DOI QR코드

DOI QR Code

Shear locking-free analysis of thick plates using Mindlin's theory

  • Ozdemir, Y.I. (Department of Civil Engineering, Karadeniz Technical University) ;
  • Bekiroglu, S. (Department of Civil Engineering, Karadeniz Technical University) ;
  • Ayvaz, Y. (Department of Civil Engineering, Karadeniz Technical University)
  • 투고 : 2006.04.18
  • 심사 : 2007.03.01
  • 발행 : 2007.10.20

초록

The purpose of this paper is to study shear locking-free analysis of thick plates using Mindlin's theory and to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to uniformly distributed loads. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. 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, 8- and 17-noded quadrilateral finite elements are used. Graphs and tables are presented that should help engineers in the design of thick plates. 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. It is also concluded, in general, that the maximum displacement and bending moment increase with increasing aspect ratio, and that the results obtained in this study are better than the results given in the literature.

키워드

과제정보

연구 과제 주관 기관 : Karadeniz Technical University

참고문헌

  1. Ayvaz, Y. (1992), Parametric Analysis of Reinforced Concrete Slabs Subjected to Earthquake Excitation, Ph. D. Thesis, Graduate School of Texas Tech University, Lubbock, Texas
  2. Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey
  3. Batoz, J.L. and Tahar, M.B. (1982), 'Evaluation of a new quadrilateral thin plate bending elements', Int. J Num. Meth. Eng., 18, 1655-1677 https://doi.org/10.1002/nme.1620181106
  4. 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
  5. Cai, L., Rong, T. and Chen, D. (2002), 'Generalized mixed variational methods for reissner plate and its application', Comput. Mech., 30, 29-37 https://doi.org/10.1007/s00466-002-0364-5
  6. Cen, S., Long, Y, Yao, Z. and Chiew, S. (2006), 'Application of the quadrilateral area coordinate method', Int. J. Num. Eng., 66, 1-45 https://doi.org/10.1002/nme.1533
  7. Cook, R.D., Malkus, D.S. and Michael, E.P. (1989), Concepts and Applications of Finite Element Analysis. John Wiley & Sons, Inc., Canada
  8. Celik, M. (1996), Plak sonlu elemanlarda kayma sekildegistirmelerinin gozonune alnmas ve iki parametreli zemine oturan plaklarn hesab icin bir yontem, Ph. D. Thesis, Istanbul Technical University, Istanbul
  9. Ibrahimbegovic, A. (1993), 'Quadrilateral finite elements for analysis of thick and thin plates', Comput. Meth. Appl. M, 110, 195-209 https://doi.org/10.1016/0045-7825(93)90160-Y
  10. 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
  11. Mindlin, R.D. (1951), 'Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates', J. Appl. M., 18, 31-38
  12. Owen, D.R.J. and Zienkiewicz, O.C. (1982), 'A refined higher-order $C^{0}$ plate bending element', Comput. Struct., 15, 83-177
  13. 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
  14. Ozdemir, Y.I. and Ayvaz, Y. (2004), 'Analysis of clamped and simply supported thick plates using finite element method', Proc. of the 6th Int. Cong. on Advances in Civil Engineering, Istanbul, 1, 652-661
  15. Panc, V. (1975), Theory of Elastic Plates, Noordhoff, Leidin
  16. Reissner, E. (1947), 'On bending of elastic plates', Q. Appl. Math., 5, 55-68 https://doi.org/10.1090/qam/20440
  17. Reissner, E. (1950), 'On a variational theorem in elasticity', J. Math. Phys., 29, 90-95 https://doi.org/10.1002/sapm195029190
  18. 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-Solids, 20, 299-326 https://doi.org/10.1016/S0997-7538(00)01129-3
  19. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells. Second edition, McGraw-Hill., New York
  20. Ugural, A.C. (1981), Stresses in Plates and Shells, McGraw-Hill, New York
  21. Wanji, C. and Cheung, Y.K. (2000), 'Refined quadrilateral element based on Mindlin/Reissner plate theory', Int. J. Numer. Meth. Eng., 47, 605-627 https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<605::AID-NME785>3.0.CO;2-E
  22. Weaver, W. and Johnston, P.R. (1984), Finite Elements for Structural Analysis, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 200-212
  23. Weaver, W. and Johnston, P.R. (1984), Finite Elements for Structural Analysis, Prentice Hall, Englewood Cliffs; New Jersey
  24. Yuan, F.-G. and Miller, R.E. (1988), 'A rectangular finite element for moderately thick flat plates', Comput. Struct., 30, 1375-1387 https://doi.org/10.1016/0045-7949(88)90202-7
  25. Yuan, F.-G and Miller, R.E. (1989), 'A cubic triangular finite element for flat plates with shear', Int. J. Num. Eng., 18(1), 1-15
  26. Yuqiu, L. and Fei, X. (1992), 'A universal method for including shear deformation in thin plates elements', Int. J. Num. Eng., 34, 171-177 https://doi.org/10.1002/nme.1620340110
  27. 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. Num. Meth. Eng., 36, 3043-3056 https://doi.org/10.1002/nme.1620361802

피인용 문헌

  1. Development of a higher order finite element on a Winkler foundation vol.48, pp.1, 2012, https://doi.org/10.1016/j.finel.2011.08.010
  2. An Integrated Kirchhoff Element by Galerkin Method for Free Vibration Analysis of Plates on Elastic Foundation vol.24, 2016, https://doi.org/10.1016/j.protcy.2016.05.021
  3. Is it shear locking or mesh refinement problem? vol.50, pp.2, 2014, https://doi.org/10.12989/sem.2014.50.2.181
  4. Problems with a popular thick plate element and the development of an improved thick plate element vol.29, pp.3, 2007, https://doi.org/10.12989/sem.2008.29.3.327
  5. Shear locking-free earthquake analysis of thick and thin plates using Mindlin's theory vol.33, pp.3, 2007, https://doi.org/10.12989/sem.2009.33.3.373
  6. Dynamic behaviour of thick plates resting on Winkler foundation with fourth order element vol.16, pp.3, 2007, https://doi.org/10.12989/eas.2019.16.3.359
  7. Dynamic Analysis of Thick Plates Resting on Winkler Foundation Using a New Finite Element vol.44, pp.1, 2007, https://doi.org/10.1007/s40996-019-00260-4