Assumed strain and hybrid destabilized ten-node C 0 triangular shell elements

Abstract

The conventional ten-node C 0 triangular shell element is in general too stiff. In this paper, several less stiff formulations are proposed. To reduce the transverse shear stiffness, the assumed strain method is adopted. On the other hand, both assumed strain method and hybrid destabilization are employed for softening the membrane stiffness. The improvement is validated by popular numerical problems.

Refined 15‐DOF triangular discrete degenerated shell element with high performances

“…In literature, there exist a number of successful quadrilateral or higher order triangular degenerated shell elements, such as the 6-node triangular element TRI-6 [9] by Zienkiewicz and Lefebvre, elements MITC (MITC7, MITC9 [10] with two internal rotation freedoms, third-order triangular element MITC12 [11]) proposed by Bathe, assumed strain and hybrid destabilized ten-node C 0 triangular shell elements, quadratic assumed natural strain curved triangular shell element by Sze and Zhu [12,13], and recently the mixed model of quadratic triangular degenerated shell elements by Bucalem et al [6,14]. However, to the author's knowledge, no prior work has been done to establish the successful 15-DOF triangular degenerated shell elements.…”

Curved quadratic triangular degenerated‐ and solid‐shell elements for geometric non‐linear analysis

“…Our literature survey reveals that the majority of the triangular shell elements are facet shells due to either the limitation in the number of nodes or the avoidance of membrane locking. It is di cult to trace all the work in curved triangular shell elements but it is hoped that most of them have been listed [1][2][3][4][5][6][7][8]. Among them, Lee et al proposed two cubic hybrid-strain degenerated-shell elements [2].…”

“…Membrane locking of the two TQQL elements is overcome by sampling the membrane strain either along the element edges or at the vertex nodes. Recently, cubic triangular degenerated-shell elements satisfying criteria (a) to (e) have been derived by using ANS (assumed natural strain) and destabilization [8].…”

“…Matrix inversion is normally required to express the polynomial coe cients in terms of the nodal d.o.f.s [7,9,[11][12][13]. Unlike the assumed strain method, ANS interpolates each natural strain component independently at pre-identiÿed sampling points and, thus, does not require matrix inversion [1,8,[14][15][16][17]. The major di cult in applying ANS to triangular elements is that the natural or area co-ordinates for triangles are dependent.…”