Monoclinic Elastic Medium Under the Effect of Initial Stress with Repeated Eigen Values

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Advances in Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 953))

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Abstract

With the help of equal eigen value technique, we have derived the closed form analytical expression for an initially stressed monoclinic elastic medium under the effect of inclined line-load. For the procedure, we have assumed the field to be distributed sinusoidally and then uses matrix method for computation. The effect of inclined line-load and initial stress on the dimensionless displacements and stresses has been depicted graphically with the help of MATLAB. Further, we have also presented the particular case for Orthotropic, Isotropic and Transversely isotropic elastic medium.

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References

  1. Biot, M.A.: Mechanics of Incremental Deformation. Wiley, New York

    Google Scholar 

  2. Chugh, S., Madan, D.K., Singh, K.: Plain strain deformation of initially unstressed elastic medium. Appl. Math. Comput. 217, 8683–8692 (2011)

    MathSciNet  Google Scholar 

  3. Cosserat, E., Cosserat, F.: Theoie des Corps Deformables. A. Hermann et Fils, Paris (1909)

    Google Scholar 

  4. Garg, N.R., Kumar, R., Goel, A., Miglani, A.: Plain strain deformation of an orthotropic elastic medium using an eigenvalue approach. Earth Planet. Sci. 55, 3–9 (2003)

    Google Scholar 

  5. Khan, A.A., Afzal, A.: Influence of initial stress and gravity on refraction and reflection of SV wave at interface between two viscoelastic liquids under three thermoelastic theories. J. Brazil. Soc. Mech. Sci. Eng. 40, 1–13 (2018)

    Google Scholar 

  6. Khan, A.A., Umar, A., Zaman, A.: Rayleigh waves propagation in anisotropic layer superimposed a monoclinic medium. Indian J. Phys. 95(3), 449–457 (2019)

    Article  Google Scholar 

  7. Khan, A.A, Zafar, S.: Laser Impact on harmonic waves through microstretch medium under the DPL theory. In: Waves in Complex and Random Media (2019)

    Google Scholar 

  8. Kumar, R., Miglani, A., Garg, N.R.: Plane strain problem of poroelasticity using eigenvalue approach. Proc. Ind. Acad. Sci. (Earth Planet Sci.) 109, 371–380 (2000)

    Article  Google Scholar 

  9. Kumar, R., Miglani, A., Garg, N.R.: Response of an anisotropic liquid saturated porous medium due to two-dimensional sources. Proc. Ind. Acad. Sci. (Earth Planet Sci.) 111, 143–151 (2002)

    Article  Google Scholar 

  10. Kumari, A., Madan, D.K.: Deformation field due to seismic source with imperfect interface. J. Earth Syst. Sci. 130(4), 1–19 (2021)

    Article  Google Scholar 

  11. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover Publication, New York (1944)

    Google Scholar 

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

    Google Scholar 

  13. Ostoja-Starzewski, M., Boccara, S., Jasiuk, S.: Couple-stress moduli and characteristic length of composite materials. Mech. Res. Comm. 26(4), 387–397 (1999)

    Article  Google Scholar 

  14. Selim, M.M.: Orthotropic elastic medium under the effect of initial and couple stress. Appl. Math. Comput. 181, 185–192 (2006)

    Google Scholar 

  15. Selim, M.M., Ahmed, A.K.: Plain strain deformation of initially stressed orthotropic elastic medium. Appl. Maths. Comput. 175, 221–237 (2006)

    Google Scholar 

  16. Singh, K., Madan, D.K., Goel, A., Garg, N.R.: Two-dimensional static deformation of anisotropic medium. Sadhana 30(4), 565–583 (2005)

    Article  Google Scholar 

  17. Voigt, W.: Abh. Gesch. Wissenschaften 34 (1887)

    Google Scholar 

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Correspondence to Aanchal Gaba .

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Gaba, A., Goyal, R. (2024). Monoclinic Elastic Medium Under the Effect of Initial Stress with Repeated Eigen Values. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2023. Lecture Notes in Networks and Systems, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-031-56304-1_23

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  • DOI: https://doi.org/10.1007/978-3-031-56304-1_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-56303-4

  • Online ISBN: 978-3-031-56304-1

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