DOI QR코드

DOI QR Code

New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

  • Dhananjaya, H.R. (Department of Civil Engineering, Manipal Institute of Technology) ;
  • Pandey, P.C. (Department of Civil Engineering, Indian Institute of Science) ;
  • Nagabhushanam, J. (Department of Aerospace Engineering, Indian Institute of Science)
  • 투고 : 2009.04.21
  • 심사 : 2009.09.13
  • 발행 : 2009.11.10

초록

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

키워드

참고문헌

  1. Bahattin Kanber, and Yavuz Bozkurt (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
  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. Chen, Wanji 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
  5. Darlmaz, K. (2005), "An assumed-stress finite element for static and free vibration analysis of Reissner-Mindlinplates", Struct. Eng. Mech., 19(2), 199-215 https://doi.org/10.12989/sem.2005.19.2.199
  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. Dimitris, K., Hung, L.T. and Atluri, S.N. (1984), "Mixed finite element models for plate bending analysis, Anew element and its applications", Comput. Struct., 19(4), 565-581 https://doi.org/10.1016/0045-7949(84)90104-4
  8. Jane Liu, Riggs, H.R. and Alexander Tessler (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
  9. Kaljevic, I., Patnaik, S.N. and Hopkins, D.A. (1996), "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. (1996), "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. Kaneko, L., Lawo, H. and Thierauf, G. (1983), "On computational procedures for the force method", Int. J. Numer. Meth. Eng., 18, 1469-1495 https://doi.org/10.1002/nme.1620181004
  12. Krishnam Raju, N.R.B. and Nagabhushanam, J. (2000), "Non-linear structural analysis using integrated forcemethod", Sadhana, 25(4), 353-365 https://doi.org/10.1007/BF03029720
  13. Kutlu Darlmaz and Nahit Kumbasar (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
  14. Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity, Dover, New York
  15. Morley, L.S.D. (1963), Skew Plates and Structures, Pergamon press, Oxford
  16. 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
  17. Nagabhushanam, J. and Srinivas, J. (1991), "Automatic generation of sparse and banded compatibility matrix for the Integrated Force Method, Computer Mechanics 91", International Conference on Computing in Engineering Science, Patras, Greece, 20-25
  18. Ozgan, K. and Ayse, T. Daloglu (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
  19. Patnaik, S.N. (1973), "An integrated force method for discrete analysis", Int. J. Numer. Meth. Eng., 6, 237-251 https://doi.org/10.1002/nme.1620060209
  20. 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
  21. Patnaik, S.N., Berke, L. and Gallagher, R.H. (1991), "Integrated force method verses displacement method forfinite element analysis", Comput. Struct., 38(4), 377-407 https://doi.org/10.1016/0045-7949(91)90037-M
  22. Patnaik, S.N., Hopkins, D.A. and Coroneos, R. (1986), "Structural optimization with approximate sensitivities",Comput. Struct., 58, 407-418 https://doi.org/10.1016/0045-7949(95)00123-X
  23. 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
  24. 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
  25. 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
  26. Przemieniecki, J.S. (1968), Theory of Matrix Structural Analysis, McGraw Hill, New York
  27. Razzaque, A. (1973), "Program for triangular plate bending element with derivative smoothing", Int. J. Numer.Meth. Eng., 6, 333-345 https://doi.org/10.1002/nme.1620060305
  28. Reissner, E. (1945), "The effect of transverse shear deformation on bending of plates", J. Appl. Mech., 12, A69-A77
  29. Robinson, J. (1973), Integrated Theory of Finite Elements Methods, Wiley, New York
  30. Robinson, J. and Haggenmacher, G.W. (1971), "Some new developments in matrix force Analysis, In Recent advances in matrix methods of structural analysis and design", University Alabama, 183-228
  31. 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
  32. 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
  33. Timoshenko, S.P. and Krieger, S.W. (1959), Theory of Plates and Shells, Second Edition, McGraw_Hill international editions

피인용 문헌

  1. Development of the large increment method in analysis for thin and moderately thick plates vol.19, pp.3, 2014, https://doi.org/10.1007/s12204-014-1498-2
  2. Two higher order hybrid-Trefftz elements for thin plate bending analysis vol.85, 2014, https://doi.org/10.1016/j.finel.2014.03.003
  3. New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM vol.41, pp.2, 2012, https://doi.org/10.12989/sem.2012.41.2.205
  4. Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates vol.34, pp.2, 2017, https://doi.org/10.1108/EC-04-2016-0143
  5. New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method vol.36, pp.5, 2010, https://doi.org/10.12989/sem.2010.36.5.625
  6. Developments of Mindlin-Reissner Plate Elements vol.2015, 2015, https://doi.org/10.1155/2015/456740
  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. 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
  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. Influence of aspect ratio and fibre orientation on the stability of simply supported orthotropic skew plates vol.11, pp.5, 2009, https://doi.org/10.12989/scs.2011.11.5.359
  11. 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