Abstract
We investigate the performance of the Naghdi shell model using a family of hierarchic high order finite elements. We solve two cylindrical shell problems, representative of extremely discriminating situations: the membrane dominated Scordelis-Lo problem and a bending dominated problem already tested by Leinoand Pitkäranta. As it is well known, these problems are hard tests for shell elements, especially when the thickness of the shell is approaching to zero, since the presence of hidden constraints can lead to numerical convergence problems, known as shear and membrane locking. The numerical results show the robustness of the finite elements developed, able to avoid the locking behavior.
References
[1] K.-J . Bathe, E.N. Dvorkin. A formulation of general shell elements - The use of mixed interpolation of tensorial components. Internat. J. Numer. Meths. Engrg., 22: 697-722, 1986.
[2] Y. Leino, J . Pitkäranta. On the membrane locking of h-p finite elements in a cylindrical shell problem. Internat. J. Numer. Meths. Engrg., 37: 1053-1070, 1994.
[3] R.H. MacNeal, R.L. Harder. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design, 1: 3-20, 1985.
[4] J. Pitkäranta. The problem of membrane locking in finite element analysis of cylindrical shells, Numer. Math. , 61: 523- 542, 1992
[5] A.C. Scordelis, K.S. Lo. Computer analysis in cylindrical shells. J. Am. Concr. Inst., 61: 561- 593, 1964.
[2] Y. Leino, J . Pitkäranta. On the membrane locking of h-p finite elements in a cylindrical shell problem. Internat. J. Numer. Meths. Engrg., 37: 1053-1070, 1994.
[3] R.H. MacNeal, R.L. Harder. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design, 1: 3-20, 1985.
[4] J. Pitkäranta. The problem of membrane locking in finite element analysis of cylindrical shells, Numer. Math. , 61: 523- 542, 1992
[5] A.C. Scordelis, K.S. Lo. Computer analysis in cylindrical shells. J. Am. Concr. Inst., 61: 561- 593, 1964.
