Open Access

ABSTRACT

Optimal 4-node shell and 3d-shell finite elements for nonlinear analysis

B. Brank¹

1 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Slovenia

The International Conference on Computational & Experimental Engineering and Sciences 2007, 2(3), 81-86. https://doi.org/10.3970/icces.2007.002.081

Abstract

First we shortly present several low-order (4-node) shell finite element formulations (based on Reissner-Mindlin kinematics) that allow for accurate and efficient (with coarse and distorted meshes) analysis of shell-like structures subjected to large deformations and rotations. The formulations are based on mixed variational principle, enhanced assumed strain (EAS) method (based on Green-Lagrange strains) and assumed natural strain (ANS) method. The EAS method is used in all formulations in order to improve both membrane and bending behavior of the 4-node element (the formulations differ from one another by the number of assumed EAS parameters), and the ANS method is used to avoid shear locking. An optimal number of membrane/bending EAS parameters is then identified by comparing results of a set of characteristic numerical examples (in this paper we only present results of two illustrative examples). Thus an optimal 4-node EAS/ANS nonlinear shell element is derived. In the second part of the paper we shortly present enhancement of the previously derived optimal shell element leading to an optimal low-order (4-node) nonlinear 3d-shell element; i.e. an element that accounts for through-the-thickness stretching. The enhancement, which introduces incompatible Green-Lagrange strains in the through-the-thickness direction, is based on EAS method. The derived 3d-shell element looks as a surface (with extensible directors) from the outside but it can build fully 3d stress and 3d strain states. Finally, we present a numerical example, which illustrates performance of an optimal 4-node EAS/ANS 3d-shell element.

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