Within the Kirchhoff–Love shell theory, a new quadrilateral shell element is proposed in the framework of Cartan’s moving frames [1]. The static and dynamic formulations are derived from the Hu–Washizu variational principle, where the displacements, the frames, the deformation 1-forms and the traction 1-forms are regarded as independent variables. For spatial discretization, the deformation 1-forms are approximated using Whitney 1-forms from Finite Element Exterior Calculus (FEEC) [2], which are naturally defined on 2-simplices (triangles). Therefore, a partitioned interpolation scheme, is proposed where a quadrilateral element is split into two 2-simplices, allowing Whitney 1-forms to be employed on quadrilateral meshes. As shown in Fig. 1, the proposed quadrilateral element has four nodes and five edges. For time integration of the dynamic equations, the Lie group generalized-α method [3] is adopted. Static examples and dynamic examples are implemented to demonstrate the accuracy of the proposed quadrilateral elements. Fig. 2 shows a benchmark example where a cantilever plate is coiled into a complete circle under a bending moment. And comparisons are made with the triangular elements proposed by Jamun et al. [4] also based on Cartan’s moving frames. Results show that the proposed quadrilateral element achieves higher accuracy and computational efficiency than their triangular element with the same element size. REFERENCES [1] J.N. Clelland, From Frenet to Cartan: The Method of Moving Frames, American Mathematical Soc., Vol. 178, (2017). [2] D. Arnold, R. Falk and R. Winther. Finite element exterior calculus: From Hodge theory to numerical stability. Bull. Am. Math. Soc., Vol. 47(2), pp. 281-354, 2010. [3] O. Brüls, A. Cardona and M. Arnold. Lie group generalized-α time integration of constrained flexible multibody systems. Mech. Mach. Theory, Vol. 48, pp. 121-137, 2012. [4] Jamun Kumar N., J.N. Reddy, Arun R. Srinivasa and Debasish Roy. A new mixed variational approach for Kirchhoff shells and 𝐶0 discretization with finite element exterior calculus. Comput. Methods Appl. Mech. Engrg., Vol. 432, pp. 117351, 2024.