Physical and geometrical non-linear analysis of plane frames considering elastoplastic semi-rigid connections by the positional FEM

This study presents an alternative Finite Element formulation based on positions to model plane frames considering geometrical non-linear and elastoplastic behavior for members and semi-rigid connections. The formulation includes shear effects and allows the consideration of important mechanical behavior of structures in design decisions and verifications. The principle of stationary energy is used to find the equilibrium equations. A multi-linear elastoplastic constitutive law is developed for both continuum members and semi-rigid connections in order to comprise any proposed stress-strain diagram. Large rotations and displacements are considered for both semi-rigid connections and structure. The most important steps used to derive the formulation are described along the paper and various examples are used to validate and show the possibilities of the proposed technique