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This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and eneralized unconstrained vectors as the variables of the problem, not displacements and fiiterotations. The full 3D Saint-Venant-Kirchhoff onstitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, thesecond Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.