A quadratic assumed natural strain triangular element for plate bending analysis

Abstract

SUMMARYIn this paper, a six-node triangular C 0 plate bending element is developed by the assumed natural strain method. In the element, all the sampled natural transverse shear strains are chosen such that the latter has a favourable constraint index and the strains are optimized with respect to a linear pure moment ®eld. The element passes the patch tests, yields satisfactory accuracy and shows no sign of shear locking in all the problems considered. #

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

“…Both ANS shell and ANS solid are of the proper rank and pass all the patch tests prescribed by MacNeal and Harder for plate=shell elements [37]. The predictions of ANS shell in commonly employed linear benchmark problems such as cantilever, curved beam, pre-twisted beam, square plate, circular plate, hemispherical shell, pinched cylinder and Scordelis-Lo roof were reported [1,17]. The element yields promising accuracy as compared to other state-of-the-art elements and shows no sign of shear and membrane lockings.…”

“…Having various lockings resolved does not necessarily imply an accurate element (see, e.g., Reference [30]). In order to identify the optimal strain sampling locations and directions, the nodal values of a subparametric six-node triangle are prescribed according to a complete third order polynomial ÿeld in References [1,17]. As a quadratic element, the interpolated ÿeld and its spatial derivatives are di erent from that of the original third order ÿeld.…”

“…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.…”

Developments of Mindlin-Reissner Plate Elements

“…This method had been proved to be mathematically valid by Brezzi et al [40], and the key to the success was related to the choices of these preselected points. After then, based on this concept, many models were successfully developed [41][42][43][44][45]. For instance, Tessler and Hughes [42,43] proposed the quadrilateral and triangular plate elements, named as MIN4 and MIN3, in which "anisoparametric" representations were used together with continuous transverse shear edge constraints.…”

“…Sze et al [44] developed a triangular element AST6, which had a favorable constraint index of shear locking and optimized strains with respect to a linear pure bending field. Afterwards, they gave an improved model [45] in where the matrix inversion in original formulations can be avoided.…”