.111, No.4, pp.303-310.
- Sharma M.D. (1992): Comments on 'Lamb's problem for fluid-saturated porous media. - Bulletin of the Seismological Society of America, vol.82, pp.2263-2273.
- Sneddon I.N. (1974): The use of integral transforms. - New Delhi: Tata McGraw Hill.
- Yew C.H. and Jogi P.N. (1976): Study of wave motions in fluid-saturated porous rocks. - J. Acoust. Soc. Am., vol.60, pp.2-8.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ2-0034-0033