Structural Engineering and Mechanics

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Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method

  • Dhananjaya, H.R. (Department of Civil Engineering, Faculty of Engineering, University of Malaya) ;
  • Pandey, P.C. (Department of Civil Engineering, Indian Institute of Science) ;
  • Nagabhushanam, J. (Department of Aerospace Engineering, Indian Institute of Science) ;
  • Othamon, Ismail (Department of Civil Engineering, Faculty of Engineering, University of Malaya)
  • Received : 2010.05.01
  • Accepted : 2011.07.19
  • Published : 2011.10.10
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Abstract

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

Keywords

References

  1. ANSYS, Software and manual (Version 5.6).
  2. Cecchi, M.M. and Lami, C. (1977, online 2005), "Automatic generation of stiffness matrices for finite element analysis", Int. J. Numer. Meth. Eng., 11, 396-400.
  3. Chang, T.Y., Tan, H.Q., Zheng, D. and Yuan, M.W. (1990), "Application of symbolic method to hybrid and mixed finite elements and computer implementation", Comput. Struct., 35, 293-299. https://doi.org/10.1016/0045-7949(90)90055-7
  4. 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
  5. Dhananjaya, H.R., Nagabhushanam, J. and Pandey, P.C. (2008), "Automatic generation of equilibrium and flexibility matrices for plate bending elements using integrated force method", Struct. Eng. Mech., 30(4), 387-402. https://doi.org/10.12989/sem.2008.30.4.387
  6. Eriksson, A. and Pacoste, C. (1999), "Symbolic software tools in the development of finite elements", Comput. Struct., 72, 579-593. https://doi.org/10.1016/S0045-7949(98)00333-2
  7. Griffiths, D.V. (1994), "Stiffness matrix of the four node quadrilateral element in closed form", Int. J. Numer. Meth. Eng., 37, 1028-1038.
  8. Gunderson, R.H. and Ayhan Cetiner (1971), "Element stiffness matrix generator", J. Struct. Div.-ASCE, 363-375.
  9. Hoa, S.V. and Sankar, S. (1980), "A program for automatic generation of stiffness and mass matrices in finite element analysis", Comput. Struct., 11, 147-161. https://doi.org/10.1016/0045-7949(80)90154-6
  10. 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
  11. Lee, C.K. and Hobbs, R.E. (1998), "Closed form stiffness matrix solutions for some commonly used hybrid finite elements", Comput. Struct., 67, 463-482. https://doi.org/10.1016/S0045-7949(98)00055-8
  12. Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
  13. Luft, R.W., Roesset, J.M. and Connor, J.J. (1971), "Automatic generation of finite element matrices", J. Struct. Div.-ASCE, 349-362.
  14. 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
  15. Nagabhushanam, J. and Srinivas, C.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.
  16. Nagabhushanam, J., Srinivas, C.J. and Gaonkar, G.H. (1992), "Symbolic generation of elemental matrices for finite element analysis", Comput. Struct., 42(3), 375-380. https://doi.org/10.1016/0045-7949(92)90033-V
  17. NISA, Software and manual (Version 9.3).
  18. Noor, A.K. and Andersen, C.M. (1979), "Computerized symbolic manipulation in structural mechanics-progress and potential", Comput. Struct., 10, 95-118. https://doi.org/10.1016/0045-7949(79)90077-4
  19. Oztorun, N.K. (2006), "A rectangular finite element formulation", Finite Elem. Analy. Des., 42, 1031-1052. https://doi.org/10.1016/j.finel.2006.03.004
  20. 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
  21. 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
  22. 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
  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. Pavlovic, M.N. (2003), "Review article on symbolic computation in structural engineering", Comput. Struct., 81, 2121-2136. https://doi.org/10.1016/S0045-7949(03)00286-4
  25. Reissner, E. (1945), "The effect of transverse shear deformation on bending of plates", J. Appl. Mech., 12, A69-A77.
  26. 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
  27. Thompson, L.L. (2003), "On optimal stabilized MITC4 plate bending elements for accurate frequency response analysis", Comput. Struct., 81(8-11), 995-1008. https://doi.org/10.1016/S0045-7949(02)00405-4
  28. Timoshenko, S.P. and Krieger, S.W. (1959), Theory of Plates and Shells, Second Edition, McGraw Hill International Edition.
  29. Yew, C.K., Boyle, J.T. and MacKenzle, D. (1995), "Closed form integration of element stiffness matrices using a computer algebra system", Comput. Struct., 56(4), 529-539. https://doi.org/10.1016/0045-7949(94)00549-I
  30. Zhou, S.J. (2002), "Load induced stiffness matrix of plates", Can. J. Civil Eng., 29, 181-184. https://doi.org/10.1139/l01-064
  31. Zhov, C.E. and Vecchio, J. (2006), "Closed-form stiffness matrix for the four-node quadrilateral element with a fully populated material stiffness", J. Eng. Mech., 132(12), 1392-1395. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:12(1392)

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