COMPARISON OF NONLINAR DYNAMIC RESPONSES OF EULER-BERNOULLI BEAMS AND TWO-DIMENSIONAL PLANE STRESS STATE OBTAINED FROM VEHICLE, IRREGULARITIES AND REINFORCED CONCRETE BRIDGE DYNAMIC INTERACTION SYSTEM

Thiago de Oliveira Abeche¹; Roberto Dalledone Machado¹; Ana Paula Imai¹; Marcos Arndt¹

¹ Federal University of Paraná (UFPR)

doi:10.20906/CPS/CILAMCE2017-1337

Resumo

A numerical model is oftentimes considered representative if capable to approach the analytical solution with the least amount of error in the process. The measure of this approximation is an effective test for mathematical models by simulation of linear problems in well-known regimes or initial states of nonlinear problems. Several engineering problems, however, do not have an analytical solution. For these, in order to reach a consistent solution, it is necessary to consider some significant physical effects of the experiment. The damage mechanics and the plasticity theory are egregious sciences for representing the nonlinear dynamic diffuse cracking propagation on the concrete and the permanent deformations of the steel bars, respectively, in the dynamic interaction between vehicles, irregularities and reinforced concrete beams phenomena. These effects change the linear dynamic model into a nonlinear dynamic one with arduous convergence. Furthermore, a mathematical convergence not necessarily can represent a plausible physical solution. Moreover, the amount of nonlinear physical effects on the dynamic interaction systems can even make the problem more onerous, requiring greater computational efficiency, regarding both CPU time and memory requirements, and improved numerical methods. This works presents the theoretical foundations of the ABXDNL scientific research program developed with Euler-Bernoulli beam finite element, in order to compare the nonlinear dynamic responses with new proposed nonlinear dynamic model through two-dimensional plane stress nonlinear finite element theory. Additional routines in C++ programming language are developed to consider this new model. It is adopted a constitutive nonlinear dynamic damage model based on the Mazars' damage model, which also regards the effects of the inversion of mechanical solicitations due to vibrations. The structural damping is defined by the Rayleigh method with updated coefficients due to damage. The continuum damage mechanics is considered dynamically,

Palavras-chave: Nonlinear Dynamics; Damage Mechanics; Nonlinear Finite Element Method; Dynamic Interaction; Computational Mechanics