In this paper, a plane quadrilateral element with rotational degrees of freedom is developed. Present formulation is based on a hybrid functional with independent boundary displacement and internal optimum strain field. All the optimality constraints, including being rotational invariant, omitting the parasitic shear error and satisfying Fliepa’s pure bending test, are considered. Moreover, the static equilibrium equations are satisfied in this scheme. Authors’ element has only four nodes and twelve degrees of freedom. For the boundary displacement field, Alman’s second-order displacement function is employed. The validities of the proposed element are demonstrated by eleven numerical examples: thick curved beam, thin cantilever beam, Cooke’s skew beam, thin curved beam, cantilever beam with distortion parameter, high-order patch test, cantilever beam with five and four irregular mesh, Mc Neal’s thin cantilever beam and cantilever shear wall with and without openings. When utilizing the coarse and irregular meshes, numerical tests show the high accuracy, rapid convergence and robustness of the suggested element. Less sensitivity to distortion is another property of the new element.

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