Elastoplastic analysis of plane structures using improved membrane finite element with rotational DOFs

In this work, the small-strain elastoplastic behavior of structures is analyzed using an improved nonlinear finite element formulation. In this framework, an eight-node quadrilateral finite element denoted PFR8 (Plane Fiber Rotation) that belongs to the set of elements with rotational degrees of freedom is developed. Its formulation stems from the plane adaptation of the Space Fiber Rotation (SFR) concept that considers virtual rotations of nodal fiber within the element. This approach results in an enhancement of the displacement vector approximation. Von-Mises yield criteria have been applied for yielding of the materials along with the associated flow rule. Newton-Raphson method has been used to solve the nonlinear equations. To assess the performance of the proposed element, benchmark problems are addressed and the results are compared with some analytical and numerical solutions from the literature.