KSME International Journal

, Volume 13, Issue 1, pp 50–62 | Cite as

A three-node triangular plate bending element based on mindlin/reissner plate theory and mixed interpolation

  • Pal -Gap Lee


A new three-node triangular plate bending element, MT3, is presented for linear elastic analysis. MT3 is obtained by separate interpolation of transverse displacements and section rotations, and also of the transverse shear strains. The key to the MITC family element is a proper assumption of strain fields, and in this paper the torsional shear mode present in a standard displacement-based element by one-point reduced integration is exactly incorporated to form the stiffness matrix with two other constant shear modes. The procedure renders the element free of any locking phenomena. Low-order MITC family elements are also compared to the proposed element. A detailed formulation of the plate elemenet is given, and several example solutions are presented that demonstrate the superior predictive capabilities of the element.

Key Words

Mindlin Plate Shear Locking Mixed Formulation 


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  1. Lee, P.-G. and Sin, H.-C., 1994, “Mindlin Plate Finite Elements by a Modified Transverse Displacement,”KSME International Journal. Vol. 8, No. 1, pp. 19–27.Google Scholar
  2. Bathe, K. J. and Brezzi, F., 1985, “On the Convergence of a Four-Node Plate Bending Element Based on Mindlin-Reissner Plate Theory and a Mixed Interpolation,”Conference on Mathematics of Finite elements and Applications V (Edited by Whiteman, J. R.), Academic Press, New York, pp. 491–503.Google Scholar
  3. Bathe, K. J. and Brezzi, F., 1987, “A Simplified Analysis of Two Plate Bending Elements the MITC4 and MITC9 Elements,”Proc. NUMETA Conf., University College of Swansea, Wales.Google Scholar
  4. Bathe, K. J., Brezzi, F. and Cho, S. W., 1989, “The MITC7 and MITC9 Plate Bending Elements,”Comput Struct. Vol. 32, pp. 797–814.MATHCrossRefGoogle Scholar
  5. Bathe, K. J. and Dvorkin, E., 1985, “A Four-Node Plate Bending Element Based on Mindlin-Reissner Plate Theory and a Mixed Interpolation,”Int J. Numer. Meth. Engng., Vol. 21, pp. 367–383.MATHCrossRefGoogle Scholar
  6. Bathe, K. J. and Dvorkin, E., 1986, “A Formulation of General Shell Elements: The Use of Mixed Interpolation of Tensorial Components,”Int. J. Numer. Meth. Engng., Vol. 22, pp. 697–722.MATHCrossRefGoogle Scholar
  7. Brezzi, F. and Bathe, K. J., 1986, “Studies of Finite Element Procedures the Inf-Sup Condition, Equivalent Forms and Applications,”Conference on Reliability of Methods for Engineering Analysis (Edited by Bathe, K. J. and Owen, D. R. J.), Pineridge Press, SwanseaGoogle Scholar
  8. Dvorkin, E. and Bathe, K. J., 1984, “A Continuum Mechanics Based Four-Node Shell Element for General Nonlinear Analysis,”Engng Comput, Vol. 1, pp. 77–88.CrossRefGoogle Scholar
  9. Green, A. E. and Zerna, W., 1968,Theoretical Elasticity, 2nd edn, Oxford University PressGoogle Scholar
  10. Raviart, P. A. and Thomas, J. M., 1975, “A Mixed Finite Element Method for Second-Order Elliptic Problems,”In Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics, Vol. 606, Springer, Berlin, pp. 292–315.CrossRefGoogle Scholar
  11. Saleeb, A. F., Chang, T. Y. and Yingyeunyong, S., 1988, “A Mixed Formulation of C10-Linear Triangular Plate/Shell Element the role of Edge Shear Constraints,”Int. J. Numer. Meth. Engng., Vol. 26, pp. 1101–1128.MATHCrossRefGoogle Scholar
  12. Sussman, T. and Bathe, K. J., 1987, “A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis,”Comput. Struct., Vol. 26, pp. 357–409.MATHCrossRefGoogle Scholar
  13. Timoshenko, S. P. and Woinowsky-Krieger, S., 1959,Theory of Plates and Shells, 2nd Edn. McGraw-Hill.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1999

Authors and Affiliations

  • Pal -Gap Lee
    • 1
  1. 1.Steel Engineering CenterDongtan HwasungKorea

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