Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

  • Dhananjaya, H.R. (Department of Civil Engineering, Faculty of Engineering, University of Malaya) ;
  • Nagabhushanam, J. (Department of Aerospace Engineering, Indian Institute of Science Bangalore) ;
  • Pandey, P.C. (Department of Civil Engineering, Indian Institute of Science Bangalore) ;
  • Jumaat, Mohd. Zamin (Department of Civil Engineering, Faculty of Engineering, University of Malaya)
  • Received : 2010.03.07
  • Accepted : 2010.08.18
  • Published : 2010.11.30
⟨ Previous Next ⟩

Abstract

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Keywords

References

  1. Chen, W. and Cheung, Y.K. (1987), "A new approach for the hybrid element method", Int. J. Numer. Meth. Eng., 24, 1697-1709. https://doi.org/10.1002/nme.1620240907
  2. Choi, C.K. and Park, Y.M. (1999), "Quadratic NMS Mindlin-plate-bending element", Int. J. Numer. Meth. Eng., 46(8), 1273-1289. https://doi.org/10.1002/(SICI)1097-0207(19991120)46:8<1273::AID-NME754>3.0.CO;2-N
  3. Choi, C.K., Lee, T.Y. and Chung, K.Y. (2002), "Direct modification for nonconforming elements with drilling DOF", Int. J. Numer. Meth. Eng., 55(12), 1463-1476. https://doi.org/10.1002/nme.550
  4. Dar lmaz, K. (2005), "An assumed-stress finite element for static and free vibration analysis of Reissner-Mindlin plates", Struct. Eng. Mech., 19(2), 199-215. https://doi.org/10.12989/sem.2005.19.2.199
  5. Darilmaz, K. and Kumbasar, N. (2006), "An 8-node assumed stress hybrid element for analysis of shells", Comput. Struct., 84, 1990-2000. https://doi.org/10.1016/j.compstruc.2006.08.003
  6. Dhananjaya, H.R., Nagabhushanam, J. and Pandey, P.C. (2007), "Bilinear plate bending element for thin and moderately thick plates using Integrated Force Method", Struct. Eng. Mech., 26(1), 43-68. https://doi.org/10.12989/sem.2007.26.1.043
  7. Dhananjaya, H.R., Pandey, P.C. and Nagabhushanam, J. (2009), "New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method". Struct. Eng. Mech., 33(4), 485-502. https://doi.org/10.12989/sem.2009.33.4.485
  8. Dimitris, K., Hung, L.T. and Atluri, S.N. (1984), "Mixed finite element models for plate bending analysis, A new element and its applications", Comput. Struct., 19(4), 565-581. https://doi.org/10.1016/0045-7949(84)90104-4
  9. Kaljevic, I., Patnaik, S.N. and Hopkins, D.A. (1996a), "Development of finite elements for two-dimensional structural analysis using Integrated Force Method", Comput. Struct., 59(4), 691-706. https://doi.org/10.1016/0045-7949(95)00294-4
  10. Kaljevic, I., Patnaik, S.N. and Hopkins, D.A. (1996b), "Three dimensional structural analysis by Integrated Force Method", Comput. Struct., 58(5), 869-886. https://doi.org/10.1016/0045-7949(95)00171-C
  11. Kanber, B. and Bozkurt, Y. (2006), "Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements", Acta Mech. Sinica, 22, 355-365. https://doi.org/10.1007/s10409-006-0012-y
  12. Kim, S.H. and Choi, C.K. (2005), "Modelling of Plates and Shells: Improvement of quadratic finite element for Mindlin plate bending", Int. J. Numer. Meth. Eng., 34(1), 197-208.
  13. Krishnam Raju, N.R.B. and Nagabhushanam, J. (2000), "Non-linear structural analysis using integrated force method", Sadhana J., 25(4), 353-365. https://doi.org/10.1007/BF03029720
  14. Lee, S.W. and Wong, S.C. (1982), "Mixed formulation finite elements for Mindlin theory plate bending", Int. J. Numer. Meth. Eng., 18, 1297-1311. https://doi.org/10.1002/nme.1620180903
  15. Liu, J., Riggs, H.R. and Tessler, A. (2000), "A four node shear-deformable shell element developed via explicit Kirchhoff constraints", Int. J. Numer. Meth. Eng., 49, 1065-1086. https://doi.org/10.1002/1097-0207(20001120)49:8<1065::AID-NME992>3.0.CO;2-5
  16. Morley, L.S.D. (1963), Skew Plates and Structures, Pergamon press, Oxford.
  17. Nagabhushanam, J. and Patnaik, S.N. (1990), "General purpose program to generate compatibility matrix for the Integrated Force Method", AIAA J., 28, 1838-1842. https://doi.org/10.2514/3.10488
  18. Nagabhushanam, J. and Srinivas, J. (1991), "Automatic generation of sparse and banded compatibility matrix for the Integrated Force Method", Proceedings of the Computer Mechanics '91, International conference on Computing in Engineering Sceince, Patras, Greece.
  19. NISA Software and Manual (Version 9.3)
  20. Ozgan, K. and Daloglu, A.T. (2007), "Alternate plate finite elements for the analysis of thick plates on elastic foundations", Struct. Eng. Mech., 26(1), 69-86. https://doi.org/10.12989/sem.2007.26.1.069
  21. Patnaik, S.N. (1973), "An integrated force method for discrete analysis", Int. J. Numer. Meth. Eng., 41, 237-251.
  22. Patnaik, S.N. (1986), "The variational energy formulation for the Integrated Force Method", AIAA J., 24, 129-137. https://doi.org/10.2514/3.9232
  23. Patnaik, S.N. and Yadagiri, S. (1976), "Frequency analysis of structures by Integrated Force Method", Comput. Meth. Appl. Mech. Eng., 9, 245-265. https://doi.org/10.1016/0045-7825(76)90030-X
  24. Patnaik, S.N., Berke, L. and Gallagher, R.H. (1991), "Integrated force method verses displacement method for finite element analysis", Comput. Struct., 38(4), 377-407. https://doi.org/10.1016/0045-7949(91)90037-M
  25. Patnaik, S.N., Coroneos, R.M. and Hopkins, D.A. (2000), "Compatibility conditions of structural mechanics", Int. J. Numer. Meth. Eng., 47, 685-704. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<685::AID-NME788>3.0.CO;2-Y
  26. Patnaik, S.N., Hopkins, D.A. and Coroneos, R. (1986), "Structural optimization with approximate sensitivities", Comput. Struct., 58, 407-418.
  27. Pian, T.H.H. (1964), "Derivation of element stiffness matrices by assumed stress distributions", AIAA J., 2, 1333-1336. https://doi.org/10.2514/3.2241
  28. Pian, T.H.H. and Chen, D.P. (1982), "Alternative ways for formulation of hybrid stress elements". Int. J. Numer. Meth. Eng., 19, 1741-1752.
  29. Przemieniecki, J.S. (1968), Theory of Matrix Structural Analysis, McGraw Hill, New York.
  30. Razzaque, A. (1973), "Program for tringular plate bending element with derivative smoothing", Int. J. Numer. Meth. Eng., 6, 333-345. https://doi.org/10.1002/nme.1620060305
  31. Reissner, E. (1945), "The effect of transverse shear deformation on bending of plates", J. Appl. Mech., 12, A69-A77.
  32. Robinson, J. (1973), Integrated Theory of Finite Elements Methods, Wiley, New York.
  33. Spilker, R.L. (1980), "A serendipity cubic-displacement hybrid-stress element for thin and moderately thick plates", Int. J. Numer. Meth. Eng., 15, 1261-1278. https://doi.org/10.1002/nme.1620150811
  34. Spilker, R.L. (1982), "Invariant 8-node hybrid-stress elements for thin and moderately thick plates", Int. J. Numer. Meth. Eng., 18, 1153-1178. https://doi.org/10.1002/nme.1620180805
  35. Timoshenko, S.P. and Krieger, S.W. (1959), "Theory of plates and shells", Second Edition, McGraw Hill International Editions.
  36. Tong, P. (1970), "New displacement hybrid finite element models for solid continua", Int. J. Numer. Meth. Eng., 2, 73-83. https://doi.org/10.1002/nme.1620020108

