Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Is it shear locking or mesh refinement problem?

  • Ozdemir, Y.I. (Department of Civil Engineering, Karadeniz Technical University) ;
  • Ayvaz, Y. (Department of Civil Engineering, Karadeniz Technical University)
  • Received : 2012.07.05
  • Accepted : 2014.02.25
  • Published : 2014.04.25
⟨ Previous Next ⟩

Abstract

Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 4-, 8- and 17-noded quadrilateral finite elements are used. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates.

Keywords

References

  1. Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey.
  2. Belounar, L. and Guenfoud, M. (2005), "A new rectangular finite element based on the strain approach for plate bending", Thin Wall. Struct., 43(1), 47-63. https://doi.org/10.1016/j.tws.2004.08.003
  3. Belytschko, T., Stolarski, B. and Carpenter, N. (1984), "A C0 triangular plate element with one-point quadrature", Int. J. Numer. Method. Eng., 20, 787-802. https://doi.org/10.1002/nme.1620200502
  4. Cen, S., Long, Y., Yao, Z. and Chiew, S. (2006), "Application of the quadrilateral area coordinate method", Int. J. Numer. Eng., 66, 1-45. https://doi.org/10.1002/nme.1533
  5. Cook, R.D., Malkus, D.S. and Michael, E.P. (1989), Concepts and Applications of Finite Element Analysis, John Wiley & Sons, Inc., Canada.
  6. Celik, M. (1996), "Plak sonlu elemanlarda kayma sekildegistirmelerinin gozonune alınması ve iki parametreli zemine oturan plaklarin hesabi icin bir yontem", Ph. D. Thesis, Istanbul Technical University, Istanbul.
  7. Duster, A. (2001), "High order finite elements for three-dimensional thin-walled nonlinear continua", Ph.D. Thesis of Technische Universitat Munchen.
  8. Flanagan, D.P. and Belytscho, T. (1981), "Uniform strain hexahedron and quadrilateral with orthogonal hourglass control", Int. J. Numer. Method. Eng., 17, 679-706. https://doi.org/10.1002/nme.1620170504
  9. Hughes, T.J.R. (2000), The Finite Element Method, Dover Publications.
  10. Hughes, T.J.R., Cohen, M. and Harou, M. (1978), "Reduced and selective integration techniques in the finite element analysis of plates", Nucl. Eng. Des., 46, 203-222. https://doi.org/10.1016/0029-5493(78)90184-X
  11. Hughes, T.J.R., Taylor, R.L. and Kalcjai, W. (1977), "Simple and efficient element for plate bending", Int. J. Numer. Meth. Eng., 11, 1529-1543. https://doi.org/10.1002/nme.1620111005
  12. Ibrahimbegovic, A. (1993), "Quadrilateral finite elements for analysis of thick and thin plates", Comput. Meth. App. M., 110, 195-209. https://doi.org/10.1016/0045-7825(93)90160-Y
  13. Lovadina, C. (1996), "A new class of mixed finite element methods for Reissner-Mindlin Plates", SIAM J. Numer. Anal., 33, 2457-2467. https://doi.org/10.1137/S0036142994265061
  14. Mindlin, R.D. (1951),"I"nfluence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. M., 18, 31-38.
  15. Olovsson, L., Simonsson, K. and Unosson, M. (2006), "Shear locking reduction in eight-noded tri-linear solid finite elements", Comput. Struct., 84, 476-484. https://doi.org/10.1016/j.compstruc.2005.09.014
  16. Owen, D.R.J. and Zienkiewicz, O.C. (1982), "A refined higher-order Co plate bending element", Comput. Struct., 15, 83-177.
  17. Ozkul, T.A. and Ture, U. (2004), "The transition from thin plates to moderately thick plates by using finite element analysis and the shear locking problem", Thin Wall. Struct., 42, 1405-1430. https://doi.org/10.1016/j.tws.2004.05.003
  18. Ozdemir, Y.I., Bekiroglu, S. and Ayvaz, Y. (2007), "Shear locking-free analysis of thick plates using Mindlin's theory", Struct. Eng. Mech., 27(3), 311-331. https://doi.org/10.12989/sem.2007.27.3.311
  19. Ozdemir, Y.I. (2007), "Parametric analysis of thick plates subjected to earthquake excitations by using Mindlin's theory", Ph. D. Thesis, Karadeniz Technical University, Trabzon.
  20. Panc, V. (1975), Theory of Elastic Plates, Noordhoff, Leidin.
  21. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech. (ASME), 12, A69-A77.
  22. Reissner, E. (1950), "On a variational theorem in elasticity", J. Math. Phys., 29, 90-95.
  23. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, Second Edition, McGraw- Hill., New York.
  24. Soh, A.K., Cen, S., Long, Y. and Long, Z. (2001), "A new twelve DOF quadrilateral element for analysis of thick and thin plates", Eur. J. Mech., A-Solid., 20, 299-326. https://doi.org/10.1016/S0997-7538(00)01129-3
  25. Weaver, W. and Johnston, P.R. (1984), Finite elements for structural analysis, Prentice Hall, Englewood Cliffs; New Jersey.
  26. Yuan, F.G. and Miller, RE. (1988), "A rectangular finite element for moderately thick flat plates", Comput. Struct., 30, 1375-87. https://doi.org/10.1016/0045-7949(88)90202-7
  27. Yuan, F-G. and Miller, R.E. (1989), "A cubic triangular finite element for flat plates with shear", Int. J. Numer. Eng., 18(1), 1-15.
  28. Yuqiu, L. and Fei, X. (1992), "A universal method for including shear deformation in thin plates elements", Int. J. Numer. Eng., 34, 171-177. https://doi.org/10.1002/nme.1620340110
  29. Zienkiewich, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration technique in general analysis of plates and shells", Int. J. Numer. Meth. Eng., 3, 275-290. https://doi.org/10.1002/nme.1620030211
  30. Zienkiewicz, O.C., Xu, Z., Ling, F.Z. and Samuelsson, A. (1993), "Linked interpolation for Reissner- Mindlin plate element: part I-a simple quadrilateral", Int. J. Numer. Meth. Eng., 36, 3043-3056. https://doi.org/10.1002/nme.1620361802

Cited by

  1. Critical Plate Thickness for Energy Dissipation During Sphere–Plate Elastoplastic Impact Involving Flexural Vibrations vol.139, pp.4, 2017, https://doi.org/10.1115/1.4035338
  2. Eigenfrequencies of simply supported taper plates with cut-outs vol.63, pp.1, 2017, https://doi.org/10.12989/sem.2017.63.1.103