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
Biot, M.A.: Mechanics of Incremental Deformation. Wiley, New York
Chugh, S., Madan, D.K., Singh, K.: Plain strain deformation of initially unstressed elastic medium. Appl. Math. Comput. 217, 8683–8692 (2011)
Cosserat, E., Cosserat, F.: Theoie des Corps Deformables. A. Hermann et Fils, Paris (1909)
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)
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)
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)
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)
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)
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)
Kumari, A., Madan, D.K.: Deformation field due to seismic source with imperfect interface. J. Earth Syst. Sci. 130(4), 1–19 (2021)
Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover Publication, New York (1944)
Maruyama, T.: On two-dimensional elastic dislocations in an infinite and semi-infinite medium. Bull. Earthq. Res. Inst. 44, 811–871 (1966)
Ostoja-Starzewski, M., Boccara, S., Jasiuk, S.: Couple-stress moduli and characteristic length of composite materials. Mech. Res. Comm. 26(4), 387–397 (1999)
Selim, M.M.: Orthotropic elastic medium under the effect of initial and couple stress. Appl. Math. Comput. 181, 185–192 (2006)
Selim, M.M., Ahmed, A.K.: Plain strain deformation of initially stressed orthotropic elastic medium. Appl. Maths. Comput. 175, 221–237 (2006)
Singh, K., Madan, D.K., Goel, A., Garg, N.R.: Two-dimensional static deformation of anisotropic medium. Sadhana 30(4), 565–583 (2005)
Voigt, W.: Abh. Gesch. Wissenschaften 34 (1887)
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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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