A continuum mechanics based four‐node shell element for general non‐linear analysis

Abstract

A new four-node (non-flat) general quadrilateral shell element for geometric and material non-linear analysis is presented. The element is formulated using threedimensional continuum mechanics theory and it is applic able to the analysis of thin and thick shells. The for mulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

Basic mechanisms of fluting formation and retention in paper

“…The web was modelled with an elastic, orthotropic, moisture-dependent material and 4-node fully integrated shell elements (ANSYS, 2005). The elements used the assumed shear strain formulation to alleviate shear locking (Dvorkin and Bathe, 1984). In addition, the method of incompatible modes was employed in formulation, in order to enhance the accuracy in bending-dominated states (Simo and Armero, 1992).…”

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

“…Most of the earlier developed methods were based on enhanced assumed strain fields and consisted of either the use of a conventional integration with appropriate control of all locking phenomena, or the application of a reduced integration technique with hourglass control. Both approaches have been extensively investigated and evaluated on various structural applications as reported in the work of (Dvorkin et al, 1984;Belytschko et al, 1993;Zhu et al, 1996;Wriggers et al, 1996;Klinkel et al, 1997Klinkel et al, , 1999Wall et al, 2000;Reese et al, 2000;Puso et al, 2000).…”

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

“…Thereafter, the calculated components are evaluated at the Gauss points using bilinear or linear interpolation functions (depending on the number of sampling points) from their values at the sampling points. This method was originally applied for four shell elements by Dvorkin and Bathe [4] ant it has proven to be efficient, very robust and to give very good results for four node plate bending theory based on Mindlin/Reissner plate theory in [30] (applied on the transverse shear strain components E 13 , E 23 ). 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].…”

“…These solid-shell elements possess eight nodes with only displacement nodal degrees of freedom (DOF). In order to overcome various locking pathologies, the SSH3D formulation employs the well known Enhanced Assumed Strain (EAS) concept originally introduced by Simo and Rifai [3] and based on the Hu-Veubeke-Washizu variational principle combined with the Assumed Natural Strain (ANS) technique based on the work of Dvorkin and Bathe [4]. For the RESS solid-shell element, on the other hand, only the EAS technique is used with a Reduced Integration (RI) Scheme.…”