Cited by

  1. Two higher order hybrid-Trefftz elements for thin plate bending analysis vol.85, 2014, https://doi.org/10.1016/j.finel.2014.03.003
  2. Two efficient hybrid-trefftz elements for plate bending analysis vol.9, pp.1, 2012, https://doi.org/10.1590/S1679-78252012000100003
  3. Developments of Mindlin-Reissner Plate Elements vol.2015, 2015, https://doi.org/10.1155/2015/456740
  4. A quadrilateral plate bending element based on deformation modes vol.41, 2017, https://doi.org/10.1016/j.apm.2016.09.007
  5. Application of the dual integrated force method to the analysis of the off-axis three-point flexure test of unidirectional composites vol.50, pp.3, 2016, https://doi.org/10.1177/0021998315576377
  6. Hybrid stress and analytical functions for analysis of thin plates bending vol.11, pp.4, 2014, https://doi.org/10.1590/S1679-78252014000400001
  7. A parametric study for thick plates resting on elastic foundation with variable soil depth vol.83, pp.4, 2013, https://doi.org/10.1007/s00419-012-0703-8
  8. OPTIMAL NODE LOCATION IN TRIANGULAR PLATE BENDING ELEMENTS vol.11, pp.05, 2014, https://doi.org/10.1142/S0219876213500758
  9. Comparison between the stiffness method and the hybrid method applied to a circular ring vol.40, pp.2, 2018, https://doi.org/10.1007/s40430-018-1013-z
  10. Correction of node mapping distortions using universal serendipity elements in dynamical problems vol.40, pp.2, 2011, https://doi.org/10.12989/sem.2011.40.2.245