A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Large deformation problems

Abstract

SUMMARYIn this paper we address the extension of a recently proposed reduced integration eight-node solid-shell finite element to large deformations. The element requires only one integration point within the shell plane and at least two integration points over the thickness. The possibility to choose arbitrarily many Gauss points over the shell thickness enables a realistic and efficient modeling of the non-linear material behavior. Only one enhanced degree-of-freedom is needed to avoid volumetric and Poisson thickness locking. One key point of the formulation is the Taylor expansion of the inverse Jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes. The transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept. Further crucial points are the Taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the Taylor expansion of the second Piola-Kirchhoff stress tensor with respect to the normal through the center of the element.

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

“…From these tests, we found out that the use of the second or the third ANS version (see Figure 3) leads almost to the same results. This observation agrees with the remark of Cardoso et al [32] and Schwarze and Reese [10] concerning the use of a full integration scheme. Therefore, the second ANS version is used for SSH3D solid-shell element.…”

“…The pinched hemisphere with an 18° hole is a popular benchmark and one of the most stringent examples to test the behavior of the finite element formulation in geometrical non-linear domain due to its double curvature [6,8,10,22,47,48]. As shown in Figure 13 the problem consists in a hemispherical shell with an 18° hole at the top subjected to concentrated forces, i.e.…”

“…In this context, several published works were focused on the development of solid-shell elements (e.g. see [5][6][7][8][9][10][11][12][13]) which form a class of finite element models that are intermediate between the conventional solid and shell elements. Despite their attractive features, low-order solid-shell displacement-based finite elements suffer from different types of locking effects.…”

“…This method was later extended to overcome the curvature thickness locking by modifying the interpolation of the transverse normal strain component E 33 for four-node shell elements, as proposed by Betsch and Stein [29] and also Bischoff and Ramm [31]. In the recent development of solid-shell elements, numerous formulations are developed based on the combination of the EAS and ANS methods such as the work of Hauptman et al [5], Miehe [16], Klinkel et al [18], Vu-Quoc and Tan [6], Cardoso et al [32], Schwarze and Reese [10] and the recent works of Rah et al [12] and Pramin et al [33]. Taking all these references and achievements in the literature, the main goal of the present paper is to present the formulations of the SSH3D (=Solid-SHell element in 3D) and RESS (=Reduced Enhanced Solid-Shell element) solid-shell elements.…”

Finite Element Simulation of Crack Propagation and Delamination in Layered Shells Due to Blade Cutting

“…A solid-shell finite element discretization is adopted, by using the element proposed in [15] and successive modifications (in particular we use the selective mass scaling described in [3] and [4]). In the paper we assume the following numbering for the reference element: since the thickness is small, it is always possible to identify nodes 1-4 for the lower surface, and nodes 5-8 for the upper surface.…”