On the development of a solid-shell finite element for the analysis of thin structures and sheet metal forming

PhD candidate: Amine Ben Bettaieb

Supervisor: Laurent Duchêne

Benbettaieb PhD


Since the first development of the Finite Element Method (FEM), the development of reliable, efficient and accurate element formulations for the analysis of shell-like structures presents a big challenge. It has been the main objective of several research works. It is in this context that, through this thesis, we try to contribute to these efforts.

The objective of this thesis is to develop and present a new low-order solid-shell finite element, named SSH3D, which can effectively model the behavior of thin structures. This is an eight-node brick element with a preferential direction denoted ‘thickness’. This element possesses only displacement degrees-of-freedom (DOFs) which allow a direct connection with solid elements without the need of using transition elements. In contrast to its shell counterpart, 3D material models can be directly used with this element without any modification. In addition, due to the presence of physical nodes on its top and bottom surfaces double-sided contact is accurately considered. This element is integrated with an in-plane full integration scheme (four Gauss points) and an arbitrary number of points through the element thickness direction.

This special integration scheme makes this element very attractive in the analysis of some applications, i.e. sheet metal forming, indeed in this case, several integration points are required to correctly evaluate the through–thickness stress distribution. Despite these advantages, solid-shell elements are known to be sensitive to different types of numerical pathologies, known as locking phenomena. For certain types of structural analyses, e.g. for the analysis of bending dominated situations and nearly incompressible materials, the solid-shell element exhibits too stiff response to deformation if no remedial methods are used. To overcome locking a combination of the well-known Enhanced Assumed Strain (EAS) and Assumed Natural Strain (ANS) techniques is currently used. The developed element has some distinctive features compared to other solid-shell elements described in the literature thanks to its user-defined number of EAS parameters, ANS scheme and number of integration points over the element thickness.

To find a compromise between accuracy and computational efficiency, an optimal choice of these parameters has been carried out taking into account the type of the problem analyzed by the FE simulation using the present element formulation. The development of the SSH3D solid-shell formulation and its implementation within the in-house research finite element code LAGAMINE are detailed in this manuscript. To validate and assess the performance of the developed element, a set of popular linear and non-linear benchmark problems were investigated and presented. These numerical tests demonstrate the high performance of the developed element even for complex problems.

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