Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Moving load response on the stresses produced in an irregular microstretch substrate

  • Received : 2016.03.04
  • Accepted : 2016.06.10
  • Published : 2016.10.25
⟨ Previous Next ⟩

Abstract

The present article is aimed at an investigation of stresses produced in a microstretch elastic half-space due to a moving load. The expressions of normal stress, shear stress and tangential couple stress produced in this case have been obtained in closed form. To find the displacement fields the perturbation method is applied. Significant effect of moving load on variation of stresses developed at different depths below the surface due to the depth of substrate and frictional coefficient of the rough surface of the medium has been observed. The effects of different shapes of irregularity and depth of irregularity on normal, shear and tangential couple stresses have been discussed. Some particular cases have also been deduced from the present investigation. Finally, the analytical developments have been illustrated numerically for aluminium-epoxy-like material substrate under the action of moving load.

Keywords

References

  1. Eringen, A.C. (1971), "Micropolar elastic solids with stretch", Ari Kitap Evi Matbassi, 24, 1-18.
  2. Iesan, D. and Pompei, A. (1995), "On the equilibrium theory of microstretch elastic solids", Int. J. Eng. Sci., 33, 399-410. https://doi.org/10.1016/0020-7225(94)00067-T
  3. Tomar, S.K. and Monica, G. (2005), "Reflection and transmission of waves from a plane interface between two microstretch solid half spaces", Int. J. Eng. Sci., 43, 139-169. https://doi.org/10.1016/j.ijengsci.2004.08.006
  4. Forest, S. and Sievert, R. (2006), "Non-linear microstrain theories", Int. J. Solid. Struct., 43, 7224-7245. https://doi.org/10.1016/j.ijsolstr.2006.05.012
  5. Sharma, V. and Kumar, S. (2016), "Influence of microstructure, heterogeneity and internal friction on SH waves propagation in a viscoelastic layer overlying a couple stress substrate", Struct. Eng. Mech., 57(4), 703-716. https://doi.org/10.12989/sem.2016.57.4.703
  6. Sharma, J.N., Kumar, S. and Sharma, Y.D. (2007), "Propagation of Rayleigh surface waves in microstretch thermoelastic continua under inviscid fluid loadings", J. Therm. Stress., 31, 18-39. https://doi.org/10.1080/01495730701737845
  7. Cole, J. and Huth, J. (1958), "Stresses produced in a half plane by moving loads", J. Appl. Mech., 25, 433- 436.
  8. Craggs, J.W. (1960), "One two-dimensional wave in an elastic half plane", Proceedings of the Cambridge Philosophical Society, 56, 269-275. https://doi.org/10.1017/S0305004100034551
  9. Sneddon, I.N. (1952), "Stress produced by a pulse of pressure moving along the surface of semi-infinite solid", Rend Del Circ Matem di Paler, 2, 57-62.
  10. Mukherjee, S. (1969), "Stresses produced by a load moving over a rough boundary of a semi-infinite transversely isotopic solid", Pure Appl. Geophys., 72, 45-50. https://doi.org/10.1007/BF00875691
  11. Sackman, J.L. (1961), "Uniformly moving load on a layered half plane", J. Eng. Mech. Div. Proc., ASCE, 75-89.
  12. Miles, I.W. (1966), "Response of a layered half space to a moving load", J. Appl. Mech., 33, 680-681. https://doi.org/10.1115/1.3625141
  13. Achenbach, J.D., Keshava S.P. and Herrmann, G. (1967), "Moving load on a plate resting on an elastic half space", J. Appl. Math. Mech., 34, 910-914.
  14. Chonan, S. (1976), "Moving load on a pre-stressed plate resting on a fluid half-space", Arch. Appl. Mech., 45, 171-178.
  15. Ungar, A. (1976), "Wave generation in an elastic half-space by a normal point load moving uniformly over the free surface", Int. J. Eng. Sci., 14, 935-945. https://doi.org/10.1016/0020-7225(76)90105-1
  16. Olsson, M. (1991), "On the fundamental moving load problem", J. Sound Vib., 145, 299-307. https://doi.org/10.1016/0022-460X(91)90593-9
  17. Lee, H.P. and Ng, T.Y. (1994), "Dynamic response of a cracked beam subject to a moving load", Acta Mechanica, 106, 221230.
  18. Alekseyeva, L.A. (2007), "The dynamics of an elastic half-space under the action of a moving load", J. Appl. Math., 71, 511-518.
  19. Mukhopadhyay, A. (1965), "Stress produced by a normal moving load over a transversely isotropic layer of ice lying on a rigid foundation", Pure Appl. Geophys., 60, 29. https://doi.org/10.1007/BF00874804
  20. Selim, M.M. (2007), "Static deformation of an irregular initially stressed medium", Appl. Math. Comput., 188, 1274-1284.
  21. Chattopadhyay, A. and Saha, S. (2006), "Dynamic response of normal moving load in the plane of symmetry of a monoclinic half space", Tamkang J. Sci. Eng., 9, 307.
  22. Chattopadhyay, A., Gupta, S., Sharma V.K. and Pato Kumari (2011), "Stresses produced on a rough irregular half-space by a moving load", Acta Mechanica, 221, 271-280. https://doi.org/10.1007/s00707-011-0507-x
  23. Singh, A.K, Kumar, S. and Chattopadhyay, A. (2014), "Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space", Meccanica, 49(12), 2861-2878. https://doi.org/10.1007/s11012-014-0033-8
  24. Kaur, T., Sharma S.K. and Singh, A.K. (2015), "Dynamic response of moving load on a micropolar halfspace with irregularity", Appl. Math. Model., doi:10.1016/j.apm.2015.09.102.
  25. Szyiko-Bigus, O. and Sniady, P. (2015), "Dynamic response of a Timoshenko beam to a continuous distributed moving load", Struct. Eng. Mech., 54 (4), 771-792. https://doi.org/10.12989/sem.2015.54.4.771
  26. Zhu, H., Mao, L., Weng, S. and Xia, Y. (2015), "Structural damage and force identification under moving load", Struct. Eng. Mech., 53 (2), 261-276. https://doi.org/10.12989/sem.2015.53.2.261
  27. Kaur, T., Singh, A.K., Chattopadhyay, A. and Sharma, S.K. (2016), "Dynamic response of normal moving load on an irregular fiber-reinforced half-space", J. Vib. Control, 22(1), 77-88. https://doi.org/10.1177/1077546314528525
  28. Lin, G., Zhang, P., Liu, J. and Wang, W. (2016), "Elastic solutions due to a time-harmonic point load in isotropic multi-layered media", Struct. Eng. Mech., 57(2), 327-355. https://doi.org/10.12989/sem.2016.57.2.327
  29. Eringen, A.C. (1990), "Theory of thermomicrostretch elastic solids", Int. J. Eng. Sci., 28, 1291-1301. https://doi.org/10.1016/0020-7225(90)90076-U
  30. Singh, B. and Kumar, R. (1998), "Wave propagation in a generalized thermomicrostretch elastic solid", Int. J. Eng. Sci., 36, 891-912. https://doi.org/10.1016/S0020-7225(97)00099-2