An Efficient Geometrically‐Exact Nonlinear Shell Formulation Based on Rodrigues Parameters

Thin‐walled structures are part of many engineering applications, as wind turbine blades, pressure vessels, and sheet metal products. A thin‐walled structure is characterized by one significantly smaller dimension compared to the others. To numerically support the designing process of such industrial structures, a robust and efficient approximation algorithm is required. In this work a nonlinear shell formulation is developed and presented, including its discretization with a triangular element. The proposed displacement‐based triangular shell element, which comprises six nodes, has a compatible linear interpolation scheme for displacements and a nonconforming linear rotation field. This particular formulation is based on the Reissner–Mindlin kinematic assumption and an initial plane reference configuration for the shell. The proposed formulation also accounts for finite strains, large displacements, and rotations. The rotation field has been re‐parameterized using the Rodrigues rotation parameters, facilitating an efficient update of the rotational field compared to the classical Euler rotation vector. Furthermore, the presented formulation is compared to established methods in terms of suitable numerical examples.