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Plane strain deformation of an orthotropic elastic medium using an eigenvalue approach

Abstract

The analytic expressions for the displacements and stresses at any point of an infinite orthotropic elastic medium as a result of an inclined line load have been obtained. This plane strain problem has been solved by using eigenvalue approach and the use of matrix notation avoids unwieldy mathematical expressions. The technique developed in the present paper is simple, straightforward and convenient for numerical computation. The variations of the displacements and stresses with the horizontal distance have been shown graphically.

References

  • Aki, K. and P. G. Richards, Quantitative Seismology. Theory and Methods, W. H. Freeman, San Francisco, 932, 1980.

    Google Scholar 

  • Burridge, R. and L. Knopoff, Body force equivalents for seismic dislocations, Bull. Seismol. Soc. Am., 54, 1875–1888, 1964.

    Google Scholar 

  • Crampin, S., Suggestions for a consistent terminology for seismic anisotropy, Geophys. Prospect., 37, 753–770, 1989.

    Article  Google Scholar 

  • Debnath, L., Integral Transforms and their Application, CRC Press. Inc., New York, 1995.

  • Dziewonski, A. M. and D. L. Anderson, Preliminary reference earth model, Phys. Earth Planet. Inter., 25, 297–356, 1981.

    Article  Google Scholar 

  • Garg, N. R., D. K. Madan, and R. K. Sharma, Two-dimensional deformation of an orthotropic elastic medium due to seismic sources, Phys. Earth Planet. Inter., 94, 43–62, 1996.

    Article  Google Scholar 

  • Kumar, R., A. Miglani, and N. R. Garg, Plane strain problem of poroelasticity using eigenvalue approach, Proceeding Indian Acad. Sci. (Earth Planet Sci.), 109, 371–380, 2000.

    Google Scholar 

  • Kumar, R., A. Miglani, and N. R. Garg, Response of an anisotropic liquidsaturated porous medium due to two-dimensional sources, Proceeding Indian Acad. Sci. (Earth Planet Sci.), 111, 143–151, 2002.

    Google Scholar 

  • Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944.

    Google Scholar 

  • Maruyama, T., On two-dimensional elastic dislocations in an infinite and semi-infinite medium, Bull. Earthq. Res. Inst., 44, 811–871, 1966.

    Google Scholar 

  • Mase, G. T. and G. E. Mase, Continuum Mechanics for Engineers, CRC Press. LLC, New York, 1999.

    Google Scholar 

  • Okada, Y., Surface deformation due to inclined shear and tensile faults in a homogeneous isotropic half space, Bull. Seismol. Soc. Am., 75, 1135–1154, 1985.

    Google Scholar 

  • Okada, Y., Internal deformation due to shear and tensile faults in a halfspace, Bull. Seismol. Soc. Am., 82, 1018–1040, 1992.

    Google Scholar 

  • Pan, E., Static response of a transversely isotropic and layered half space to general dislocation sources, Phys. Earth Planet. Inter., 58, 103–117, 1989.

    Article  Google Scholar 

  • Payton, R. G., Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff Publishers, The Hague, 1983.

  • Saada, A. S., Elasticity—Theory and Application, Pergamon Press Inc., New York, 1974.

    Google Scholar 

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Garg, N.R., Kumar, R., Goel, A. et al. Plane strain deformation of an orthotropic elastic medium using an eigenvalue approach. Earth Planet Sp 55, 3–9 (2003). https://doi.org/10.1186/BF03352457

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