An Alternative Positional FEM Formulation for Geometrically Non-linear Analysis of Shells: Curved Triangular Isoparametric Elements

This work presents an alternative finite element shell formulation based on non-conventional nodal parameters. The considered parameters are nodal positions (not displacements) and generalized vector components that comprise both director cossines and shell thickness variation at the same time. Although any objective strain measure could be adopted to develop the proposed formulation, non-linear engineering strain is chosen in order to take advantage of well know linear engineering stress–strain relations and to complement the easy geometrical appeal of positional formulation. The resulting formulation presents six degrees of freedom by each node and considers constant thickness variation. Consequently, the formulation fulfills a three dimensional compatible mapping and requires a relaxed three-dimensional constitutive relation to avoid thickness locking. Curved triangular elements with cubic approximation are adopted following a very simple notation. Several numerical simulations illustrate and confirm the accuracy and applicability of the proposed formulation.