A nine nodes solid-shell finite element with enhanced pinching stress

Mouhamadou Dia,Nahiene Hamila,Mickaël Abbas,Anthony Gravouil

doi:10.1007/s00466-020-01825-1

Abstract

In this paper we present a low-order solid-shell element formulation—having only displacement degrees of freedom (DOFs), i.e., without rotational DOFs. The element has an additional middle node, that allows efficient and accurate analyses of shell structures using elements at extremely high aspect ratio. The formulation is based on the Hu–Washizu variational principle leading to a novel enhancing strain and stress tensor that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness locking). The middle-node is endowed with only one degree of freedom, in the thickness direction, allowing the assumption of a quadratic interpolation of the transverse displacement. Unlike solid-shell finite elements reported previously in the literature and formulated under the hypothesis of plane stress or with enhanced assumed strain parameter, the new solid-shell element here mentioned uses a complete three-dimensional constitutive law and gives an enhanced pinching stress, thanks to the middle-node. Moreover, to handle the various locking problems that usually arise on solid-shell formulation, the reduced integration technique is used as well as the assumed shear strain method. Finally to assess the effectiveness and performance of this new formulation, a set of popular benchmark problems, involving geometric non-linear analysis as well as elastic-plastic behavior has been investigated.

Highlights

Shell-like structures are largely present in most engineering design and process control
Either the coupling terms have to be removed from the constitutive law by a plane stress state or the shell formulation has to be extended by a linear normal strain, leading to a 7-parameter model
The ninth node degrees of freedom (DOF) plays the role of an extra parameter essential for a quadratic interpolation of the displacement in the thickness direction

Summary

Introduction

Shell-like structures are largely present in most engineering design and process control. Either the coupling terms have to be removed from the constitutive law by a plane stress state or the shell formulation has to be extended by a linear normal strain, leading to a 7-parameter model. This is achieved by a quadratic variation of the normal displacement field and the details can be found in References [15,16,17,18,20,21,22,24]. The second advantage of the additional DOF is that it has a physical meaning and, for instance, a strength equivalent to a normal pressure can be prescribed to improve the normal stress

Objectives

Methods

Conclusion