Quadrilateral membrane finite elements with rotational DOFs for the analysis of geometrically linear and nonlinear plane problems

•Two four-node quadrilateral membrane elements with rotational DOFs are proposed.•They are based on the so-called Space Fiber Rotation (SFR) concept.•An updated Lagrangian framework is chosen to describe large displacement kinematics.•Several geometrically linear and nonlinear benchmarks are considered.•The accuracy of the proposed elements is close to the eight-node quadrilateral element. In this paper, we present the formulations of two four-node quadrilateral membrane finite elements with rotational degrees of freedom to analyze geometric linear and nonlinear plane problems. They are based on a plane adaptation of the space fiber rotation concept that considers virtual rotations of a nodal fiber within the element enhancing the displacement vector approximation of low-order elements. An updated Lagrangian approach is chosen to describe large displacement with small strain kinematics. Several geometric linear and nonlinear benchmarks are presented to assess the performance of the proposed membrane elements and the obtained results demonstrate their efficiency.