Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analytical studies on stress concentration due to a rectangular small hole in thin plate under bending loads

  • Yang, Y. (School of Civil Engineering and Transportation, South China University of Technology) ;
  • Liu, J.K. (Department of Mechanics, Sun Yat-sen University) ;
  • Cai, C.W. (Department of Mechanics, Sun Yat-sen University)
  • Received : 2009.10.09
  • Accepted : 2010.08.10
  • Published : 2010.12.20
⟨ Previous Next ⟩

Abstract

In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings.

Keywords

References

  1. Cai, C.W., Liu, J.K. and Chan, H.C. (2002), Exact Analysis of Bi-Periodic Structures, World Scientific, Singapore.
  2. Chan, H.C., Cai, C.W. and Cheung, Y.K. (1998), Exact Analysis of Structures with Periodicity Using UTransformation, World Scientific, Singapore.
  3. East China Technical University of Water Resources (1978), The Finite Element Method for Elastic Mechanics Problem, Water Conservancy and Electric Power Press, Beijing. (in Chinese)
  4. Jain, N.K. and Mittal, N.D. (2008), "Finite element analysis for stress concentration and deflection in isotropic orthotropic and laminated composite plates with central circular hole under transverse static loading", Mater. Sci. Eng. A, 498, 115-124. https://doi.org/10.1016/j.msea.2008.04.078
  5. Kubair, D.V. and. Bhanu-Chandar B. (2008), "Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension", Int. J. Mech. Sci., 50(4), 732-742. https://doi.org/10.1016/j.ijmecsci.2007.11.009
  6. Pilkey, W.D. (1997), Peterson's Stress Concentration Factors, 2nd Edition, John Wiley and Sons, New York.
  7. Savin, G.N. (1961), Stress Concentration around Holes, Pergamon Press, New York.
  8. Timoshenko, S.P. and Goodier, J.N. (1951), Theory of Elasticity, 2nd Edition, McGraw-Hill, New York.
  9. Toubal, L., Karama, M. and Lorrain B. (2005), "Stress concentration in a circular hole in composite plate", Compos. Struct., 68(1), 31-36. https://doi.org/10.1016/j.compstruct.2004.02.016
  10. Troyani, N., Gomes, C. and Sterlacci, G. (2002), "Theoretical stress concentration factor for short rectangular plates with centered circular holes", J. Mech. Design, 124, 126-128. https://doi.org/10.1115/1.1412849
  11. Yang, Y., Cai, M. and Liu, J.K. (2009), "Convergence studies on static and dynamic analysis of beams by using the U-transformation method and finite difference method", Struct. Eng. Mech., 31(4), 383-392. https://doi.org/10.12989/sem.2009.31.4.383
  12. Yang, Y., Liu, J.K. and Cai, C.W. (2008), "Analytical solutions to stress concentration problem in plates containing a rectangular hole under biaxial tensions", Acta Mech. Solida Sin., 21(5), 411-419. https://doi.org/10.1007/s10338-008-0850-1
  13. Yang, Y., Liu, J.K. and Huang, P.Y. (2007), "Exact convergence studies on static and dynamic analyses of plates by using the double U-transformation and the finite element method", J. Sound Vib., 305(1-2), 85-96. https://doi.org/10.1016/j.jsv.2007.03.035
  14. Young, W.C. and Budynas, R.G. (2002), Roark's Formulas for Stress and Strain, 7th Ed., McGraw-Hill, New York.
  15. Younis, N.T. (2006), "Assembly stress for the reduction of stress concentration", Mech. Res. Commun., 33(6), 837-845. https://doi.org/10.1016/j.mechrescom.2006.03.007
  16. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method, 7th Edition, Elsevier Science & Technology Books.

Cited by

  1. An Analytical Study on Stress Concentration due to a Cuboid Hole in Structures vol.510, pp.1662-7482, 2014, https://doi.org/10.4028/www.scientific.net/AMM.510.168
  2. Stress concentration around a rectangular cuboid hole in a three-dimensional elastic body under tension loading vol.88, pp.8, 2018, https://doi.org/10.1007/s00419-018-1369-7