Hierarchic finite elements for thin plates and shells

  • Claudia Chinosi Università di Pavia
  • Lucia Della Croce Università di Pavia
  • Terenzio Scapolla Università di Pavia


We consider the numerical approximation of thin plate and shell structures. The plate model is described following the Reissner-Mindlin assumptions while the shell is described using the Naghdi formulation. It is well known that the numerical approximation witl} standard finite elements suffers of the so-calledlocking phenomenon, i.e., the numerical solution degenerates as the thickness of the structure becomes smaller. Plates exhibit shear locking and shells show both shear and membrane locking. Several techniques to avoid the numerical locking have been proposed. Here we solve the problems using a family of high order hierarchic finite elements. We present several numerical results that show the robustness of the finite elements, able to avoid in many circumstances the locking behavior.



[1]I. Babuška. The p and h-p versions of the finite element method. The state of the art. In: D.L. Dwoyer, M.Y. Hussaini, R.G. Voigt, eds., Finite Elements: Theory and Application, 199- 239. Springer, 1988.
[2] I. Babuška, H.C. Elman. Performance of the h-p version of the finite element method with various elements. Int. J. Num. Methods in Eng., 36: 2503-2523, 1993.
[3] I. Babuška, T. Scapolla. Benchmark computation and performance evaluation for a rhombic plate bending problem. Int. J. Num. Methods in Eng., 28: 155-179, 1989.
[4] K.J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982
[5] C. Chinosi, L. Della Croce, T. Scapolla. Hierarchic finite elements for thin Naghdi shell model, Int. J. of Solids and Structures, 35: 1863-1880, 1998.
May 31, 2023
How to Cite
CHINOSI, Claudia; CROCE, Lucia Della; SCAPOLLA, Terenzio. Hierarchic finite elements for thin plates and shells. Computer Assisted Methods in Engineering and Science, [S.l.], v. 5, n. 2, p. 151-160, may 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1351>. Date accessed: 18 july 2024.

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