Método dos elementos finitos posicional em análise viscoelástica: elementos de pórtico com cinemática de Reissner

Abstract

This research presents the development of a numerical formulation capable of describing creep viscoelastic mechanical behavior of frame elements accounting shear effects. It is based on the positional formulation of the Finite Element method, which is grounded on the variational concepts of the Minimum Total Potential Energy Principle. Developed to analyze problems with physical and geometrical nonlinearities, the adopted formulation considers the position of the nodes instead of nodal displacements in relation to a Total Lagrangian reference system to describe the kinematics of the finite elements. In the present study, the physical nonlinearity is related to the description of viscoelastic behavior by adopting stress-strain relations that are adequate to the response of the material and inferred based on rheological models. In order to consider the shear effects on viscoelastic mechanical behavior, frame elements with Reissner kinematics are adopted in developing the formulation. This consideration enables the decoupling between the rotation of cross sections and the displacements. Additionally, to enable the assessment of the contribution of the viscoelastic behavior along the height and depending on the stress level, a height parameterization approach is adopted that makes it possible to consider the cross section as laminated. A parametric analysis is presented in order to assess the consistency and sensitivity of the developed formulation. Based on this analysis, it is possible to observe that the obtained results are in agreement with the theory of viscoelasticity and with the expected behavior of the adopted rheological models. Next, the developed formulation is used in some examples and practical applications. The obtained numerical results are then compared to the analytical and experimental results that are available in the literature. Based on the produced results, it is possible to observe that, by adopting Reissner kinematics, the strains and displacements due viscoelastic behavior can be significantly greater compared to those obtained by adopting the Bernoulli-Euler kinematics. Furthermore, it is possible to verify an improvement in adapting the numerical results in relation to the experimental results when Reissner kinematics is adopted. Thus, it is possible to observe that the use of Reissner kinematics in the developed formulation allows to evaluate the shear effects on viscoelastic behavior and that these effects can be significant and should not be neglected without prior evaluation.