POSITIONAL FORMULATION FOR CREEP MECHANICAL BEHAVIOR OF BEAMS AND FRAMED STRUCTURES

Abstract

The present work aims to develop a nonlinear numerical formulation used to describe the viscoelastic mechanical behavior of framed structures and beams under a constant stress state (known as creep phenomenon) and discretized by plane framed elements. The development is based on the nonlinear positional formulation of the Finite Element Method and it takes into consideration the beam kinematics of Bernoulli-Euler. This approach allows to perform a structural analysis with physical and geometrical nonlinearities. The geometrical nonlinearity involved refers to structural equilibrium in the deformed position obtained by the Newton-Raphson method. The physical nonlinearity is associated with the adoption of a viscoelastic behavior through a suitable rheological relation. This rheological relation is derived from the uniaxial rheological model, based on the generalized Maxwell model. Three numerical examples are analyzed by the developed formulation. The first two examples describe and compare the creep behavior of a beam with different boundary conditions. The third example describes the creep behavior of a framed structure, formed by two columns and one beam. Furthermore, a simple calibration of the formulation is performed considering axial loading experimental results of bar made by Glass Fiber Reinforced Polymers material. Keywords: Viscoelasticity, Creep, Positional Formulation, Finite Elements Method, Rheological Model.