Large‐strain elasto‐plastic shell analysis using low‐order elements

Abstract

Describes two low‐order shell elements, one (quadrilateral) with 16 degrees‐of‐freedom; twelve translations and four rotations and another (triangular) with 12 degrees‐of‐freedom; nine translations and three rotations. The elements are formulated in a geometrically non‐linear manner and large strains, which may be hyper‐elastic or elasto‐plastic, are also considered. Hills yield criterion with a Lankford constant for the special case of transversely isotropic problem is introduced into the large‐strain formulations. To illustrate its application, the hydrostatic bulging of rectangular diaphragms with different aspect ratios is analysed and the obtained results are compared with the experimental ones. The elements have advantageous nodal configuration that makes them particularly suitable for analysing structures with junctions. Such a problem is an initially square steel box loaded with internal pressure. This problem is analysed and comparisons are made with experimental results.

A finite-strain quadrilateral shell element based on discrete Kirchhoff-Love constraints

“…• Director shape functions are newly developed, characterized by the absence of nonsymmetric terms (see previous developments [29,30,35]). …”

“…The idea of using a quadrilateral plate with this configuration originates in the work of Fraejis de Veubeke [19] (Herrmann [24] proposed the use of 'crossed-triangles' to form a quadrilateral). It was later extended by Nagtegaal and Slater [29], Batoz et al [25] and Crisfield and Tan [30]. The use of mid-side rotations is of paramount importance for our current work as in a recent attempt to extend our methodology for crack propagation in shells (inaugurated in Reference [31]) to folded geometries, we found that nodal spin degrees-of-freedom presented difficulties with the extended finite element method (XFEM).…”

“…Compared with co-rotational approaches (e.g. Reference [30]), the resulting equations are concise and transparent.…”

“…The proposed element degrees-of-freedom are mid-side rotations and nodal displacements, a nodal arrangement previously used in References [19,25,29,30,34]. Although the nodal arrangement is identical, the element is different from these developments in the general derivations and, in particular, its director shape functions and numerical quadrature.…”

“…Reference [30]) such as moderate rotations and co-rotational formulations based on the super-position of a plane element with a plate bending element, valid for triangular elements only. Non-symmetric shape functions are employed in References [29,35].…”