On the use of an enhanced transverse shear strain shell element for problems involving large rotations

Abstract

This paper presents the extension of a previously developed formulation for shell elements in order to account for non-linear geometric effects, particularly in the presence of large rotations. To eliminate transverse shear locking, the developed shell formulation provides an enlargement of the transverse shear strain field coming from the usual degenerated concept. Doing so, additional transverse shear strain terms are included into the original displacement-based functional, following the enhanced strain approach. To reproduce the behavior of shell structures under large rotations and displacements, a rotation-free configuration is considered, where constitutive relations are stated. Dealing with finite incremental rotations, a singularity-free procedure is employed, characterizing the evolution of normal vectors to shell's mid-surface. Representative non-linear examples are considered, providing the validation of the enhanced shell element as well as the algorithmic procedures implemented, when compared to other formulations in the literature.

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

“…The present problems have been considered in Refs. (Sze et al 2004(Sze et al , 2002a(Sze et al , 2002bBrank et al 1995;Klinkel et al 1999 andFontes et al 2003).…”

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

“…In this purpose, an analysis of the efficiency of the EAS method using the framework of the subspace analysis is now underway and will be reported in future publications. This method was initially developed by César de Sà and Owen [54] for 2D elements and successfully applied later for 2D plane strain quadrilateral in [55,56], shell elements [43,48], 3D solid-shell elements by Alves de Sousa et al [25] and Caseiro et al [40].…”

“…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.…”

“…To assess the convergence behavior, the results are compared to shell elements presented in [22,48]. The numerical results are plotted in Figure 14 and Figure 15 and compared to the solution published in the works of Valente et al [48] to assess the performance and the convergence behavior of the present two solid-shell elements. The results obtained by the proposed formulations are in good agreement with those provided by the reference.…”

Computational shell mechanics by helicoidal modeling, II: Shell element

“…Others are based on particular techniques, such as reduced integration [Wriggers and Gruttmann 1993;Hauptmann et al 2000;Cardoso and Yoon 2005], discrete Kirchhoff-Love constraints [Areias et al 2005], or incompatible modes [Ibrahimbegović and Frey 1994]. Most of the elements proposed in the literature, however, use the assumed natural strain or enhanced assumed strain concepts, such as those developed by [Büchter et al 1994;Bischoff and Ramm 1997;Sansour and Kollmann 2000;Fontes Valente et al 2003;Chróścielewski and Witkowski 2006;Brank 2008], to mention just a few. Few are the successful low-order displacement-based elements free of any of the above techniques; see, for example, [Campello et al 2003;Pimenta et al 2004].…”