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. Key wordsFrames, Physical and geometrical non-linear analysis, Positional FEM, Elastoplastic connections, Laminate cross sections.Physical and geometrical non-linear analysis of plane frames considering elastoplastic semi-rigid connections by the positional FEM
REIS, M.C.J. (2012). Geometric nonlinear analysis of plane frames considering elastoplastic semi-rigid connections. Dissertation This work presents a technique to consider elastoplastic semi-rigid connections for geometric nonlinear analysis of plane frames. The connections were considered semirigid with elastoplastic behavior and modeled by The Finite Element Method (FEM). This technique was coupled to AcadFrame program, based on the Finite Element Method for geometric nonlinear analysis of plane frames and trusses flat. The numerical coupling is made by an algebraic formulation where, at each iteration of the Newton-Raphson process, the connection's stiffness matrix and elastoplastic internal forces of are added to the Hessian matrix and the internal force vector of the structure. Concepts of linear and tensor algebra, non-linear strain, stress, variational principles and numerical methods are needed for this purpose. Several examples with semi-rigid connections are solved to verify the proosed formulation and performed implementations. This study allows geometric nonlinear analysis of plane frames considering elastoplastic semi-rigid connections, as steel and precast concrete structures.
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