Unconstrained Vector Positional Shell FEM formulation applied to thin-walled members instability analysis

Abstract

In this study, for the first time, we present a shell finite element based on positions and generalized vectors for instability analysis of thin-walled members. The presence of generalized vectors and transverse strain enhancement guarantee to the proposed formulation a good representation of strain and stress fields inside the element, allowing the use of complete three-dimensional constitutive law without any locking. The proposed formulation is total Lagrangian and naturally covers large displacement modeling. In past studies, the presence of generalized vectors limited the connection of shell portions or non-tangential panels, making it difficult to model thin-walled members. To solve this problem, a strategy to ensure the connection between non-coplanar elements, considering the stiffness of the connecting material, is originally developed and presented in this paper.In numerical examples we explore differences among buckling load achieved using small displacements and first limit points (or bifurcation points) using large displacements. The influence and the sensitivity of the connection stiffness are also tested when comparing these values. Results are validated against literature reference values and new examples are proposed to show the applicability of the positional formulation.