Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Bilinear plate bending element for thin and moderately thick plates using Integrated Force Method

  • Dhananjaya, H.R. (Dept. of Civil Engineering, Manipal Institute of Technology) ;
  • Nagabhushanam, J. (Dept. of Aerospace Engineering, Indian Institute of Science) ;
  • Pandey, P.C. (Dept. of Civil Engineering, Indian Institute of Science)
  • Received : 2006.01.20
  • Accepted : 2006.11.03
  • Published : 2007.05.10
⟨ Previous Next ⟩

Abstract

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing 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. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.

Keywords

References

  1. 'ANSYS' Software and Manual (Version 5.6)
  2. Bathe, K.J. and Dvorkin, E.H. (1985), 'A four node plate bending element based on Mindlin/Reissner plate theory and mixed interpolation', Int. J. Numer. Meth. Eng., 21, 367-383 https://doi.org/10.1002/nme.1620210213
  3. Batoz, J.L. and Tahar, M.B. (1982), 'Evaluation of a new quadrilateral thin plate bending element', Int. J. Numer. Meth. Eng., 18, 1655-1677 https://doi.org/10.1002/nme.1620181106
  4. Dhananjaya, H.R. (2004), 'A family of plate bending finite elements using Integrated Force Method' - Ph.D thesis, Department of Civil Engineering, Indian Institute of Science, Bangalore-12, India
  5. Dhatt, G. (1969), 'Numerical analysis of thin shells by curved triangular elements based on discrete Kirchhoff Hypothesis', Symposium, Nashville, ASCE, November, 255-278
  6. 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
  7. 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
  8. Kikuchi, F. and Ando, Y. (1972), 'Some finite element solutions for plate bending problems by simplified hybrid displacement method', Nucl. Eng. Des., 23, 155-178 https://doi.org/10.1016/0029-5493(72)90046-5
  9. Krishnam Raju, N.R.B. and Nagabhushanam, J. (2000), 'Non-linear structural analysis using integrated force method', Sadhana, 25(4), 353-365 https://doi.org/10.1007/BF03029720
  10. Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity, Dover, New York
  11. Malkus, D.S. and Hughes, T.J.R. (1978), 'Mixed finite element methods-reduced and selective integration Techniques: A unification concept', Comput. Method Appl. Mech. Eng., 15, 63-81 https://doi.org/10.1016/0045-7825(78)90005-1
  12. Mallikarjuna Rao, K. and Srinivasa, U. (2001), 'A set of pathological tests to validate new finite elements', Sadhana, 26(6), 549-590 https://doi.org/10.1007/BF02703459
  13. 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
  14. Nagabhushanam, J. and Srinivas, J. (1991), 'Automatic generation of sparse and banded compatibility matrix for the Integrated Force Method', Computer Mechanics '91, Int. Conf. on Comput. Eng. Sci., Patras, Greece, 20-25
  15. 'NISA' Software and Manual (Version 9.3)
  16. Patnaik, S.N. (1973), 'An integrated force method for discrete analysis', Int. J. Numer. Meth. Eng., 41, 237-251
  17. 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
  18. Patnaik, S.N., Igor, K., Hopkins, D.A. and Sunil Saigal. (1996), 'Completed Beltrami-Michell Formulation for analyzing mixed boundary value problems in elasticity', AIAA J., 34(1), 143-148 https://doi.org/10.2514/3.13034
  19. Patnaik, S.N. and Yadagiri, S. (1976), 'Frequency analysis of structures by Integrated Force Method', Comput. Method. Appl. Mech. Eng., 9, 245-265 https://doi.org/10.1016/0045-7825(76)90030-X
  20. Reissner, E. (1945), 'The effect of transverse shear deformation on bending of plates', J. Appl. Mech., 12, A69-A77
  21. Robinson, J. and Haggenmacher, G.W. (1971), 'Some new developments in matrix force Analysis', Proc. of Recent Advances in Matrix Methods of Structural Analysis and Design, University Alabama, 183-228
  22. Stricklin, J.A., Haislor, W., Tisdale, P. and Ganderson, R. (1969), 'A rapidly converging triangular plate element', AIAA J., 7, 180-181 https://doi.org/10.2514/3.5068
  23. Timoshenko, S.P. and Krieger, S.W. (1959), Theory of Plates and Shells, Second Edition, McGraw Hill, New York
  24. Wanji Chen 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
  25. Zienkiewicz, 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

Cited by

  1. 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
  2. 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
  3. New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method vol.33, pp.4, 2007, https://doi.org/10.12989/sem.2009.33.4.485
  4. New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method vol.36, pp.5, 2007, https://doi.org/10.12989/sem.2010.36.5.625
  5. Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method vol.40, pp.1, 2011, https://doi.org/10.12989/sem.2011.40.1.121