Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An analytical solution of the annular plate on elastic foundation

  • Pavlou, D.G. (Department of Mechanical Engineering, TEI Halkidas) ;
  • Vlachakis, N.V. (Department of Mechanical Engineering, TEI Halkidas) ;
  • Pavlou, M.G. (ERGOSE S.A., Works of Greek Federal Railway Organization)
  • Received : 2004.08.31
  • Accepted : 2005.03.14
  • Published : 2005.05.30
⟨ Previous Next ⟩

Abstract

A new method for deriving analytical solution of the annular elastic plate on elastic foundation under axisymmetric loading is presented. The formulation is based on application of Hankel integral transforms and Bessel functions' properties in the corresponding boundary-value problem. A representative example is studied and the obtained solution is compared with published numerical results indicating excellent agreement.

Keywords

References

  1. Chandrashekhara, K. and Antony, J. (1997), 'Elastic analysis of an annular slab-soil interaction problem using hybrid method', Comput. Geotech., 20, 161-176 https://doi.org/10.1016/S0266-352X(96)00017-1
  2. Cheung, Y.K. and Zienkiewicz, O.C. (1965), 'Plates and tanks on elastic foundations-an application of finite element method', Int. J. Solids Struct., 1, 451-461 https://doi.org/10.1016/0020-7683(65)90008-9
  3. Krysl, P. and Belytschko, T. (1995), 'Analysis of thin plates by the Element-Free Galerking method', Computational Mechanics, 17, 26-35 https://doi.org/10.1007/BF00356476
  4. Long, S. and Alturi, S.N. (2002), 'A meshless local Petrov-Galerkin method for solving the bending problem of a thin plate', Computer Modeling in Engineering & Sciences, 3(1), 53-63
  5. Melerski, E.S. (1989), 'Circular plate analysis by finite differences: energy approach', J. Engng. Mech., ASCE, 115, 1205-1224 https://doi.org/10.1061/(ASCE)0733-9399(1989)115:6(1205)
  6. Naruoka, M. (1981), Bibliography on Theory of Plates, 1st ed., Gihodo, Tokyo
  7. Oztorun, N.K. and Utku, M. (2002), 'Computer aided design of post-tensioned concrete reservoirs', Comput. Struct., 80, 2195-2207 https://doi.org/10.1016/S0045-7949(02)00244-4
  8. Papakaliatakis, G. and Simos, T.E. (1997), 'A finite difference method for the numerical solution of fourth-order differential equations with engineering applications', Comput. Struct., 65(4), 491-495 https://doi.org/10.1016/S0045-7949(97)00002-3
  9. Pavlou, D.G. (2002), 'Boundary integral equation analysis of twisted internally cracked axisymmetric bi-material elastic solids', Computational Mechanics, 29(3), 254-264 https://doi.org/10.1007/s00466-002-0338-7
  10. Sneddon, I.N. (1972a), The Use of Integral Transforms, McGraw-Hill, N.Y
  11. Sneddon, I.N. (1995b), Fourier Transforms, Dover Publications, N.Y
  12. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, 2nd ed., McGraw-Hili, N.Y
  13. Utku, M., Citipitioglu, E. and Inceleme, I. (2000), 'Circular plates on elastic foundations modeled with annular plates', Camput. Struct., 78, 365-374 https://doi.org/10.1016/S0045-7949(00)00063-8
  14. Van Daele, M., Vanden Berge, G. and De Meyer, H. (1994), 'A smooth approximation for the solution of a fourth-order boundary value problem based on nonpolynomian splines', J, Computational and Applied Mathematics, 51, 383-394 https://doi.org/10.1016/0377-0427(92)00112-M
  15. Wang, W. and Ishikawa, H. (2001), 'A method for linear elasto-static analysis of multi-layered axisymmetrical bodies using Hankel's transform', Computational Mechanics, 27, 474-483 https://doi.org/10.1007/s004660100258
  16. Wolfram Research Europe Ltd. (2000), MATHEMATICA for Microsoft Windows, Version 4.1.1

Cited by

  1. Simulation of the spiral wound RO membranes deformation under operating conditions vol.25, pp.1-3, 2011, https://doi.org/10.5004/dwt.2011.1851
  2. Seabed Dynamic Response of Offshore Wind Turbine Foundation under Vertical Harmonic Loading: An Analytic Solution vol.2018, pp.1563-5147, 2018, https://doi.org/10.1155/2018/6250158
  3. Soil-Structure-Wave Interaction of Gravity-Based Offshore Wind Turbines: An Analytical Model vol.143, pp.3, 2005, https://doi.org/10.1115/1.4048997