Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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Eigenfunction expansion solution and finite element solution for orthotropic hollow cylinder under sinusoidal impact load

  • Wang, X. (Department of Engineering Mechanics, The School of Civil Engineering and Mechanics, Shanghai Jiaotong University) ;
  • Dai, H.L. (Department of Engineering Mechanics, The School of Civil Engineering and Mechanics, Shanghai Jiaotong University)
  • Received : 2002.04.11
  • Accepted : 2003.05.06
  • Published : 2003.07.25
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Abstract

The histories and distributions of dynamic stresses in an orthotropic hollow cylinder under sinusoidal impact load are obtained by making use of eigenfunction expansion method in this paper. Dynamic equations for axially symmetric orthotropic problem are founded and results are carried out for a practical example in which an orthotropic hollow cylinder is in initially at rest and subjected to a dynamic interior pressure $p(t)=-{\sigma}_0(sin{\alpha}t+1)$. The features of the solution appear the propagation of the cylindrical waves. The other hand, a dynamic finite element solution for the same problem is also got by making use of structural software (ABAQUS) program. Comparing theoretical solution with finite element solution, it can be found that two kinds of results obtained by two different solving methods are suitably approached. Thus, it is further concluded that the method and computing process of the theoretical solution are effective and accurate.

Keywords

References

  1. Baker, W.E. (1961), "Axisymmetric modes of vibration of thin spherical shell", J. Acoust. Soc. Am., 33, 1749- 1758. https://doi.org/10.1121/1.1908562
  2. Baker, W.E., Hu, W.C.L. and Jackson, T.R. (1966), "Elastic response of thin spherical shell to axisymmetric blast loading", J. Appl. Mech., ASME, 33, 800-806. https://doi.org/10.1115/1.3625185
  3. Cho, H., Kardomateas, G.A. and Valle, C.S. (1998), "Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell", J. Appl. Mech., 65, 184. https://doi.org/10.1115/1.2789024
  4. Cinelli, G. (1965), "An extension of the finite Hanke transform and application", Int. J. Engng. Sci., 3, 539-550. https://doi.org/10.1016/0020-7225(65)90034-0
  5. Cinelli, G. (1966), "Dynamic vibrations and stresses in elastic cylinders and spheres", J. Appl. Mech., ASME, 33, 825-830. https://doi.org/10.1115/1.3625189
  6. Eringen, A.C. and Suhubi, E.S. (1975), Elastodynamics. (Vol. 2, Linear Theory), Academic press. New York.
  7. Gong, Y.N. and Wang, X. (1991), "Radial vibrations and dynamic stresses in elastic hollow cylinder", In Structural Dynamic: Recent Advances. Elsevier Science Publication Ltd. Oxford.
  8. Lekhnitskii, S.G. (1981), Theory of Elasticity of an Anisotropic Body, Mir Publishers Moscow.
  9. Pao, Y.H. and Ceranoglu, A.N. (1978), "Determination of transient responses of a thick-walled spherical shell by the ray theory", J. Appl. Mech., ASME, 45, 114-122. https://doi.org/10.1115/1.3424212
  10. Pao, Y.H. (1983), "Elastic wave in solids", J. Appl. Mech., ASME, 50, 1152-1164. https://doi.org/10.1115/1.3167197
  11. Wang, X. and Gong, X.N. (1992), "An elastodynamic solution for multilayered cylinders", Int. J. Engng. Sci., 30(1), 25-33. https://doi.org/10.1016/0020-7225(92)90118-Z
  12. Wang, X. (1993), "Stress wave propagation in a two layered cylinder with initial interface pressure", Int. J. Solids Struct., 30(12), 1693-1700. https://doi.org/10.1016/0020-7683(93)90198-G
  13. Wang, X. (1995), "Thermal shock in a hollow cylinder caused by rapid arbitrary heating", J. Sound Vib., 183(5), 899-906. https://doi.org/10.1006/jsvi.1995.0294
  14. Yin, X.C. (1997), "Multiple impacts of two concentric hollow cylinders with zero clearance", Int. J. Solids Struct., 34(35), 4597-4616. https://doi.org/10.1016/S0020-7683(97)00049-8