Formulação posicional não linear do método dos elementos finitos para descrição do comportamento mecânico viscoelástico de fluência em vigas e estruturas de pórtico

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 finite elements. The development is based on the nonlinear positional formulation of the Finite Element Method and takes into consideration the beam kinematics of Bernoulli-Euler. This approach is based on variational concepts as the principle of stationary total potential energy, developed to analyze physical and geometrical nonlinearities. It considers the nodal positions of a structure, rather than nodal displacements, regarding a system of reference fixed in the space in order to describe the kinematics of the finite elements. The geometrical nonlinearity involved considers the structural equilibrium at the deformed position obtained by the Newton-Raphson method. The adopted physical nonlinearity refers to the description of viscoelastic behavior through the adoption of a rheological relation derived from the standard solid model, with stress dependent material parameters. The proposed formulation is computational implemented. Qualitative examples and analyses of the influence of material parameters and numerical parameters are presented to verify the consistency and the behavior of such implementation. Moreover, through the least squares method, three examples of calibration are presented based on the adjustment of the parameters of the standard solid model in relation to the stress levels. Two of these examples are based on experimental results of creep tests of traction and the other one is based on experimental results of creep tests of bending. To achieve such results an approach of height parametrization that provides an idealization of the structural component as bundled bars is adopted. This approach enables the consideration of the creep behavior not only in relation to its contribution on the central line, but also in relation to the contribution of creep on each part along the height. Then, the calibrated formulation is used to analyze tests and real structures from the literature. The obtained numerical results are compared to the experimental results to confirm the fitting capacity and the quantitative representation of the creep behavior based on the proposed approach.